{"id":787,"date":"2026-03-30T11:20:52","date_gmt":"2026-03-30T11:20:52","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/?page_id=787"},"modified":"2026-03-30T11:20:52","modified_gmt":"2026-03-30T11:20:52","slug":"inferential-statistics","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/inferential-statistics\/","title":{"rendered":"Inferential Statistics"},"content":{"rendered":"<section id=\"h.12b88c2cf1f30222_7\" class=\"yaqOZd\">\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_10\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div class=\"CjVfdc\"><span class=\"VbJjl C9DxTc \">Inferential<\/span><span class=\"VbJjl C9DxTc \">\u00a0Statistics<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_12\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Inferential statistics help to identify relationships, test hypothesis draw conclusions about sets of data.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Most of these statistical methods will be new to you, but none of the maths behind them is tricky! If you follow the instructions step-by-step, they&#8217;re a really worthwhile technique to encorporate in your Geographical study. You will also find they come up in university courses such as Geography, Psychology, Science and Humanities subjects.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_13\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_16\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">These are not statistical methods, but are important foundations.<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Significance<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_19\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Chi<\/span><span class=\"C9DxTc aw5Odc \">\u00b2<\/span><span class=\"C9DxTc aw5Odc \">\u00a0<\/span><span class=\"C9DxTc aw5Odc \">Analysis<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Linear regression<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Nearest Neighbour<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_25\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Pearson&#8217;s Product Moment Correlation Coefficient<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc aw5Odc \">Spearman&#8217;s Rank correlation coefficient<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_26\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_29\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_30\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_33\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.7lwsa4i2wv75\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Hypothesis<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_36\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A hypothesis is a statement or a hunch. It is used to set up a question which can then be tested &#8211; data gathered, processed and a conclusion drawn.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_37\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_40\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.2e0va7z1fod4\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Hypothesis<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_453\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSlG_lKifLdb5ARUMSfarG5NCZlVW0kUgjOx085j2EM-n6tQ1kMz87DR0WYYCWsW4tisg1RmA4_yfCPytp2r5ycWSJCv4rVuUZAYokmenWfqtiutEDWE99QqEui5EQLfYkGSPhyH8CXj4GcX790Y9bAv_iX7N2XBPf4Bp7MkIUh2WJbK3v5BVzZyz8zLrCPW3-tGfV1ZC1kVAivNt2nrL0rxEfyWAHM5BP2Q8s=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_45\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Most of the time in Geography, research is centred around testing whether a geographical model is true.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">For example, understanding the process of attrition means that we would expect that the size of sediment\u00a0<\/span><span class=\"C9DxTc \">should<\/span><span class=\"C9DxTc \">\u00a0get smaller as you move downstream.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">To test whether this is true for a particular river, a\u00a0<\/span><span class=\"C9DxTc \">hypothesis<\/span><span class=\"C9DxTc \">\u00a0would be written.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">&#8220;There is a relationship between the size of the bedload in River X and the distance in which it is found from the source.\u201d<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_433\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">However, as in a court of law it&#8217;s &#8220;innocent until proven guilty.&#8221; It&#8217;s better to assume there&#8217;s no relationship and then find one!\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A better hypothesis would be:<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">&#8220;There is no relationship between the size of bedload in River X and the distance in which it is found from the source.&#8221;<\/span><span class=\"C9DxTc \">\u00a0This is an example of a\u00a0<\/span><span class=\"C9DxTc \">null hypothesis<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_71\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_74\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_434\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_437\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.4rptywnp08d2\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Null Hypothesis<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_439\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">To test a hypothesis we first write the\u00a0<\/span><span class=\"C9DxTc \">null hypothesis<\/span><span class=\"C9DxTc \">\u00a0(H<\/span><span class=\"C9DxTc \">0<\/span><span class=\"C9DxTc \">).<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">This is the &#8220;no change&#8221; position. Phrases included in null hypothesis include&#8230;<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_441\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There is no difference between&#8230;&#8221;<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There has been no change since&#8230;&#8221;<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There is no relationship between&#8230;&#8221;<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_458\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The reason we do this is because it&#8217;s good practice to assume a relationship doesn&#8217;t exist, and then prove that one does.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_444\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If you later prove a relationship does exist you can\u00a0<\/span><span class=\"C9DxTc \">reject<\/span><span class=\"C9DxTc \">\u00a0the null hypothesis and accept the\u00a0<\/span><span class=\"C9DxTc \">alternative hypothesis<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">(H<\/span><span class=\"C9DxTc \">1<\/span><span class=\"C9DxTc \">).<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_447\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.p7rfk9ylas1p\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Alternative Hypothesis<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_449\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There is a difference between&#8230;&#8221;<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There has been a change since&#8230;&#8221;<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">&#8220;There is a relationship between&#8230;&#8221;<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_61\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_64\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_143\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"vhaaFf qUO6Ue\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_146\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.sht3tsbtlp1j\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Question:\u00a0<\/span><span class=\"C9DxTc \">Practice writing out more hypothesis, using the model above.<\/span><\/div>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/mrgeogwagg.wordpress.com\/wp-content\/uploads\/2015\/08\/bradshaw-model1.jpg\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">Bradshaw Model<\/span><\/a><span class=\"C9DxTc \">\u00a0is commonly used by Geographers to predict how river characteristics will change downstream. Practice writing out some null &amp; alternative hypothesis for other river characteristics. You can use the one above, for sediment size, to help you.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_84\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_87\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_49\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_52\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.8e2d63r9lv2f\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_54\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">For each of the investigations, write out the\u00a0<\/span><span class=\"C9DxTc \">null<\/span><span class=\"C9DxTc \">\u00a0and\u00a0<\/span><span class=\"C9DxTc \">alternative<\/span><span class=\"C9DxTc \">\u00a0hypotheses.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_464\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">1. The\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.hutton.ac.uk\/\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">James Hutton Institute<\/span><\/a><span class=\"C9DxTc \">\u00a0want to find out if the yield of wheat on Scottish farms has changed after using brand X fertiliser instead of using brand Y fertiliser.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_468\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">2. The\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.walkwheelcycletrust.org.uk\/\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">Walk Wheel Cycle Trust<\/span><\/a><span class=\"C9DxTc \">\u00a0found that the mean travel time to work for Glasgow residents in 2015 was 20 minutes. A transport official wants to use a sample of this year&#8217;s travel times to see if they have changed since 2015.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_472\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">.\u00a0<\/span><span class=\"C9DxTc \">The team at\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/ourworldindata.org\/\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">Our World in Data<\/span><\/a><span class=\"C9DxTc \">\u00a0are writing an article about improvements in healthcare. They want to establish whether a relationship exists between the GDP per capita ($) of ten low-income countries and the provision of doctors per 1,000 people in those countries.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_88\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_91\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.o7jsu0fqb1we\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Significance<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_94\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Significance is our measure of at what stage we accept or reject the null hypothesis. Using significance ensures your data isn&#8217;t just demonstrating a relationship by chance.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_95\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_100\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">When you calculate the result of a statistical test, you will have to check it against a\u00a0<\/span><span class=\"C9DxTc \">significance table<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_481\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STQ5V4xvOfJl2izl2E29yYUSlVGw1eprapAjt7wSGg8J_ug3LfUYKdUCkkR9SFbUsSKKmdZcJ7k5dTMmkcKx6FAu1oQwIjVpnoVKXmFIUmDvCeU9ykeWaMlgc7AbcZcIzxNK4HMVEsg8OnTLJolZks7isoYASGrqiYX2RYWWUr9WutyVm6jt3K624Z-6REI0Mu87-v4C3gXTpnQdctw8vabGxvtn_OK1GN8HJA=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_493\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">We will use data tables sourced from the\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.theislandgeographer.co.uk\/statistical-tests\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">Island Geographer<\/span><\/a><span class=\"C9DxTc \">\u00a0website. These should be referenced if you use them in your Geographical Study.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_507\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_510\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_504\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_519\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.jd3y8dpx6krt\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Chi Squared Significance Table<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_501\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd OWlOyc baZpAe\">\n<div>\n<div class=\"WIdY2d M1aSXe\" data-embed-doc-id=\"1QZkr7ModjoJxikU3SNUrZxuw-wY8HIUk\" data-embed-open-url=\"https:\/\/drive.google.com\/open?id=1QZkr7ModjoJxikU3SNUrZxuw-wY8HIUk\" data-embed-thumbnail-url=\"https:\/\/drive.google.com\/thumbnail?id=1QZkr7ModjoJxikU3SNUrZxuw-wY8HIUk&amp;sz=w464-h470-p-k-nu\" data-embed-download-url=\"https:\/\/drive.google.com\/uc?id=1QZkr7ModjoJxikU3SNUrZxuw-wY8HIUk&amp;export=download\">\n<div class=\"t5qrWd\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_524\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.x2mm671w3op7\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Spearman&#8217;s Rank<\/span><span class=\"C9DxTc \">\u00a0Significance Table<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_511\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd OWlOyc baZpAe\">\n<div>\n<div class=\"WIdY2d M1aSXe\" data-embed-doc-id=\"1KDaB-DSA9-VV3dGOX1Nfa56c7NwKen-P\" data-embed-open-url=\"https:\/\/drive.google.com\/open?id=1KDaB-DSA9-VV3dGOX1Nfa56c7NwKen-P\" data-embed-thumbnail-url=\"https:\/\/drive.google.com\/thumbnail?id=1KDaB-DSA9-VV3dGOX1Nfa56c7NwKen-P&amp;sz=w464-h470-p-k-nu\" data-embed-download-url=\"https:\/\/drive.google.com\/uc?id=1KDaB-DSA9-VV3dGOX1Nfa56c7NwKen-P&amp;export=download\">\n<div class=\"t5qrWd\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_527\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.kqe0tek4ga4o\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Pearson&#8217;s Product<\/span><span class=\"C9DxTc \">\u00a0Significance Table<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_515\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd OWlOyc baZpAe\">\n<div>\n<div class=\"WIdY2d M1aSXe\" data-embed-doc-id=\"1U_uF3zRyyzZ0q0AJp16Bk0uKHqylp4w4\" data-embed-open-url=\"https:\/\/drive.google.com\/open?id=1U_uF3zRyyzZ0q0AJp16Bk0uKHqylp4w4\" data-embed-thumbnail-url=\"https:\/\/drive.google.com\/thumbnail?id=1U_uF3zRyyzZ0q0AJp16Bk0uKHqylp4w4&amp;sz=w464-h470-p-k-nu\" data-embed-download-url=\"https:\/\/drive.google.com\/uc?id=1U_uF3zRyyzZ0q0AJp16Bk0uKHqylp4w4&amp;export=download\">\n<div class=\"t5qrWd\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_107\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_110\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_111\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_116\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Significance tables show values of probability.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">This example uses the Pearson&#8217;s Product significance table.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_541\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQZwN1Bj-EUkNDThwJt3V03-pw8eJWrxHQ4D-doQEsYhcIVeLsf1VUJv1FEfp07rWLtBSuM4LcnDGIYJywgMWTfBSRant4Y7EJttmfY3WFAFZi2maFZbMcYiVIThNL2jahmr_azxWA31INGnyaiB3prQF9J80Z6GpoqR767E0_-4V9Tp91l7wTe7PYYnGt7b41GDdS4_NvSTDEgU9VwTgxlidJE2wjA6A=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_537\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A significance level of 0.01 says that there is a 1 in 100 chance of your data being a chance event. That means that there is 99% certainty that the relationship exists.<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">If the value that you&#8217;ve calculated in your statistical test is more than this (e.g. more than 0.995 &#8211; the\u00a0<\/span><span class=\"C9DxTc \">critical value<\/span><span class=\"C9DxTc \">) then you can say that you&#8217;re highly certain the relationship exists.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">e.g. The result of 0.998 exceeds the 0.01 significance level. The null hypothesis must be rejected and replaced by the alternative hypothesis &#8211; that there is a relationship between the size of sediment in River X and the distance from the source.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">However,\u00a0<\/span><span class=\"C9DxTc \">the\u00a0<\/span><span class=\"C9DxTc \">degrees of freedom<\/span><span class=\"C9DxTc \">\u00a0refers to the numbers of values that have been studied to reach this conclusion. The more data the better &#8211; but also the more likely the data is to have anomalies. This means that at higher degrees of freedom, the number which needs to be reached is less. Be sure to calculate the degrees of freedom correctly &#8211; it&#8217;s done differently depending on the test conducted.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_123\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_126\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_546\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"vhaaFf qUO6Ue\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_549\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.ib5lxswi6esf\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Question:\u00a0<\/span><span class=\"C9DxTc \">You&#8217;re studying the change in house prices as you move away from the city centre. You have done a Spearman&#8217;s Rank statistical test and got a result of 0.826 based on 8 sets of data (n).<\/span><\/div>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Based on a significance level of 0.02 (98%), do you:<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A &#8211; Reject the null hypothesis and accept the alternative hypothesis.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">B &#8211; Accept the null hypothesis.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">C &#8211; Change the level of significance you&#8217;re looking at because although it doesn&#8217;t meet it at 98%, it would at 95%.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_139\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_142\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_127\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_130\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.sj1tsecm3mrl\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_556\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STEMETq-3iVGiyidtnUAgBhpwgNVY3gk_bMuEgCc0LohPLkuBuOY3cJTmpwh_vwejc7DvoZn4wVQLIxk7Kg2Ta_0a4YepGh2YPUI1gMGLogyBlImh-d35PbZe3dBWDIHfOeTvw42l59hWpwIdTYxj5wb_h9qD87qNapvKaR88DSZnk90OhD58HuZQO3o19UdusIHvWVgPshvpl91_62bwup4tLubqtmZciEDxk=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.12b88c2cf1f30222_132\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The Scottish Geology Trust are investigating the feasibility of a new path and interpretation centre at\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.scottishgeologytrust.org\/geology\/51-best-places\/siccar-point\/\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">Siccar Point<\/span><\/a><span class=\"C9DxTc \">. They&#8217;ve compared the occurrences of path erosion at Siccar Point to locations on other parts of the coastal path. They want to see if visitors to Siccar Point are causing an increase in path erosion.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_552\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A chi squared analysis was undertaken to statistically test the data. The result (critical value) of this was 24.57. The degrees of freedom was 18.<\/span><span class=\"C9DxTc \"><\/p>\n<p><\/span><\/p>\n<ol class=\"n8H08c BKnRcf \">\n<li class=\"zfr3Q TYR86d lsiHE \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Write down the null hypothesis and the alternative hypothesis.<\/span><span class=\"C9DxTc \"><\/p>\n<p><\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d lsiHE \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Open the significance table for Chi squared. Is the critical value of 24.57 high enough to pass at any of the listed significant levels? If so, which ones?<\/span><span class=\"C9DxTc \"><\/p>\n<p><\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d lsiHE \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Write down whether you accept or reject the null hypothesis.<\/span><span class=\"C9DxTc \"><\/p>\n<p><\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d lsiHE \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Suggest two other data gathering techniques, other than measuring path erosion, that they might want to use to collect data to inform their plans.<\/span><\/p>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.12b88c2cf1f30222_403\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.12b88c2cf1f30222_406\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.32c40bce5514a9cf_0\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.32c40bce5514a9cf_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.9deysvqqdo3z\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Pearson&#8217;s Product<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.32c40bce5514a9cf_6\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Pearson&#8217;s Product Moment Correlation Coefficient, to give it it&#8217;s full name, is a way to examine two sets of data and find out if there is a significant relationship between them.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It gives us an idea of the strength of the relationship and what direction &#8211; i.e. is it a positive or negative relationship.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.32c40bce5514a9cf_16\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.32c40bce5514a9cf_7\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Before learning about how to do the statistical calculation, it might be worth reminding yourself about\u00a0<\/span><span class=\"C9DxTc \">correlation<\/span><span class=\"C9DxTc \">. This was covered in the\u00a0<\/span><a href=\"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/graphical-data-presentation\/\"><span class=\"C9DxTc aw5Odc \">Graphical Data Presentation<\/span><\/a><span class=\"C9DxTc \">\u00a0part of the course.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A Pearson&#8217;s Product calculation will give us a value which will allow us to decide what kind of correlation the data has &#8211; and if it&#8217;s strong enough for us to accept a hypothesis.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.32c40bce5514a9cf_14\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STVNfx6YvXdii3fAl5WtlMh8fBNCPmyfysHpD9IWkdhcJspy7b4KEajHlZETBvhEKZ720qdhnhx77SBfxf71qpDgok8eHYk61XkFtWnL9dBtg-OEhffTDgNSzmjl2fsZDeKnOQAJdkGGCC7KMFDmMgDADTW0Qr13gytDURV04PF6yXMrJXhWb5Ws_p6vA_lXe-zuQqDWMxAnJX6v6p4u8GTkmWQoB2lRJiuFvQ=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_3\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_0\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The formula for Pearson&#8217;s Product looks complicated, but it just has to be calculated in steps. Each of these steps is represented with a heading in the table.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.32c40bce5514a9cf_19\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STZpPGj2YXlGXFMYz1-sdIjT4YzqeLZmJ4ESmz1vZXWRj6FI3c771VY-98s8VqdPU60Y9MHqumZj4q7lg7M-pc4j-mUh7SSkTOpiqpUPYhfk_AHyKMCyHzuGLDP2G-f7bGzAG7CrnoMH02pz2zgfjb4W0xb_9NLAHYmakCEstb5ZnmWaBU49aYCDLg_sQmaWyY2gzC2kRZeFupujePUgOmuI90lZUknxMmh=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_91\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_94\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_4\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_7\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.7slw37ehjty7\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Worked Example<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_20\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STwg4Gqx5cwdIKkuowBVTGvaCOw8HbG5DbULxcFCd4H8bd8CWFTMjaTHb0AZ92gClTHlTgVvGeZKQKA7BKbKQfCMyzo0RifQ7SD_fyqPoxdi1r4970C1MKZN80EXxDcdE52-4hWBySEVLeVm72gffoyTDBQZuL56jQX2lNvi_SivenaB-0yDhRwls8W6CnLzXriK1HS30T0tf9wa-covhCyn8_v6gHENGFR=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_11\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A geographical researcher is examining how air pollution levels vary with distance from the CBD in Inverness. Nitrogen dioxide levels were recorded and mapped across the city at regular intervals along a transect.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The researcher believed that as the centre of the city was quite old and contained few roads wide enough for large volumes of traffic, it would not have as high a level of nitrogen dioxide as the city outskirts.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The researcher therefore formulated the following null hypothesis:<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">\u201cThere is no correlation between the level of nitrogen dioxide in the air and the distance from the CBD.\u201d\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_16\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0ST2wEIvTDZIUeKJ5haIPfsxS8xgEWvEcrKblHToXnKdrEnN9aPN-UTKurJX_-QK9lLvOhDHGfzwRvugKbT_3SMd0XtxvA9SDqSBg2dR-8sW1y4ZnCsRawIiy90crKnqpMdph0vol9Q47sOeDUPcJQnijWMrYt_B1aRsBhvgzNLh1PzOuptAI9LplliTVn_iJ5-We7tGXAX8vGOPaGZoav8sMUiZ3-lRT9gxJyY=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_40\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_37\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:\u00a0<\/span><span class=\"C9DxTc \">Use the data to create a scattergraph. This will allow you to determine what kind of correlation to expect.&#8217;<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In this case, the data shows a negative correlation. We will expect the result of our Pearson&#8217;s Product calculation to be a negative number.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_41\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQNUpqaf2POQOOGk6jqmIxRD0bSCF2fyAiajBoEf8pyDln_EX5LkmBntd3wQeA9sSCsyIge9f2qHcW66TEX8HQQlUtqIsyhoeuWwbOYRMRB9PfPSSn7mt8dPFtNAPF5E1FAAM8JXo-hfvl-v31uW36MIwN2tsn-LdU1AceosGglcjOZmMjVJBR_kgsiN1SO23yMh4eTU1qrGID5FtVZnnt1FGh_NH4msFLHOL4=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_28\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_25\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 2:\u00a0<\/span><span class=\"C9DxTc \">Create a table as shown. This gives you all the components you need to work out Pearson&#8217;s Product using the formula.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If you need more rows (for a higher number of data sets), then just add them!<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">What are all the columns for?<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the first column, put the values for your independent variable\u00a0<\/span><span class=\"C9DxTc \">x<\/span><span class=\"C9DxTc \">\u00a0(in this case, distance from the CBD).\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the second column, put the values for your dependent variable\u00a0<\/span><span class=\"C9DxTc \">y<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">(in this case, nitrogen dioxide levels).<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">(x &#8211; x\u0305)\u00a0<\/span><span class=\"C9DxTc \">column\u00a0<\/span><span class=\"C9DxTc \">is<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">how different the x values are from the mean.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">(y &#8211; y\u0305)\u00a0<\/span><span class=\"C9DxTc \">column is how different the y values are\u00a0<\/span><span class=\"C9DxTc \">from the mean.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">(x &#8211; x\u0305)(y &#8211; y\u0305)\u00a0<\/span><span class=\"C9DxTc \">column is these two figures multiplied together, for each data set.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">(x &#8211; x\u0305)<\/span><span class=\"C9DxTc \">\u00b2\u00a0<\/span><span class=\"C9DxTc \">and<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">(y &#8211; y\u0305)<\/span><span class=\"C9DxTc \">\u00b2\u00a0<\/span><span class=\"C9DxTc \">columns are the square.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_29\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SR3Ir3QRt0IGDqbrSl7ub1gDm-ixLfhj059dqvm-JwzOQGfqELW1v1stfgtBoG-qAaMuy9oVEQIcbN0wRw8ASicU4hT-LzlTq5Dl_VbsXckk8_XemoYLKfkvXrULedmHImpGa9L5VXzFuY0ywHSdXFH-89V7ZGipwa6Wx7aXahw53q8R4zg2ql-nKN07DQT2aKyJfBQCKR2kO6Wi0wffRW_yLedUwc31RN33H4=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_55\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_52\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 3:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Calculate the mean of x (xbar) and the mean of y (ybar).<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 4:<\/span><span class=\"C9DxTc \">\u00a0Use the table to work through and calculate all the components you will need to use the formula.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">These are:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Total (\u2211) of (x &#8211; x\u0305)(y &#8211; y\u0305)\u00a0<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Total (\u2211) of (x &#8211; x\u0305)\u00b2<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Total (\u2211) of (y &#8211; y\u0305)\u00b2<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The completed table is shown.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_60\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSRPsa_Z6G0iIXvwUDTv_kXVSDURWrHf6bBHQUqtlDky5Zego2D0p9GwJrjizoBP-RA59tLMN86m3qrz0J9TD_BGMqyupmmi20mgC9VpgMrsb4rRwaKCCqqad7J5I1Z_-0oTd6ZeESNsU2HppTwEeeL5MUe4dRe75Z45-zLzTsZmVXRCK531TpnPzwjafe5cNlSAuU40yoF20Yw2jtFJH74eLInA2445ndE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_71\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_68\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 5:<\/span><span class=\"C9DxTc \">\u00a0Use the components to slot into the formula.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The negative value confirms to us that there is a negative correlation. The value is also close to -0.9, which tells us that there is a\u00a0<\/span><span class=\"C9DxTc \">strong, negative correlation.<\/span><span class=\"C9DxTc \">\u00a0But, before we can accept or reject the hypothesis we should check it&#8217;s significance.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 6:<\/span><span class=\"C9DxTc \">\u00a0Check the calculated value against the critical value, using the\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/drive.google.com\/file\/d\/1U_uF3zRyyzZ0q0AJp16Bk0uKHqylp4w4\/view\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">significance table<\/span><\/a><span class=\"C9DxTc \">. The\u00a0<\/span><span class=\"C9DxTc \">degrees of freedom<\/span><span class=\"C9DxTc \">\u00a0for Pearson&#8217;s Product is<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">n-1 so in this case would be 12. When checking the level of significance, ignore any negative signs.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_72\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSk603oayZImB4lNtJAW1AYldYw7kLuCoWMWKKi_ZjmtjqmMiiPxc4kryrBaMk29UXyDFaa9bTj1eI8rLyzowvTleGwD_AsC6MIYCaJK45-eOmZDpqfsKtZ_TR50kOlxOfQ0kJDS7IEGx7lt44XrQ7gRy1d1b1hb2wOjpV0Djwu2FZp4Ms89snAKPSmEmfC6SZoQPa6z5ay8ueHVuBqySEDjZ8VmKyRD2-R=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_77\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">We can see from the table that the value has to be above 0.661 to be accepted. Our value of 0.908 is therefore above and we can say there is a significant relationship.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 7:\u00a0<\/span><span class=\"C9DxTc \">Write out your answer in full, referring to the\u00a0<\/span><span class=\"C9DxTc \">calculated value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">critical value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">significance level<\/span><span class=\"C9DxTc \">\u00a0and\u00a0<\/span><span class=\"C9DxTc \">hypothesis<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_87\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STiLwzCak8HSyxZ4qgYbdZwUi5DFpg2_NHJCWjhXUncBgdTXXRw7NRbd4wib5HCHCXX9iVoFw8bYrFurJlZIjUNbuW_0QAImcwg_8TCaAe8i5SPzQvBoKdWp-ZQh08EnGx6VMqanVn4gK8CmmDOK1apfZ08yPgE8H_a7ul3mHOahXIBoYBplEVoRLDMmNLjDiL_uWdqD14psHlPtrbNAfZMT5CR8UQRCKZTnPo=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_82\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQpsN1c2Uhz6HLZgbHPTie_6z8KM91p-GeCiHPLShTDxN1W2m3n5Z1cEm2YsyGwNJXhJZGRHLS_7dp9wfmukIWffurK8LMslxcT8rJVYCuNY3KNk2N_UcW-Q2ca1QvPeQyXG95pj_SjaJuyGHvXXZqvdvLtEx_1WxX52S3mjc3KbuPrpGd4Fxr2qgsZ696K-7OJUX1A4v768vCE3KIZGuOak5RVRce0W_0w1Co=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_86\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_83\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The Pearson\u2019s value result of\u00a0<\/span><span class=\"C9DxTc \">-0.908<\/span><span class=\"C9DxTc \">\u00a0exceeds the 0.0<\/span><span class=\"C9DxTc \">05<\/span><span class=\"C9DxTc \">\u00a0or 99.5% significance level at\u00a0<\/span><span class=\"C9DxTc \">12<\/span><span class=\"C9DxTc \">\u00a0degrees of freedom of 0.<\/span><span class=\"C9DxTc \">661<\/span><span class=\"C9DxTc \">. The null hypothesis must be rejected and replaced by the alternative hypothesis \u2013 that there is a significant, strong,\u00a0<\/span><span class=\"C9DxTc \">negative<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">correlation between the level of nitrogen dioxide in the air and the distance from the CBD.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_95\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_98\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_99\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"vhaaFf qUO6Ue\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_102\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.7h2pnmxqiwz1\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Question:\u00a0<\/span><span class=\"C9DxTc \">Pearson&#8217;s Product isn&#8217;t suitable for use with all types of data or hypothesis.<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">Which of these could it be used with?\u00a0<\/span><\/div>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A &#8211;\u00a0<\/span><span class=\"C9DxTc \">To find out if there&#8217;s a relationship between the depth of soil and distance up a slope<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">B &#8211;<\/span><span class=\"C9DxTc \">\u00a0To find out if two towns are seeing a similar rise in incidences of coastal erosion<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">C &#8211;\u00a0<\/span><span class=\"C9DxTc \">To find out if there is a correlation between the GDP per capita and carbon dioxide emissions in South American countries<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.3a38301788268956_59\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.3a38301788268956_62\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Pearson\u2019s Product Moment Correlation Coefficient tests the strength and direction of a correlation between two sets of data.<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">It uses absolute values, which is more accurate than relative (ranked) values.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">It is useful when examining interval data; which means that it can be used with a mixture of negative and positive numbers.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">It can also be used with ratio data (which has a true zero).<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">It assumes a linear relationship, and does not work well with data which might have a different relationship (e.g. logarithmic).<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">There are many steps to the calculation, which increases the likelihood of a calculation error.<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.31c9214f30f51e0e_109\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_112\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.qra4khhr5hzl\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_124\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRvYDTPUF0jPjbkQtn6OGOwCIRUL3VPwhduVL7o1xcKCd8U6oV-IyOnBQhB-yrM8iSSIRopS41BL4WJ4JzIzOoH0KEOcUf7fnbzn26r3dAa21ZzSdzyFJP2c6R5fdOU049SqQHqlnCfsSvLXBsRbSOY83mNGEc9LPobUG32fsqGVACC7zsrmf7lx7KdXmmVXf_3P6d7kSI788MTuh3yJDCxatsn6LCgAPXL=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.31c9214f30f51e0e_116\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">\u00a0A researcher for a health charity is looking to find out if there is a relationship between the % of people who work in agriculture and the life expectancy. She has randomly sampled 8 countries and sourced data from Gapminder.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Write out the\u00a0<\/span><span class=\"C9DxTc \">null hypothesis<\/span><span class=\"C9DxTc \">\u00a0for the investigation and undertake a Pearson&#8217;s Product analysis to determine whether it should be accepted or rejected.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_120\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQXfAXhEZ9-iNSpdilwptmU0Syjl65bgyNQS8rxHV3bTEEsauCiESadMy9HbiYk09gvHzZyJk7GuilCunk1yswBgYKpH7auoqR383yBZV8QbLockcBpbkCJq0WAOETXjdujYiU6Up05S6LyLK1tIqRW_tSbpSzW7yEugJtD5ryryrgZAAks_anXVqdh-3Mf5Chnmnksy7joRAIOR-b8FD_XZwMOlpYSoXqm=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.31c9214f30f51e0e_129\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:<\/span><span class=\"C9DxTc \">\u00a0Scattergraph<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 2:<\/span><span class=\"C9DxTc \">\u00a0Table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 3<\/span><span class=\"C9DxTc \">: Calculate mean<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 4:\u00a0<\/span><span class=\"C9DxTc \">Complete table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 5:<\/span><span class=\"C9DxTc \">\u00a0Formula<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 6:<\/span><span class=\"C9DxTc \">\u00a0Significance table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 7:\u00a0<\/span><span class=\"C9DxTc \">Write-out in full<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.61ebab5f6a3743f0_0\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.61ebab5f6a3743f0_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.dnt8n9mxx0uy\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Spearman&#8217;s Rank<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.61ebab5f6a3743f0_6\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Spearman&#8217;s Rank\u00a0<\/span><span class=\"C9DxTc \">\u00a0Coefficient, to give it it&#8217;s full name, is\u00a0<\/span><span class=\"C9DxTc \">a<\/span><span class=\"C9DxTc \">nother<\/span><span class=\"C9DxTc \">\u00a0way to examine two sets of data and find out if there is a significant relationship between them.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It gives us an idea of the strength of the relationship and what direction &#8211; i.e. is it a positive or negative relationship.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It uses\u00a0<\/span><span class=\"C9DxTc \">ranked<\/span><span class=\"C9DxTc \">\u00a0data rather than the true values.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad49477971239de_0\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Spearman&#8217;s Rank has a lot of similarities to Pearson&#8217;s Product and is used with similar data sets. However, it has some key differences:<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_7\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It uses the data&#8217;s rank, rather than it&#8217;s true value.\u00a0<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">This is an\u00a0<\/span><span class=\"C9DxTc \">advantage<\/span><span class=\"C9DxTc \">\u00a0because it reduces the impact of extreme values.\u00a0<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">This makes the technique<\/span><span class=\"C9DxTc \">\u00a0less powerful<\/span><span class=\"C9DxTc \">\u00a0than Pearson&#8217;s Product which gives more reliability and precision.<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It has an fewer steps than Pearson&#8217;s Product, which makes it an easier statistical test to complete.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad49477971239de_14\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_18\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The formula for Spearman&#8217;s Rank has fewer components:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">\u2211d\u00b2 = the total o<\/span><span class=\"C9DxTc \">f the differences in rank for each set of paired data<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">n = the number of sets of paired data<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">However, there are still a number of steps to follow to get the information you need.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_11\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SS5ylXLTmELlAY3zccdU1IH4kZEP9H8FDciTjspPuXoCy5U4lYjb4KIM3llZP8pub0OwNf039dvmC7Hib7sHED3V22HkH4THT7RYxexr6xSc_5pnHS03NOC9N0ZZz_SsXbgfSrmmxmwazml_fJAMOBBVyI5-XpnEON0gP2utq-ZIojyGYfB30fjmhSOjtkt2MzcP3KV7T_VX7o2vtzrNwBzEukHl4L3KjiwKMs=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad49477971239de_24\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_27\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad49477971239de_28\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_31\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.gl1mcumt54wy\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Worked Example<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.4f78463fc5f285e1_0\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQAnP0G5Ap1T0zHJkwKittl0NkJccrYCC6t9-6xF2yaG36iPS_WL0S1Wkc0M5Iwroyts06itD4du8qteIWKOujB1ZoW3ib8__miBbQnjIwfUGeiVsrwisjWyyi1ipV7NHABX790HYskGAxfKO8Dogf6XAKfeYfx3dhlhutZY1xeQxC9O0_WEernbmH0W1ag42o7bGWhVJiV8q2NAPJhX7d0T7hKBSQZX0kpF3U=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad49477971239de_35\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A Geography class are investigating whether there is a relationship between the adult literacy of countries and their fertility rate.<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">The adult literacy rate is the percentage of people ages 15 and above who can both read and write, with understanding, a short simple statement about their everyday life.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Total fertility rate represents the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with age-specific fertility rates of the specified year.<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In order to see if there is a relationship, and if it&#8217;s significant, they will undertake a Spearman&#8217;s Rank calculation. Their teacher has provided them with a\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1nIrYjhE1QeKxZF68XSdUbaQnjjS_02F1_wBYFq9d8UY\/edit?gid=0#gid=0\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">dataset<\/span><\/a><span class=\"C9DxTc \">\u00a0featuring 68 countries.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Null hypothesis: There is no relationship between the adult literacy rate and the total fertility rate in select countries.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_7\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_10\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Data sampling:\u00a0<\/span><span class=\"C9DxTc \">As the data set is very large, the students decided to use a sampling strategy to select 14 countries each. That is because ranking very large data sets is difficult and there is a higher chance of an error occurring.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">They could do this using a:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">systematic sampling approach<\/span><span class=\"C9DxTc \">, taking every 5th country<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">stratified sampling approach<\/span><span class=\"C9DxTc \">, separating the countries into those with high, medium and low human development and then selecting 4 from each<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">random sampling approach<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">generating 14 random numbers between 1-68 to select their countries.<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">This worked example, shown in the table, used a systematic sampling method and selected countries on every 5th line, starting with line 2.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_21\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQwjAktSuBsOU_Wm5HxMTw3YOt5K60B1HkUV8guEDwT2AzlTYVm41ZCIdSbqgeGjbAbViRvGE-wfheRx_vNr-O-ejMvn-XGA4XwmmWqV2nM4-wH11RqqRXOxr5XnVmDybmO5KouQbiD7LLlCdh27tAS17uDqvD9CUNqjQsHJA6LpCrQzFVF0ErG8ARKoMBCV3qeBfkPH6lxzbHIsNe1hwSd2jw12YgH0taMAWQ=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_14\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_17\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">1<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Use the data to create a scattergraph. This will allow you to determine what kind of correlation to expect.&#8217;<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In this case, the data shows a negative correlation. We will expect the result of our\u00a0<\/span><span class=\"C9DxTc \">Spearman<\/span><span class=\"C9DxTc \">&#8216;s Product calculation to be a negative number.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_29\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQGQu5Ga4EHAh5Kz6i-I45rb1OydHRvhe8FmcPPuGNds6Ik95BvICHJpQ1Jj_nkiREtztsYUmq9CEXB4F7P10KYv9Me25301m4gjxrJtfsd32dBOMPYDNlA4KkZlT-Tc_P-qwRG_ja0QOjhlaeyHC8vf-BAbccwa2s8AbKoFJQp1fYGJvhoBuXbaGewBiiaiobJM_JDSeolhi43CSEXN0FEknyOu5TO2Ol4byY=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_37\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_40\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">2<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Create a table as shown. This gives you all the components you need to work out\u00a0<\/span><span class=\"C9DxTc \">Spearman&#8217;s Rank<\/span><span class=\"C9DxTc \">\u00a0using the formula.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If you need more rows (for a higher number of data sets), then just add them!<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">What are all the columns for?<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the first column, put the values for your independent variable\u00a0<\/span><span class=\"C9DxTc \">x<\/span><span class=\"C9DxTc \">\u00a0(in this case,\u00a0<\/span><span class=\"C9DxTc \">adult literacy rate)<\/span><span class=\"C9DxTc \">.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the second column, put the values for your dependent variable\u00a0<\/span><span class=\"C9DxTc \">y<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">(in this case,\u00a0<\/span><span class=\"C9DxTc \">total fertility rate<\/span><span class=\"C9DxTc \">).<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Th<\/span><span class=\"C9DxTc \">e\u00a0<\/span><span class=\"C9DxTc \">rank x<\/span><span class=\"C9DxTc \">\u00a0and\u00a0<\/span><span class=\"C9DxTc \">rank y<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">column<\/span><span class=\"C9DxTc \">s are the rank given to the data. There is more information about how to do this below.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The<\/span><span class=\"C9DxTc \">\u00a0d\u00a0<\/span><span class=\"C9DxTc \">column is<\/span><span class=\"C9DxTc \">\u00a0the difference between the ranks for x and y (difference between column 3 and 5)<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The d<\/span><span class=\"C9DxTc \">\u00b2\u00a0<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">column is the d column squared. We do this to remove negative numbers.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_44\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQ6WiGy-nmWAALevRoHd_MDs8_zL1H5LmD4VBma8Rmz8y9BFEIkJFYCfAlRaT3gAuHAPHQDPqYAU6Fm7qIBqNSIBhzsqPsEEV0mgDu9XvetuDWK_uBmgFFhHONpbRkz4CPr9jg82_7rtxL61e1CLuhF8x3LsMPaQPDYA79xZM_9vUah0CfhO9X0dErThoWIW9L99hOdGPzs7Td8fFoqY8TZk7rK4ax0S-GL=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_48\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_51\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Rank the x and y data.\u00a0<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">You can do this in ascending (doing up) or descending (going down) order. It doesn&#8217;t matter, as long as it&#8217;s the same for both x and y.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">If there are two identical values (like the values in\u00a0<\/span><span class=\"C9DxTc \">red<\/span><span class=\"C9DxTc \">) then you give them a rank half way between the two. For example, the value of 4.8 would have come at rank position 2 and 3, so it&#8217;s given the rank of 2.5 Importantly, you then continue ranking from value 4.\u00a0<\/span><span class=\"C9DxTc \">I like to keep a track of this by writing in brackets &#8211; otherwise I get in a mess!<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">If there are three (or more!) identical values, like those shown in\u00a0<\/span><span class=\"C9DxTc \">blue<\/span><span class=\"C9DxTc \">, you give them a rank that is the average of the values. In this case, the adult literacy rate of 100 would have been ranks 1, 2 and 3 &#8211; the average of which is 2. You then continue ranking from rank 4.\u00a0<\/span><span class=\"C9DxTc \">Again, I add the numbers in brackets just for my own sake and keeping track.<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">You should know that you&#8217;ve done this step correctly as your last rank will be the same as the number of data sets you have.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_59\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRePnzjdJmFaGfZaKp5dgG6mF12bTy_ObOhAXBXH4LWGnSJbx3OnjMpRj7Mirpd4810QaxdujaiG9v2q0UlOjPbOEDx7eMevwq3ePJXQ_ctnGLCL-8QY08K6wtQEWobtk1RLjDhxilXd1KZeUDOeVpSpnxYKlj5mC0DI1NTDWdNvI6mtICMUhGBSv4w3Z9qGdbMRu5W3KP90iNJJsZWTgepFfu_--NKnO7aO10=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_63\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_66\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Calculate the difference in ranks and square, to complete the table.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 5:\u00a0<\/span><span class=\"C9DxTc \">Use the calculated\u00a0<\/span><span class=\"C9DxTc \">\u2211d\u00b2 value in the formula.\u00a0<\/span><span class=\"C9DxTc \">Remember to do the\u00a0<\/span><span class=\"C9DxTc \">1 &#8211;\u00a0<\/span><span class=\"C9DxTc \">part of the calculation.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.4f78463fc5f285e1_74\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSOmedMMyKrvKtd8LTarScSrCo7zZWGVHJHHtpqhwYEky3Fcs34UI-XBAm4NBHJBlhWdY-lHS_Sey1gC-UP5gl5uvxbwSjXfIfPQBb1ho7rQfJAx018nbiSg4_O_IfHPax7UTWeocA6-q0ANNW4SaWteAtoLtWN4INs8gl6rBbCJrQlrcXadfrNegZeDaB_zCJvYSjml9gV8bmBnCUnDlqMV8SpldHyM4i1=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_70\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRZgbqntj2PGaTf9z_GlAbFnwvEJX1bAHrBgWmJjCTZ1d5Nx16VFfYCVv6l1K51RA3cy2AIYQfx-SQxAKMs_RhMaUwtIft84sQLaAFGop6FBGtAzJKw9gfBma2tyVlLIVNQtX3H4aiX-w9eWE-Kb6O1JXmhFqka3r-UulJxI7n_2JwZn9DmzMO6RKIUBmd2A1a11yyrKEDP1QR6Fiw4yigG_ZJ_-_q9ZBp4=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.52008445f1817243_16\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.52008445f1817243_13\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The negative value confirms to us that there is a negative correlation. The value is -0.715, which tells us that the relationship isn&#8217;t strong, but it is there<\/span><span class=\"C9DxTc \">.<\/span><span class=\"C9DxTc \">\u00a0But, before we can accept or reject the hypothesis we should check it&#8217;s significance.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.4f78463fc5f285e1_79\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.4f78463fc5f285e1_82\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">6<\/span><span class=\"C9DxTc \">:<\/span><span class=\"C9DxTc \">\u00a0Check the calculated value against the critical value, using the\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/drive.google.com\/file\/d\/1KDaB-DSA9-VV3dGOX1Nfa56c7NwKen-P\/view\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">significance table<\/span><\/a><span class=\"C9DxTc \">. The\u00a0<\/span><span class=\"C9DxTc \">degrees of freedom<\/span><span class=\"C9DxTc \">\u00a0for\u00a0<\/span><span class=\"C9DxTc \">Spearman&#8217;s Rank<\/span><span class=\"C9DxTc \">\u00a0is<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">simply n,<\/span><span class=\"C9DxTc \">\u00a0so in this case would be 1<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">. When checking the level of significance, ignore any negative signs.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.52008445f1817243_4\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SReQ5MYf2BKKBJCQwa2JYQWrNl2CiYpOVEmOCItZTtjdmgJZiZ57thjpI1Sa4AjL-kbADPIAzPKEN4TQ8_jy0pKUUEjZyQBoL3kBB0z-vftTCJFLKsT__H8FfJuy11P6mBf2fwrAJHeDI57dLrGhaEJznZTc6XNVSk62ov3jlun1QDWlr1_uFLQWsEIZ-BqCH8aDxuc7TtLznrcdPYb0E6MJub2g5EWD-FJ=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.4f78463fc5f285e1_86\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">We can see from the table that the value has to be above 0.6<\/span><span class=\"C9DxTc \">75<\/span><span class=\"C9DxTc \">\u00a0to be accepted at\u00a0<\/span><span class=\"C9DxTc \">a 0.01 level of significance<\/span><span class=\"C9DxTc \">. Our value of\u00a0<\/span><span class=\"C9DxTc \">-0.715\u00a0<\/span><span class=\"C9DxTc \">is therefore above and we can say there is a significant relationship.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.52008445f1817243_17\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">7<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Write out your answer in full, referring to the\u00a0<\/span><span class=\"C9DxTc \">calculated value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">critical value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">significance level<\/span><span class=\"C9DxTc \">\u00a0and\u00a0<\/span><span class=\"C9DxTc \">hypothesis<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.52008445f1817243_9\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">Spearman&#8217;s Rank\u00a0<\/span><span class=\"C9DxTc \">value result of -0<\/span><span class=\"C9DxTc \">.715<\/span><span class=\"C9DxTc \">\u00a0exceeds the 0.0<\/span><span class=\"C9DxTc \">1<\/span><span class=\"C9DxTc \">\u00a0or 99% significance level at 1<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">\u00a0degrees of freedom of 0.6<\/span><span class=\"C9DxTc \">75<\/span><span class=\"C9DxTc \">. The null hypothesis must be rejected and replaced by the alternative hypothesis \u2013 that there is a significant negative<\/span><span class=\"C9DxTc \">\u00a0relationship<\/span><span class=\"C9DxTc \">\u00a0between the\u00a0<\/span><span class=\"C9DxTc \">adult literacy rate and total fertility rate of select countries.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.52008445f1817243_22\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.52008445f1817243_25\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.52008445f1817243_26\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.52008445f1817243_29\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.ysyrd6g143vi\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.52008445f1817243_40\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STW6IE4PEobDTTHQFki2VJrcOZ3G58z34fygan559KNy25oNgTcCZKTsep7XpES_sQXBI9Wtex4DtajDN9SGgw4NxlTa9QEserj7f51pn2D5WjAVKRjK6W0Ou6xXdQ89V5MyA2zIG4SWCF4CtCLJjyKtYKbrXp5aycXyR1_tduLzMxcgm_hK-k7=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.52008445f1817243_33\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Conduct a Spearman&#8217;s Rank analysis on another 14 countries from the\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1nIrYjhE1QeKxZF68XSdUbaQnjjS_02F1_wBYFq9d8UY\/edit?gid=0#gid=0\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">data set<\/span><\/a><span class=\"C9DxTc \">.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">You could choose to sample these with\u00a0<\/span><span class=\"C9DxTc \">random<\/span><span class=\"C9DxTc \">\u00a0or\u00a0<\/span><span class=\"C9DxTc \">stratified<\/span><span class=\"C9DxTc \">\u00a0sampling.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.52008445f1817243_39\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Sampling<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:<\/span><span class=\"C9DxTc \">\u00a0Scattergraph<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 2:<\/span><span class=\"C9DxTc \">\u00a0Table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 3<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Ranking<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 4:\u00a0<\/span><span class=\"C9DxTc \">Complete table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 5:<\/span><span class=\"C9DxTc \">\u00a0Formula<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 6:<\/span><span class=\"C9DxTc \">\u00a0Significance table<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 7:\u00a0<\/span><span class=\"C9DxTc \">Write-out in full<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf JNdkSc SQVYQc L6cTce-purZT L6cTce-pSzOP\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_0\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.55g1e8vph5o5\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Chi Squared<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_6\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Chi Squared is a statistical method used for data which is in categories. It&#8217;s useful when we&#8217;re looking at whether there is an association between data across different sites or groups of people.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_7\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_10\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Chi Squared is really useful for lots of Advanced Higher Geography studies. That&#8217;s because lots of them will compare data across different locations.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_13\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Considerations:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Both sets of data need to be categorical, so you may have to arrange any continuous data (e.g. ages, distances) into groups. For example, you could create groups labelled 0-15 years, 16-30 years, 31-45 years, 46-60 years.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Depending on the data being analysed, you might want to combine groups so that you have around 4-5 to work with.\u00a0<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">The calculated value should be checked against a\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.theislandgeographer.co.uk\/_files\/ugd\/a616e4_36b2f82b1f9b43d9a9c3aae093f88cf1.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">significance table<\/span><\/a><span class=\"C9DxTc \">\u00a0&#8211; note the different way to calculate the degrees of freedom.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Beware<\/span><span class=\"C9DxTc \">\u00a0of categories with small expected values. One or two are fine, but if there are any under 1 &#8211; or a few under 5 &#8211; it means the test isn&#8217;t very reliable for your data. You could limit the impact of this by combining groups (e.g. making the age categories larger). In reality, it&#8217;s difficult to plan for this in AH studies but the more data you have, the easier it is to manipulate it and change categories should this be the case.<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_14\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_17\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The formula for\u00a0<\/span><span class=\"C9DxTc \">Chi Squared (X<\/span><span class=\"C9DxTc \">\u00b2)<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">\u00a0works a little differently to your previous inferential statistics. You calculate the data in a table, and then total it.<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">O = the observed value for each category<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">E = the calculated, expected value for each category<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">\u2211 = the total<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_21\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSJb85rxmB9Lw5vP9yup-XqRfQDxbq0w2gOWHXrXvK6RBof95jp7q9brU84l2RRcIXuVEHDkU9qy3Vx5-FJ21K7nBQJ4R7KJSTpMqU_fB02nRwLcSWlQNMGhQKOvs5GNERvzkYQz8ToWWlw-5smkF7FfuU5B8E2CTW8OQx2xeTwfTcdNxTZ4nyfX8iyhb6k7gr-jt-HoNqIOweE7rTz84hFjeiL7Vx-ig=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_34\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_37\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_25\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_28\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.22ljaoosbm92\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Worked Example<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_44\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSi32hssu4yk5Prtfgj2T4m_bcWu7SGLb1Fep62YkZjePoAkgk2d6sbtCucPvEhsB-bSm3ZfnYOJjO8yqQ6fUfEya945tN0-N43kmg_mUXdzCUZgFZcE_-DBvKc1K7d4pnyBTsiJ4Bv7RChWW69mCpKN5ZEszYw7xFrCi_zl-ShItLg5BOFmBoj2gYBpc_02UAXauf0WxGNslHdqwTlxn3s7fjcvY4IEILf=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_38\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec wHaque g5GTcb QaN0Zc QjXeod\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRq5BMkzX7ZsUCZSBMKlSz5JsuyJB-NSsg6f9ox-hpNDnInCDgM3QvYDtwN7BJN75-F3_pmcyBGvRGcdMQxbFEZO7EIM_jvhllJmW5osivczcfIeBATbA0mDZJTuPqWstPeP1CPWGrxHo8zXzTzCdy39lV9BcIMT5usv9UYDTnVWsZcTM21CZI1iXZECyTMLxMi0siWVTaQR8k10Zk8P6F5Gt-s7CV47WwkN7U=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_33\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A geography pupil has investigated two areas of peatland. One has undergone peatland restoration, whilst the other has not. One of the things studied was the occurrences of indicator species in each peatland.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">There will be an association between species frequency and restoration status of peatlands.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In order to see if there is a<\/span><span class=\"C9DxTc \">n association,<\/span><span class=\"C9DxTc \">\u00a0and if it&#8217;s significant, they will undertake a\u00a0<\/span><span class=\"C9DxTc \">Chi Squared\u00a0<\/span><span class=\"C9DxTc \">calculation.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Null hypothesis:\u00a0<\/span><span class=\"C9DxTc \">There will be\u00a0<\/span><span class=\"C9DxTc \">no<\/span><span class=\"C9DxTc \">\u00a0association between species frequency and restoration status of peatlands.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_49\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_52\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:\u00a0<\/span><span class=\"C9DxTc \">Find out the total of each row and column in the table.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If this has been done correctly, the total of the columns and the total of the rows should be the same.\u00a0<\/span><span class=\"C9DxTc \">\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_56\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STG2hrwW8F3SIRYRkLtZu2_aMDDUK3FrYsrSeWv9qEnVjZv3pswMzWb87F3B261HyJvWe_261Es-uVmZgCIps1OxH-1cQavszeYM_4tb3Xsw1aTqbOikE6Hkm7EJ3Cx63TQ28-cKQF3CPxs9avhJ4P4LIFUD-Ob4QubBCU-SmkNaB3d_e23c2gAtnPLgdicoUTrD5w-eMu8G3Fr46y5fc_M8_rwe6BLetiN4mQ=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_60\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_63\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">2<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Calculate the expected values. The expected values assume that there is\u00a0<\/span><span class=\"C9DxTc \">no<\/span><span class=\"C9DxTc \">\u00a0difference between the two peatlands. We&#8217;re looking to see how different the observed (real) data is from this.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Expected =\u00a0<\/span><span class=\"C9DxTc \">column total x row total<\/span><span class=\"C9DxTc \"><br \/>\n<\/span> <span class=\"C9DxTc \">overall total<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If you&#8217;ve done this correctly, the row totals should still be the same!<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_67\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSS7qiUwK3qTK5QGry7wEZCnwylVAetNIB5dltNUDOzeJB6N_19rzrRC6kRtEwoDYF1mFSILiEeMaHdlZmUR7ZdKLpUXBzH1hYItiNw6DM6u1BiBGNFjmFpyrkVyOYyQLGzbl6sZRCQqAg_nQe8rTudfegrP7IFuSMtdt2XxgNka7MQ8XAb_00w04yFG_63cMua6Fj7qRdyF7dclA61E7hkhR8IE4McfAKefxE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_71\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_74\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">One more table to make, this time the components needed to total up the Chi Squared value.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_82\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRotGpqWpcZGzAmJXRtgjAAmVxnpQXSPSv5NRTdf3lHM-O0I1BcwoU6ydlKqA9c3AgAjJfmcHFyO2FtMomm3uHVyDTU-AdAHJaK5aX9Yyj_5JXAjN-kX1gFM2rhb9cav0LXI3ZRtoZ9CVXbqHPyES_-wlZ4e8K8w2jyipWEf89RBkz3Dl37Wk70wRSopsgsT5-O1a_HBLDGHcP6xh8TB-fnIjUGUztC56Uv=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-R6PoUb Ft7HRd-AhqUyc-R6PoUb JNdkSc SQVYQc L6cTce-purZT L6cTce-pSzOP\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\"><\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_86\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SR_V4gI4XN4yZunND_IJDPjmf3vQntczngPEYWvTcgIUU1NfBjArZ39_StkuKvwYZyW3XbfUHqhdiAJOY4plly21VnXR5CFR3ndfe54LQS5H_AY1DjJP4LGYe1RAbIyauKDvfBc5ZSsTyna30q_MA5sADaJajxPxS6N1L-bHv53q_0De_PSv4wy06Perg5XeOAlTsJDAFyBnkl54S9CBauZp1NOluc5Q-z3IYs=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_90\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_93\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Check the calculated value against the critical value, using the\u00a0<\/span><a class=\"XqQF9c\" href=\"https:\/\/www.theislandgeographer.co.uk\/_files\/ugd\/a616e4_36b2f82b1f9b43d9a9c3aae093f88cf1.pdf\" target=\"_blank\" rel=\"noopener\"><span class=\"C9DxTc aw5Odc \">significance table<\/span><\/a><span class=\"C9DxTc \">. The\u00a0<\/span><span class=\"C9DxTc \">degrees of freedom<\/span><span class=\"C9DxTc \">\u00a0for\u00a0<\/span><span class=\"C9DxTc \">Chi Squared<\/span><span class=\"C9DxTc \">\u00a0is:<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">\u00a0(No of\u00a0<\/span><span class=\"C9DxTc \">rows &#8211; 1) * (No of columns &#8211; 1)<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">S<\/span><span class=\"C9DxTc \">o in this case would be\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">.\u00a0<\/span><span class=\"C9DxTc \">Calculated values for Chi Squared should always be positive numbers.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_100\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRVUvBQLoYtIRHF4GXHsg8bW6wZLwpTDyxo4ZFK5Zn5iPJcBZnvSSS8icMGQcAhQ8BMsrT45bQzmI6RUstXSCfKgyiAGey_VyfnsQ16ZeFtt66O3spYqxHlkBHTALhlejoXhhdmLKNg8oGKx_ljLR1eLA67w19XjVxFrxsM3B08xaf7BpwsG8UB3f8Q8wfTsZIgxcTEpR4Brsn0UnBENrtWJ2_Mag9JOT24rLI=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_104\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">We can see from the table that the value has to be above\u00a0<\/span><span class=\"C9DxTc \">7.815<\/span><span class=\"C9DxTc \">\u00a0to be accepted at a 0.0<\/span><span class=\"C9DxTc \">5<\/span><span class=\"C9DxTc \">\u00a0level of significance. Our value of\u00a0<\/span><span class=\"C9DxTc \">8.789<\/span><span class=\"C9DxTc \">\u00a0is therefore above and we can say there is a<\/span><span class=\"C9DxTc \">n association.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_117\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_112\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 7:\u00a0<\/span><span class=\"C9DxTc \">Write out your answer in full, referring to the\u00a0<\/span><span class=\"C9DxTc \">calculated value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">critical value<\/span><span class=\"C9DxTc \">,\u00a0<\/span><span class=\"C9DxTc \">significance level<\/span><span class=\"C9DxTc \">\u00a0and\u00a0<\/span><span class=\"C9DxTc \">hypothesis<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_114\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The\u00a0<\/span><span class=\"C9DxTc \">Chi Squared<\/span><span class=\"C9DxTc \">\u00a0result of<\/span><span class=\"C9DxTc \">\u00a08.789\u00a0<\/span><span class=\"C9DxTc \">exceeds the 0.0<\/span><span class=\"C9DxTc \">5<\/span><span class=\"C9DxTc \">\u00a0or 9<\/span><span class=\"C9DxTc \">5<\/span><span class=\"C9DxTc \">% significance level at\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">\u00a0degrees of freedom of\u00a0<\/span><span class=\"C9DxTc \">7.815<\/span><span class=\"C9DxTc \">. The null hypothesis must be rejected and replaced by the alternative hypothesis \u2013 that there is a<\/span><span class=\"C9DxTc \">n association between species frequency and restoration status of peatlands.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_120\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_123\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.5ad2c3a07781cc6f_124\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_127\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.axwdbgbmah5d\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_140\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSa1sQkjJaXWYK73j1-j09smCvxHbQuLhIRqojvJ6ZBOIBQyRC9y-rIo9OzxftsZ5C_GX65Bq6xap_wqLBvMngmasAz2KmFOq0rwDN4P34RnkBfcvxGT5MOy4StLIeYnUIX_etq77Bzg9__7XxhHSEOpP22eEvU2be5k719CjBwVsetsVNgNrHHcIuYDPhKlB-oomCU1gF05gSd74NFZMxuRuhAZT4kSpaYGqo=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_131\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.5ad2c3a07781cc6f_149\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Climate Hebrides wanted to collect qualitative data, based on people&#8217;s own experiences, to contribute to work on climate change adaptations. They&#8217;ve conducted a survey of residents across the Outer Hebrides, asking information about their characteristics and opinions on the impact of climate change.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Their data indicated that people may have different opinions based on their age.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Undertake a Chi Squared analysis of the data<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Extension: How would you present this data graphically?<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.5ad2c3a07781cc6f_145\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRz3sOYfirvYE-C_1sQU5807_U_mRPEQQ3xH-oVF_o59ARE5xiBJZtcQSzrK5IYFi7Xlz4qt4ITJFU3Ec-Eg_m8G7zHV9zia9usIevZ7EQU3AIi3-kY-Imv1Qh51UZNUijBcIwd_Z9iAkUmQ2KsaaBeFQsfyGMG2ObCqVM_XD9HYGbOCx5-jvaBOV09p-qX2wBsE03tx8_etVnsu61mt3VfaeOCTEIISjxT=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.18b91b664b05539_0\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.917zifejga7s\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Nearest Neighbour<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_6\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Nearest Neighbour looks at whether data is clustered, random or dispersed orientated over a spatial area.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.18b91b664b05539_7\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_10\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The calculated nearest neighbour value will range from:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">0 &#8211; the data is very clustered\u00a0<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">1 &#8211; the data is randomly dispersed<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">2.5 &#8211; the data is regularly dispersed, spread evenly across the area<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.18b91b664b05539_28\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STEQSoN0M5cqTFC0uqaNwHJ6Qx0zMeWwhmtZK2rgPHBbwNVjM-IanEtK9uK3VJWYcoE5hPLwSoTKGS6zgTiSM8TKAhM42HYKZcVndlXmDS4QAAW73FXZ53Phmwa9kky52MBcImzB0PLAM9mcOrd3JZcY56Nyj6C65wQNvqaF_BXE6N2fJTfs1NIPIJRhNmCmfrD7wr5J2K4ACvyxV1A3xbOWlEhvbCzYEap3nE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_13\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The formula used is:<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.18b91b664b05539_19\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQ1ddS5RT0TarvhcMGswbJ_Vh0ssErcgaWVOIdaqHzE_3-ChWmDKkJE71EpYrWKCw9_UTmHXIcN7xwooGOAOCRtuOoRf1rMXv5bXUnVAxgWRRHzSL3Crfj6oijXXD24fq4lJvsTU-Pq0m9sUztB8ElZ7BnO5MfAdI5sPGRsnp-V5w5LOjpG4nWxuqvZ40hEwSaOQ3G5iKsXU7OAHN5o3gjfgIGTrxEQmCwA2Jo=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_24\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Where:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Rn = Nearest Neighbour Index<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">D = the average distance between each point and its nearest neighbour<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">n = the number of points in the study<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">a = the size of area in the study<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_218\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_221\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.18b91b664b05539_33\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_36\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.4r5392hlxes9\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Worked Example<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.18b91b664b05539_44\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSrLHSxTJzKQTyN9P5ALuEhPh_eSmBEkzXms7vl64j_GHUb0JrCi2WzSebcfyj46Qh3OPCfE6ryF9e6VJgtOLBoSeo5NS7miHoT9RxTCEGZFk18oVFsTy17U8GUma3ISKW9EodVGQUdB5H8HY3ZmwODblHHaGXyfvKqq_jVdsJAx2AdaBilWKk=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.18b91b664b05539_43\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Birch seeds are dispersed by the wind, often being carried for long distances. In a commercial coniferous forest plantation, birch trees can end up growing naturally, in amongst commercially grown trees.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Forestry and Land Scotland has visited an area of commercial forest where this has occurred. They have mapped out the location of the birch trees and wish to know how they are dispersed through the forest &#8211; in clusters, randomly or regularly dispersed.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_84\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRPsuAlmwaIxyvUXT1JYYi1nziu3i2dJ8jMbokhAgMOvecNuSlMQO8GwFJnDqui9lfOO_uvULAODDxdOgZYKcgzU9AR2Lja2SX-JDQE9kqvrM7-oAg_xYMctaDm3l-oiWX_vDMYwbMQkRZRM4ElL7GG6uoACQmwr_YFtH4MWRYNCpZvtnAtk4rYpS4Mo7DEa__O4n2bivM1PMzp9Vr3bMRg711aMzpaLEWx_gg=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_112\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_115\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:\u00a0<\/span><span class=\"C9DxTc \">Write out a hypothesis for the calculation.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">\u201cThe birch trees will be regularly dispersed across the commercial coniferous plantation.&#8221;<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb JNdkSc SQVYQc L6cTce-purZT L6cTce-pSzOP\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_4\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_7\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">2<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Find out the distance from each tree to it&#8217;s nearest neighbour. You may have to use a map to do this.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It doesn&#8217;t matter what unit you use, as long as it&#8217;s consistent with the unit used for area.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Do you predict, looking at this map, that this is going to give a clustered, random or dispersed pattern? We&#8217;re now going to use statistics to give more than just your opinion\/prediction!\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_80\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRrgUv3azPjeIkgBWKp7Rz1LE-iY62f5U-WaFP4HnqEaihOuOfDlnjz2lIyWcCZih9NjVDiS288OAnjDcBCIwW9b29n1CPplMKO4kBfYfoVpY5x9W6EpL_QI9M_B98wjf02Qm_NqKU_kus5YT0Vdp1sm2dCMRXJoiaTvhKV8u5qzKucNSTyxcJor7W4M4rJouKYcm8iOxS7C8eKUCl8lD1EQSh5oHUIm21bQ80=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_15\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_18\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Add a column to your table with the distances. Use this to calculate the average distance to nearest neighbour.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_88\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQgY12lR3lLF4XHShWSspb6w9G4pmo_mAYn0obE81h8TQPICB9Dt7hrZpfeAFKZbgNEf-YnmtY1ap4DSJTJbS8NUxcK_bY3oHqHt1S1qTvjtuycXXJq1YytmWVtqf8kL8FmsVpa7g6FX7akLEW_2QcsJ53j2TBbWFkNocTu9pr4m_wOMJqtmBqQ-E_pwri-A4AeuwpzwIxaunu60Qr3my3X7z6ectDNt1Am=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_65\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_68\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Calculate the Rn (Nearest Neighbour Index) using the formula.\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.121df5846becd258_70\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Where:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Rn = Nearest Neighbour Index<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">D =\u00a0<\/span><span class=\"C9DxTc \">18 m<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">n = 10<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">a =\u00a0<\/span><span class=\"C9DxTc \">10,000<\/span><span class=\"C9DxTc \">\u00a0m<\/span><span class=\"C9DxTc \">\u00b2<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf JNdkSc SQVYQc L6cTce-purZT L6cTce-pSzOP\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\"><\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_73\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQ1ddS5RT0TarvhcMGswbJ_Vh0ssErcgaWVOIdaqHzE_3-ChWmDKkJE71EpYrWKCw9_UTmHXIcN7xwooGOAOCRtuOoRf1rMXv5bXUnVAxgWRRHzSL3Crfj6oijXXD24fq4lJvsTU-Pq0m9sUztB8ElZ7BnO5MfAdI5sPGRsnp-V5w5LOjpG4nWxuqvZ40hEwSaOQ3G5iKsXU7OAHN5o3gjfgIGTrxEQmCwA2Jo=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.121df5846becd258_96\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec wHaque g5GTcb QaN0Zc QjXeod\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0ST9ESbUKgHQWO6zT5pw9kL5wUTom34IKBVeHOTmx9HK_K1GNw-r5KH8jfbZcFRBtJvGniXqHYwE6LS3MjASLY6wXlBZNyxD0Fk33oCAEr1T9iPxku159VO-j1rr663lHNXxE87s5jM5_v_RrJ0edybFom_U9YsDOWWX8qV8oLmY6N1Zkt8Pmj61gNSfauYpg2Ikvn6RtFa0MxC8P5ql3PAPLpyKHHypw2u0eF8=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_101\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_104\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">5:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Write your answer out in full, commenting on whether the result shows a clustered, random or dispersed distribution.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.121df5846becd258_106\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The Nearest Neighbour Index (Rn) of 1.138 shows that the data is close to randomly dispersed.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">How does that match with your prediction? In a Geographical Study, you could then:<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Compare it to other parts of the forest, or other plantations.<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">Go on to explain or suggest reasons why it might be randomly dispersed.<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_119\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-wNfPc Ktthjf-AhqUyc-wNfPc jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRb9zbgpx1lbUvMVL4nGroaONXLXH3JnZwS2mschu2Gn-q644vjBl4f6mxd7tTbp9nh6Hoypk0-XqyBUrHagNHhBgZ4etLYinnmjiMiCLcWahsLvXJRgxHpqWO9zgcRwqxt_xFckNXuV40dXp12l6Z5WpJepI5FLyd-lzgBN5YQOhBDXNb-CZ-2JoJlXMmKmnmKo8rdxhKu-ILUHxHhBrGyqYdoN8wv9Qob5EM=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_140\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_143\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.121df5846becd258_123\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_126\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.9ddx5ofg5x4d\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.121df5846becd258_135\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSV_v-l-9Bt0LKv7WGWJ9fIPMVVlTIopAoX1ktqSTfBBAP43fiIuG2h5Y_X4bOi_Y89IwTszNNAaFoAPOz-cgG01c1jTtd6yhiXHrLFUENZ4h7mRqEcYwus3eH8uEXr3IZGHbTB-VqtsKUBxsH9e0_0vSdZ_0-5NKJVkGvlcAsp0eeLD-wV182ieTve_O2by7LiCf7XxEhnrsAKFRJe8UI2AdydVFF8QwwK2yE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_131\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The Metropolitan Police, who cover London, use a system of stop and search to reduce crime across the capital.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The policy is controversial, with critics highlighting that some groups (e.g. those who are from an ethnic minority) are targeted by officers.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">They publish data each month about stop and searches which have been conducted.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Data from December 2025 shows\u00a0 25 occurrences where a person under 10 was stopped and searched. They wish to understand if this is happening in clusters or is regularly dispersed across their 1,578 k<\/span><span class=\"C9DxTc \">m<\/span><span class=\"C9DxTc \">\u00b2 beat.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.121df5846becd258_149\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">The data has been plotted on a Geographical Information Systems map, as linked below.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">You may wish to copy the map, or open it in Google Earth, to allow access to the measuring tool.<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \"><br \/>\n<\/span><span class=\"C9DxTc \">Calculate the Nearest Neighbour Index for the data.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.121df5846becd258_155\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd OWlOyc baZpAe\">\n<div>\n<div class=\"WIdY2d M1aSXe\">\n<div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_0\" class=\"yaqOZd qeLZfd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_3\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.w3edbe1xquch\" class=\"Ap4VC yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"VbJjl C9DxTc \">Linear Regression<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_6\" class=\"hJDwNd-AhqUyc-OwsYgb Ft7HRd-AhqUyc-OwsYgb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">You&#8217;re used to drawing best fit lines on scatter graphs, but how do you know where to actually draw it?\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_7\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_10\" class=\"hJDwNd-AhqUyc-wNfPc Ft7HRd-AhqUyc-wNfPc pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Linear regression allows us to calculate the best fit line mathematically. We can then use it to predict what further values might be, based on the line.\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">It uses principles that you will have learned about in maths.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_20\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">You&#8217;ll know from maths that the equation for a straight line is\u00a0<\/span><span class=\"C9DxTc \">y = mx + c<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Therefore, we need to calculate what the\u00a0<\/span><span class=\"C9DxTc \">m (gradient)\u00a0<\/span><span class=\"C9DxTc \">and\u00a0<\/span><span class=\"C9DxTc \">c (intercept)<\/span><span class=\"C9DxTc \">\u00a0is to get the formula for the line of best fit.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_21\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSgndE1zuIZLZHz0pgwFBEkeNpEsHSJD3KquQhkluAEs2CuzBT9xEKtyKldTvZP5xn7ancdi8PGziTNordHxp33N1TP1rtDB4Yav36EwsgcHUUEIXADty4uvlFPMR8v__bKf6bEaViVkYaYisdyjSPYHGla8V-UFe0mYe3TlWcU3LOV5JZjW2ur30nMXXAaP4YId0uJonPqx9awEGIi6M9ctXALGpy9iD6ifuE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_25\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_28\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_29\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_32\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.qc2kdrwtnocn\" class=\"GV3q8e yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Worked Example<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.6f07834aec73230a_49\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0STwg4Gqx5cwdIKkuowBVTGvaCOw8HbG5DbULxcFCd4H8bd8CWFTMjaTHb0AZ92gClTHlTgVvGeZKQKA7BKbKQfCMyzo0RifQ7SD_fyqPoxdi1r4970C1MKZN80EXxDcdE52-4hWBySEVLeVm72gffoyTDBQZuL56jQX2lNvi_SivenaB-0yDhRwls8W6CnLzXriK1HS30T0tf9wa-covhCyn8_v6gHENGFR=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.6f07834aec73230a_37\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the process of a Pearson&#8217;s Product Moment Correlation Coefficient calculation, you have already generated lots of the components needed to work out the formula of the best fit line.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">We will, therefore, use the existing data we have from the worked example and activity you completed during the Pearson&#8217;s Product work, further up this page.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">In the worked example, we were looking at how nitrogen dioxide levels change as you move out from the CBD of a city.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_44\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0ST2wEIvTDZIUeKJ5haIPfsxS8xgEWvEcrKblHToXnKdrEnN9aPN-UTKurJX_-QK9lLvOhDHGfzwRvugKbT_3SMd0XtxvA9SDqSBg2dR-8sW1y4ZnCsRawIiy90crKnqpMdph0vol9Q47sOeDUPcJQnijWMrYt_B1aRsBhvgzNLh1PzOuptAI9LplliTVn_iJ5-We7tGXAX8vGOPaGZoav8sMUiZ3-lRT9gxJyY=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_54\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-EehZO Ft7HRd-AhqUyc-EehZO purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_55\" class=\"hJDwNd-AhqUyc-EehZO Ft7HRd-AhqUyc-EehZO jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:\u00a0<\/span><span class=\"C9DxTc \">The formula for a straight line is\u00a0<\/span><span class=\"C9DxTc \">y = mx + c<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">First we need to calculate m. We can do this using the formula shown. If you&#8217;ve already done a Person&#8217;s Product, you will already have calculated both the numerator and denominator.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_51\" class=\"hJDwNd-AhqUyc-ibL1re Ft7HRd-AhqUyc-ibL1re purZT-AhqUyc-ibL1re ZcASvf-AhqUyc-ibL1re pSzOP-AhqUyc-ibL1re Ktthjf-AhqUyc-ibL1re jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSP-6TQs6vsMAyJLCyytLEOw0BrpUO69BynOJNB6G7f6LsKyAQC93KCg1DlaoUWsZrU_bwAxniQaoq6ZaLVuOxULNmGAApPelROLi49q9W41qQ6W_5LyHxCUntPM_RQ_TFlwGfmO9XdW9ibtv1s6b2SlAgbmoDaRjoXhsvPvHmjuvslvgJQJEspVHUpI5fROdKHA4VSPlGzKvkf2NcGNzqATCedbVBcH9dBNqw=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_63\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_67\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">2<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Substitute these values into the formula and solve for<\/span><span class=\"C9DxTc \">\u00a0m<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">m =\u00a0<\/span><span class=\"C9DxTc \">-1008<\/span><span class=\"C9DxTc \"><br \/>\n<\/span> <span class=\"C9DxTc \">182<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">m = -5.54<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">If your data shows a negative correlation, this should be reflected in the value for m.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_60\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SS3smZDeQIZtiX1zo_dQK4GI-u4ScHd2_3XzOHRTVE7EfBPQcDzW_64HlsY2oKeyL6bYZ5B-Tw4GZAFoY1vJl7PcU33g6q1WoTzE76WLVrbB57BhsgHNYtXxIHdjdgrizfkvShQ9VaGAQkGjodem7625lvD0hqb15ypk79nseYuWtiopD2FITpF0m5iTwZ2SolofEO7EY-fOeeUHo02G769h1miFTcMyciwQlQ=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_68\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_71\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">3<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Substitute these values into the formula and solve for\u00a0<\/span><span class=\"C9DxTc \">c<\/span><span class=\"C9DxTc \">.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"jgG6ef C9DxTc \">c =\u00a0<\/span><span class=\"jgG6ef C9DxTc \">y\u0305 &#8211;\u00a0\u00a0<\/span><span class=\"jgG6ef C9DxTc \">m<\/span><span class=\"jgG6ef C9DxTc \">x\u0305<\/span><span class=\"C9DxTc \">\u00a0<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">c = 43.69 &#8211; (-5.54*6)<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">c = 76.92<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_75\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SSoRv0fZ5JqoG8mBJeIe-hjCBPVi1HgkaYmI0jxWidKLoybq23sTD6EmL5064DG7SRrnrAT0vjYPHBYV_mhdf0bifA5JetlZeHUgWIGjYA1YUDoCcIjttM9DEKzNrVsd5cxe7PjcCpFgQBQjb1sP0LTa2kkS9JKvtt3Tx4nf2UeWVFLFGPKgE9lCY9qCz3N9M11Sb527um12n0oBrQPUmRoF0U81EVhddQU8PE=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_79\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_82\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">4<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Write out the equation for your line of best fit.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"jgG6ef C9DxTc \">y = -5.54x + 76.92<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_96\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQNUpqaf2POQOOGk6jqmIxRD0bSCF2fyAiajBoEf8pyDln_EX5LkmBntd3wQeA9sSCsyIge9f2qHcW66TEX8HQQlUtqIsyhoeuWwbOYRMRB9PfPSSn7mt8dPFtNAPF5E1FAAM8JXo-hfvl-v31uW36MIwN2tsn-LdU1AceosGglcjOZmMjVJBR_kgsiN1SO23yMh4eTU1qrGID5FtVZnnt1FGh_NH4msFLHOL4=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_86\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_89\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step\u00a0<\/span><span class=\"C9DxTc \">5<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">If you&#8217;re plotting the best fit line by hand, you&#8217;ll need to figure out a couple of points on the line to join up. You can do this by substituting values for x into your equation.<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">e.g.\u00a0<\/span><\/p>\n<ul class=\"n8H08c UVNKR \">\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">y = (-5.54 x\u00a0<\/span><span class=\"C9DxTc \">2<\/span><span class=\"C9DxTc \">) + 76.92<\/span><\/p>\n<\/li>\n<li class=\"zfr3Q TYR86d eD0Rn \" dir=\"ltr\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\" role=\"presentation\"><span class=\"C9DxTc \">y = (-5.54 x\u00a0<\/span><span class=\"C9DxTc \">6<\/span><span class=\"C9DxTc \">) + 76.92<\/span><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_97\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQQF6zvLSMqMZkiM5cs4M_F8RBr-tVAWowOGcs-SgRxRnh-9lc63GIxtgSGVw8W-1GrtPrM_z06WcGDZSdL-o34F_TaDc-Fi8ZwDe-vxhvvHvdQusHx3-rfF7QMtOwbkIOeYwGnw26ZDuYvU55pb31vtkzE5CeuuNRoTuklfcJGiRvSCe6B9yKWBe6O8G1qcMYyu9c2t0ZcQKlsuFP5pgSCnAqBj56fHinR5TA=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_101\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_104\" class=\"hJDwNd-AhqUyc-OiUrBf Ft7HRd-AhqUyc-OiUrBf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">A digital hack:\u00a0<\/span><span class=\"C9DxTc \">Using Google Sheets, you can have the best fit-line plotted and the equation for it displayed. You do this by using the\u00a0<\/span><span class=\"C9DxTc \">customise<\/span><span class=\"C9DxTc \">\u00a0chart, adding a trend line and asking it to label the equation of the line.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_108\" class=\"hJDwNd-AhqUyc-II5mzb Ft7HRd-AhqUyc-II5mzb pSzOP-AhqUyc-II5mzb Ktthjf-AhqUyc-II5mzb jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRAY2kvz4rdND0OA-qAfUnWbEtKUTu_jqyuUU8FlPasdEWg5zMhVI_WETieiiIB-YaIGWiRfTHU4teX2Ohz68Yo1k__XuSdj9XUSVZvr_iSfVEiv_yrgemaKQgPbqfjK65bLlgmuRRRllOcvDTC3k8DGffXYSTIXzg5GAjtxH4OyfVtpRPZMJ6KkS-ytgGEjsbFohOZL-QUl7-ql-RhbTQiGg17WtlmCyI81W0=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_112\" class=\"yaqOZd WxWicb\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_115\" class=\"hJDwNd-AhqUyc-uQSCkd Ft7HRd-AhqUyc-uQSCkd jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"iwQgFb\" role=\"presentation\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"h.6f07834aec73230a_116\" class=\"yaqOZd\">\n<div class=\"IFuOkc\"><\/div>\n<div class=\"mYVXT\">\n<div class=\"LS81yb VICjCf j5pSsc db35Fc\">\n<div class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc yYI8W HQwdzb\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_119\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<div id=\"h.av9pf1iqgge3\" class=\"CobnVe yMxPgf  aP9Z7e\"><\/div>\n<div class=\"CjVfdc\">\n<div class=\"PPhIP rviiZ\"><\/div>\n<p><span class=\"C9DxTc \">Activity<\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.6f07834aec73230a_121\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SRvYDTPUF0jPjbkQtn6OGOwCIRUL3VPwhduVL7o1xcKCd8U6oV-IyOnBQhB-yrM8iSSIRopS41BL4WJ4JzIzOoH0KEOcUf7fnbzn26r3dAa21ZzSdzyFJP2c6R5fdOU049SqQHqlnCfsSvLXBsRbSOY83mNGEc9LPobUG32fsqGVACC7zsrmf7lx7KdXmmVXf_3P6d7kSI788MTuh3yJDCxatsn6LCgAPXL=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"oKdM2c ZZyype\">\n<div id=\"h.6f07834aec73230a_123\" class=\"hJDwNd-AhqUyc-qWD73c Ft7HRd-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Revisit the activity you did for Pearson&#8217;s Product. Calculate the\u00a0<\/span><span class=\"C9DxTc \">linear regression<\/span><span class=\"C9DxTc \">\u00a0&#8211; show that you understand the steps rather than just skipping to plotting the line on Google sheets!\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_126\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-c5RTEf ZcASvf-AhqUyc-c5RTEf pSzOP-AhqUyc-c5RTEf Ktthjf-AhqUyc-c5RTEf jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd baZpAe\">\n<div class=\"t3iYD\"><img decoding=\"async\" class=\"CENy8b\" role=\"img\" src=\"https:\/\/lh3.googleusercontent.com\/sitesv\/APaQ0SQXfAXhEZ9-iNSpdilwptmU0Syjl65bgyNQS8rxHV3bTEEsauCiESadMy9HbiYk09gvHzZyJk7GuilCunk1yswBgYKpH7auoqR383yBZV8QbLockcBpbkCJq0WAOETXjdujYiU6Up05S6LyLK1tIqRW_tSbpSzW7yEugJtD5ryryrgZAAks_anXVqdh-3Mf5Chnmnksy7joRAIOR-b8FD_XZwMOlpYSoXqm=w1280\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c JNdkSc SQVYQc\">\n<div class=\"JNdkSc-SmKAyb LkDMRd\">\n<div class=\"\">\n<div class=\"oKdM2c ZZyype Kzv0Me\">\n<div id=\"h.6f07834aec73230a_129\" class=\"hJDwNd-AhqUyc-c5RTEf Ft7HRd-AhqUyc-c5RTEf purZT-AhqUyc-II5mzb ZcASvf-AhqUyc-II5mzb pSzOP-AhqUyc-qWD73c Ktthjf-AhqUyc-qWD73c jXK9ad D2fZ2 zu5uec OjCsFc dmUFtb wHaque g5GTcb\">\n<div class=\"jXK9ad-SmKAyb\">\n<div class=\"tyJCtd mGzaTb Depvyb baZpAe\">\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 1:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Formula<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 2:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Solve for m<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 3<\/span><span class=\"C9DxTc \">:\u00a0<\/span><span class=\"C9DxTc \">Solve for c<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 4:\u00a0<\/span><span class=\"C9DxTc \">Write out the equation<\/span><\/p>\n<p class=\"zfr3Q CDt4Ke \" dir=\"ltr\"><span class=\"C9DxTc \">Step 5:<\/span><span class=\"C9DxTc \">\u00a0<\/span><span class=\"C9DxTc \">Plot the line<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>Inferential\u00a0Statistics Inferential statistics help to identify relationships, test hypothesis draw conclusions about sets of data. Most of these statistical methods will be new to you, but none of the maths behind them is tricky! If you follow the instructions step-by-step, they&#8217;re a really worthwhile technique to encorporate in your Geographical study. You will also find [&hellip;]<\/p>\n","protected":false},"author":40142,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-787","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/pages\/787","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/users\/40142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/comments?post=787"}],"version-history":[{"count":1,"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/pages\/787\/revisions"}],"predecessor-version":[{"id":789,"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/pages\/787\/revisions\/789"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/er\/SNHGeographyWebsite\/wp-json\/wp\/v2\/media?parent=787"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}