{"id":1349,"date":"2013-10-31T10:54:48","date_gmt":"2013-10-31T10:54:48","guid":{"rendered":"http:\/\/www.blopig.com\/blog\/?p=1349"},"modified":"2015-01-20T11:00:10","modified_gmt":"2015-01-20T11:00:10","slug":"wilcoxon-mann-whitney-test-and-a-small-sample-size","status":"publish","type":"post","link":"https:\/\/www.blopig.com\/blog\/2013\/10\/wilcoxon-mann-whitney-test-and-a-small-sample-size\/","title":{"rendered":"Wilcoxon-Mann-Whitney test and a small sample size"},"content":{"rendered":"<p>The Wilcoxon Mann Whitney test (two samples), is a non-parametric test used to compare if the distributions of two populations are shifted , i.e. say <img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/s0.wp.com\/latex.php?latex=f_1%28x%29+%3Df_2%28x%2Bk%29&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"f_1(x) =f_2(x+k)\" class=\"latex\" \/> where k is the shift between the two distributions, thus if k=0 then the two populations are actually the same one. This test is based in the rank of the observations of the two samples, which means that it won&#8217;t take into account how big the differences between the values of the two samples are, e.g. if performing a WMW test comparing S1=(1,2) and S2=(100,300) it wouldn&#8217;t differ of comparing S1=(1,2) and S2=(4,5). Therefore when having a small sample size this is a great loss of information.<\/p>\n<p>Now, what happens when you perform a WMW test on samples of size 2 and 2 and they are as different as they can be (to what the test concerns), lest say\u00a0S1=(1,2) and S2=(4,5). Then the p-value of this test would be\u00a00.333, which means that\u00a0<strong>the smallest p-value<\/strong>\u00a0you can obtain from a WMW test when comparing two samples of size 2 and 2 is 0.3333. Hence you would only be able to detect differences between the two samples when using a level of significance greater than 0.333 .<\/p>\n<p>Finally you must understand that having a sample of two is usually not enough for a statistical test. The following table shows the smallest \u00a0p-value for different small sample sizes when the alternative hypothesis is two sided. (Values in the table are rounded).<\/p>\n<p><a href=\"https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?ssl=1\"><img data-recalc-dims=\"1\" decoding=\"async\" loading=\"lazy\" class=\"alignnone size-large wp-image-2288\" src=\"https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?resize=625%2C276&#038;ssl=1\" alt=\"Screen Shot 2015-01-20 at 10.50.56\" width=\"625\" height=\"276\" srcset=\"https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?resize=1024%2C453&amp;ssl=1 1024w, https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?resize=300%2C132&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?resize=624%2C276&amp;ssl=1 624w, https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?w=1340&amp;ssl=1 1340w, https:\/\/i0.wp.com\/www.blopig.com\/blog\/wp-content\/uploads\/2013\/10\/Screen-Shot-2015-01-20-at-10.50.56.png?w=1250&amp;ssl=1 1250w\" sizes=\"auto, (max-width: 625px) 100vw, 625px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Wilcoxon Mann Whitney test (two samples), is a non-parametric test used to compare if the distributions of two populations are shifted , i.e. say where k is the shift between the two distributions, thus if k=0 then the two populations are actually the same one. This test is based in the rank of the [&hellip;]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","wikipediapreview_detectlinks":true,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"ngg_post_thumbnail":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"ppma_author":[514],"class_list":["post-1349","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"authors":[{"term_id":514,"user_id":26,"is_guest":0,"slug":"luis","display_name":"Luis Ospina Forero","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/310cef32cd5dac5a383fe35d2e6fa0ed40cb03d0712d2b5a5ef81092db812b3e?s=96&d=mm&r=g","0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""}],"_links":{"self":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/1349","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/comments?post=1349"}],"version-history":[{"count":5,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/1349\/revisions"}],"predecessor-version":[{"id":2289,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/1349\/revisions\/2289"}],"wp:attachment":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/media?parent=1349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/categories?post=1349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/tags?post=1349"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/ppma_author?post=1349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}