{"id":211,"date":"2014-11-18T00:07:52","date_gmt":"2014-11-18T00:07:52","guid":{"rendered":"http:\/\/www.jasonbailey.net\/stuff\/?p=211"},"modified":"2014-11-18T00:10:21","modified_gmt":"2014-11-18T00:10:21","slug":"chi-square-test-statistic","status":"publish","type":"post","link":"http:\/\/www.jasonbailey.net\/stuff\/chi-square-test-statistic\/","title":{"rendered":"chi square test statistic"},"content":{"rendered":"<p>The Chi square compares the observed data with the Null Hypothesis.<\/p>\n<p>Chi square test looks at single set of data and Null Hypothesis.<\/p>\n<ul>\n<li>H<sub>o<\/sub> The <em>no difference<\/em> or <em>no association<\/em> hypothesis that shows no difference between observed and expected data.<\/li>\n<li>H<sub>1<\/sub> This postulates that there is a difference between observed and experimental data.<\/li>\n<\/ul>\n<p>Expected = row X col total \/ grand total<\/p>\n<p>\u03c7<sup>2<\/sup> = sum ((observed &#8211; expected) \/Expected)<sup>2<\/sup><\/p>\n<p>\u03c7<sup>2<\/sup>\u00a0 and DF\/degree of freedom gives the test statistic<\/p>\n<p>A big difference between observed and expected results in a large test statistic (\u03c7<sup>2<\/sup>) and so leads to a rejection of the Null Hypothesis (H<sub>o<\/sub>)<\/p>\n<p><strong>The greater the value of the test statistic, the greater the evidence against the Null hypothesis -leads to a smaller p -value<\/strong><\/p>\n<p>&#8220;&#8230;The <var>p<\/var>-value is the area under the chi-square probability density function (pdf) curve to the right of the specified <var>\u03c7<\/var><sup>2<\/sup> value&#8230;&#8221; <a title=\"link to -pvalue at du mgt com\" href=\"http:\/\/www.di-mgt.com.au\/chisquare-calculator.h\">http:\/\/www.di-mgt.com.au\/chisquare-calculator.h<\/a><\/p>\n<p>&nbsp;<\/p>\n<div style=\"width: 417px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"http:\/\/www.di-mgt.com.au\/images\/chisquare-pvalue.gif\" alt=\"p value area to right\" width=\"407\" height=\"202\" \/><p class=\"wp-caption-text\">Source: di mgt.com.au<\/p><\/div>\n<p>&nbsp;<\/p>\n<p>p value is the area to the right of the test statistic. The less the number (&lt; 0.05) the more likely to reject the Null Hypothesis<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><a title=\"link to ucla notes\" href=\"http:\/\/www.stat.ucla.edu\/~kcli\/stat13\/stat13-lecture14.pdf\">http:\/\/www.stat.ucla.edu\/~kcli\/stat13\/stat13-lecture14.pdf<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Nice video explaining it all.<\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/HwD7ekD5l0g\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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>The Chi square compares the observed data with the Null Hypothesis. Chi square test looks at single set of data and Null Hypothesis. Ho The no difference or no association hypothesis that shows no difference between observed and expected data. H1 This postulates that there is a difference between observed and experimental data. Expected = [&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":[19,7,1],"tags":[],"class_list":["post-211","post","type-post","status-publish","format-standard","hentry","category-data-analytics","category-statistics","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/211","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=211"}],"version-history":[{"count":6,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/211\/revisions"}],"predecessor-version":[{"id":217,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/posts\/211\/revisions\/217"}],"wp:attachment":[{"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/media?parent=211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/categories?post=211"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jasonbailey.net\/stuff\/wp-json\/wp\/v2\/tags?post=211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}