{"id":223,"date":"2014-11-18T23:36:19","date_gmt":"2014-11-18T23:36:19","guid":{"rendered":"http:\/\/www.jasonbailey.net\/stuff\/?p=223"},"modified":"2014-11-18T23:36:59","modified_gmt":"2014-11-18T23:36:59","slug":"two-sample-t-test","status":"publish","type":"post","link":"http:\/\/www.jasonbailey.net\/stuff\/two-sample-t-test\/","title":{"rendered":"Two sample t-test"},"content":{"rendered":"<p>Good quote from Statistics Glossary:<\/p>\n<p>&#8220;&#8230;<\/p>\n<p>A two sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution:<img decoding=\"async\" src=\"http:\/\/www.stats.gla.ac.uk\/steps\/glossary\/images\/2st.gif\" alt=\"N(mu_i,sigma_i^2), where i=1,2\" align=\"middle\" border=\"0\" hspace=\"10\" \/><\/p>\n<p>When carrying out a two sample t-test, it is usual to assume that the variances for the two populations are equal, i.e.<img decoding=\"async\" src=\"http:\/\/www.stats.gla.ac.uk\/steps\/glossary\/images\/2st2.gif\" alt=\"sigma_1^2 = sigma_2^2 = sigma^2\" align=\"middle\" border=\"0\" hspace=\"10\" \/><\/p>\n<p>The null hypothesis for the two sample t-test is:H0: \u00b51 = \u00b52<\/p>\n<p>That is, the two samples have both been drawn from the same population. This null hypothesis is tested against one of the following alternative hypotheses, depending on the question posed.H1: \u00b51 is not equal to \u00b52<br \/>\nH1: \u00b51 &gt; \u00b52<br \/>\nH1: \u00b51 &lt; \u00b52<\/p>\n<p>&#8230;&#8221;<\/p>\n<p><a title=\"Statistics glossary\" href=\"http:\/\/www.stats.gla.ac.uk\/steps\/glossary\/hypothesis_testing.html#2sampt\">http:\/\/www.stats.gla.ac.uk\/steps\/glossary\/hypothesis_testing.html#2sampt<\/a><\/p>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Good quote from Statistics Glossary: &#8220;&#8230; A two sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution: When carrying out a two sample t-test, it is usual to assume that the variances for the [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19,7],"tags":[],"class_list":["post-223","post","type-post","status-publish","format-standard","hentry","category-data-analytics","category-statistics"],"_links":{"self":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/223","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/comments?post=223"}],"version-history":[{"count":1,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/223\/revisions"}],"predecessor-version":[{"id":224,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/223\/revisions\/224"}],"wp:attachment":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/media?parent=223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/categories?post=223"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/tags?post=223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}