{"id":1435,"date":"2023-06-22T02:23:13","date_gmt":"2023-06-22T02:23:13","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/fishers-exact-test-fresh-take\/"},"modified":"2025-05-16T23:51:43","modified_gmt":"2025-05-16T23:51:43","slug":"fishers-exact-test-fresh-take","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/fishers-exact-test-fresh-take\/","title":{"raw":"Fisher's Exact Test \u2013 Fresh Take","rendered":"Fisher&#8217;s Exact Test \u2013 Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for Fisher's Exact Test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Check the conditions for Fisher\u2019s Exact Test<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Explain the relationship of two qualitative binary variables using Fisher's Exact Test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Explain the relationship of two qualitative binary variables using Fisher\u2019s Exact Test<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>[latex]\\chi^2[\/latex] Test for Independence vs. Fisher's Exact Test<\/h2>\r\n<p>We use the [latex]\\chi^2 [\/latex] <strong>test for independence<\/strong> to decide whether two variables (factors) are independent or dependent. In this case, there will be two qualitative survey questions or experiments, and a contingency table will be constructed. The goal is to see if the two variables are unrelated (independent) or related (dependent).<\/p>\r\n<p>The null and alternative hypotheses are:<\/p>\r\n<ul>\r\n\t<li>[latex]H_0[\/latex]: The variables (factors) are independent.<\/li>\r\n\t<li>[latex]H_A[\/latex]: The variables (factors) are dependent.<\/li>\r\n<\/ul>\r\n<p>Next, the conditions for the test of independence must be checked. It is important to know when you can or can not perform the [latex]\\chi^2[\/latex] test of independence.<\/p>\r\n<ul>\r\n\t<li><strong>Condition # 1: <\/strong>Independence\/Randomness Condition: The [latex]\\chi^2[\/latex] test assumes that observations are independent. This means that the outcome for one observation is not associated with the outcome of any other observation.<\/li>\r\n\t<li><strong>Condition # 2:\u00a0<\/strong>Large Sample Sizes Condition: The sample sizes need to be large enough so that the <em><span style=\"text-decoration: underline;\">expected count<\/span><\/em> in each cell is at least five.<\/li>\r\n<\/ul>\r\n<p><strong>Question:\u00a0<\/strong> So, what happens if one or more of the expected counts is less than 5? This means that the large sample sizes condition is violated, and therefore [latex]\\chi^2[\/latex] test of independence cannot be used in this case.<\/p>\r\n<p>This is when\u00a0<strong>Fisher's Exact Test<\/strong> comes into play. You would then want to consolidate the contingency table to a [latex]2 \\times 2[\/latex] contingency table and check the condition again.<\/p>\r\n<section class=\"textbox recall\"><strong>Fisher\u2019s Exact Tes<\/strong>t (also known as Fisher\u2019s Exact Test of Independence) is a statistical significance test used in the analysis of a [latex]2 \\times 2[\/latex]\u00a0contingency table.<\/section>\r\n<p>So, the null and alternative hypotheses for Fisher's Exact Test are:<\/p>\r\n<ul>\r\n\t<li>[latex]H_0[\/latex]: The <strong>two <\/strong>variables (factors) are independent.<\/li>\r\n\t<li>[latex]H_A[\/latex]: The <strong>two <\/strong>variables (factors) are dependent.<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2909[\/ohm2_question]<\/section>\r\n<section><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\r\n<section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2923[\/ohm2_question]<\/section>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for Fisher's Exact Test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Check the conditions for Fisher\u2019s Exact Test<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Explain the relationship of two qualitative binary variables using Fisher's Exact Test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Explain the relationship of two qualitative binary variables using Fisher\u2019s Exact Test<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>[latex]\\chi^2[\/latex] Test for Independence vs. Fisher&#8217;s Exact Test<\/h2>\n<p>We use the [latex]\\chi^2[\/latex] <strong>test for independence<\/strong> to decide whether two variables (factors) are independent or dependent. In this case, there will be two qualitative survey questions or experiments, and a contingency table will be constructed. The goal is to see if the two variables are unrelated (independent) or related (dependent).<\/p>\n<p>The null and alternative hypotheses are:<\/p>\n<ul>\n<li>[latex]H_0[\/latex]: The variables (factors) are independent.<\/li>\n<li>[latex]H_A[\/latex]: The variables (factors) are dependent.<\/li>\n<\/ul>\n<p>Next, the conditions for the test of independence must be checked. It is important to know when you can or can not perform the [latex]\\chi^2[\/latex] test of independence.<\/p>\n<ul>\n<li><strong>Condition # 1: <\/strong>Independence\/Randomness Condition: The [latex]\\chi^2[\/latex] test assumes that observations are independent. This means that the outcome for one observation is not associated with the outcome of any other observation.<\/li>\n<li><strong>Condition # 2:\u00a0<\/strong>Large Sample Sizes Condition: The sample sizes need to be large enough so that the <em><span style=\"text-decoration: underline;\">expected count<\/span><\/em> in each cell is at least five.<\/li>\n<\/ul>\n<p><strong>Question:\u00a0<\/strong> So, what happens if one or more of the expected counts is less than 5? This means that the large sample sizes condition is violated, and therefore [latex]\\chi^2[\/latex] test of independence cannot be used in this case.<\/p>\n<p>This is when\u00a0<strong>Fisher&#8217;s Exact Test<\/strong> comes into play. You would then want to consolidate the contingency table to a [latex]2 \\times 2[\/latex] contingency table and check the condition again.<\/p>\n<section class=\"textbox recall\"><strong>Fisher\u2019s Exact Tes<\/strong>t (also known as Fisher\u2019s Exact Test of Independence) is a statistical significance test used in the analysis of a [latex]2 \\times 2[\/latex]\u00a0contingency table.<\/section>\n<p>So, the null and alternative hypotheses for Fisher&#8217;s Exact Test are:<\/p>\n<ul>\n<li>[latex]H_0[\/latex]: The <strong>two <\/strong>variables (factors) are independent.<\/li>\n<li>[latex]H_A[\/latex]: The <strong>two <\/strong>variables (factors) are dependent.<\/li>\n<\/ul>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2909\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2909&theme=lumen&iframe_resize_id=ohm2909&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/section>\n<section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2923\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2923&theme=lumen&iframe_resize_id=ohm2923&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":40,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1388,"module-header":"fresh_take","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1435"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":3,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1435\/revisions"}],"predecessor-version":[{"id":6887,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1435\/revisions\/6887"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1388"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1435\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1435"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1435"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1435"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}