{"id":1427,"date":"2023-06-22T02:23:07","date_gmt":"2023-06-22T02:23:07","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/fishers-exact-test-learn-it-1\/"},"modified":"2025-05-16T23:48:55","modified_gmt":"2025-05-16T23:48:55","slug":"fishers-exact-test-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/fishers-exact-test-learn-it-1\/","title":{"raw":"Fisher's Exact Test \u2013 Learn It 1","rendered":"Fisher&#8217;s Exact Test \u2013 Learn It 1"},"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's 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's Exact Test<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Previously, we have\u00a0learned about hypothesis testing for categorical data. These tests range from the [latex]\\chi^2[\/latex]\u00a0goodness of fit test to the test of homogeneity to the test for independence. The one thing all of these tests have in common is that the variables of interest are categorical.<\/p>\r\n<p>However, sometimes, our data set does not fit the [latex]\\chi^2[\/latex] test for independence, particularly when our expected counts are less than 5.\u00a0 Instead, as long as we combine categories into a 2x2 contingency table, we can use a different test called <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}\"><strong>Fisher's Exact Test<\/strong>.<\/span><\/p>\r\n<p>Let's look at an example.<\/p>\r\n<p>An independent researcher wants to determine a relationship between the color of a motorcyclist\u2019s helmet and whether an injury was sustained in a crash. They randomly obtain a sample of data and organize that data into the following contingency table.<\/p>\r\n<div align=\"center\">\r\n<table class=\" aligncenter\" style=\"width: 685px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 102.535px;\">\u00a0<\/td>\r\n<td style=\"width: 87.1701px;\"><strong>Black helmet<\/strong><\/td>\r\n<td style=\"width: 88.1076px;\"><strong>White helmet<\/strong><\/td>\r\n<td style=\"width: 74.9479px;\"><strong>Red helmet<\/strong><\/td>\r\n<td style=\"width: 130.017px;\"><strong>Yellow\/orange helmet<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 102.535px;\"><strong>No injury<\/strong><\/td>\r\n<td style=\"width: 87.1701px;\">8<\/td>\r\n<td style=\"width: 88.1076px;\">4<\/td>\r\n<td style=\"width: 74.9479px;\">3<\/td>\r\n<td style=\"width: 130.017px;\">2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 102.535px;\"><strong>Injured or killed<\/strong><\/td>\r\n<td style=\"width: 87.1701px;\">20<\/td>\r\n<td style=\"width: 88.1076px;\">2<\/td>\r\n<td style=\"width: 74.9479px;\">1<\/td>\r\n<td style=\"width: 130.017px;\">1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p><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>]<\/p>\r\n<\/div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2911[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2912[\/ohm2_question]<\/section>\r\n<p>As stated above, sometimes, our data set does not satisfy the conditions for [latex]\\chi^2[\/latex] test for independence. But, by combining categories in a [latex]2 \\times 2[\/latex] contingency table, we can use a test called <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}\"><strong>Fisher's Exact Test\u00a0<\/strong>of Independence. Fisher\u2019s Exact Test is used for data in a [latex]2 \\times 2[\/latex] contingency table where one or more of the expected frequencies are less than five and certain conditions (detailed later) are met. We primarily use this test when the sample size is small. This test will provide us with an exact [latex]P[\/latex]-value and does not require any approximations.<\/span><\/p>","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&#8217;s 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&#8217;s Exact Test<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Previously, we have\u00a0learned about hypothesis testing for categorical data. These tests range from the [latex]\\chi^2[\/latex]\u00a0goodness of fit test to the test of homogeneity to the test for independence. The one thing all of these tests have in common is that the variables of interest are categorical.<\/p>\n<p>However, sometimes, our data set does not fit the [latex]\\chi^2[\/latex] test for independence, particularly when our expected counts are less than 5.\u00a0 Instead, as long as we combine categories into a 2&#215;2 contingency table, we can use a different test called <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}\"><strong>Fisher&#8217;s Exact Test<\/strong>.<\/span><\/p>\n<p>Let&#8217;s look at an example.<\/p>\n<p>An independent researcher wants to determine a relationship between the color of a motorcyclist\u2019s helmet and whether an injury was sustained in a crash. They randomly obtain a sample of data and organize that data into the following contingency table.<\/p>\n<div style=\"margin: auto;\">\n<table class=\"aligncenter\" style=\"width: 685px;\">\n<tbody>\n<tr>\n<td style=\"width: 102.535px;\">\u00a0<\/td>\n<td style=\"width: 87.1701px;\"><strong>Black helmet<\/strong><\/td>\n<td style=\"width: 88.1076px;\"><strong>White helmet<\/strong><\/td>\n<td style=\"width: 74.9479px;\"><strong>Red helmet<\/strong><\/td>\n<td style=\"width: 130.017px;\"><strong>Yellow\/orange helmet<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 102.535px;\"><strong>No injury<\/strong><\/td>\n<td style=\"width: 87.1701px;\">8<\/td>\n<td style=\"width: 88.1076px;\">4<\/td>\n<td style=\"width: 74.9479px;\">3<\/td>\n<td style=\"width: 130.017px;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 102.535px;\"><strong>Injured or killed<\/strong><\/td>\n<td style=\"width: 87.1701px;\">20<\/td>\n<td style=\"width: 88.1076px;\">2<\/td>\n<td style=\"width: 74.9479px;\">1<\/td>\n<td style=\"width: 130.017px;\">1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><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>]<\/p>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2911\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2911&theme=lumen&iframe_resize_id=ohm2911&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2912\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2912&theme=lumen&iframe_resize_id=ohm2912&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>As stated above, sometimes, our data set does not satisfy the conditions for [latex]\\chi^2[\/latex] test for independence. But, by combining categories in a [latex]2 \\times 2[\/latex] contingency table, we can use a test called <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}\"><strong>Fisher&#8217;s Exact Test\u00a0<\/strong>of Independence. Fisher\u2019s Exact Test is used for data in a [latex]2 \\times 2[\/latex] contingency table where one or more of the expected frequencies are less than five and certain conditions (detailed later) are met. We primarily use this test when the sample size is small. This test will provide us with an exact [latex]P[\/latex]-value and does not require any approximations.<\/span><\/p>\n","protected":false},"author":8,"menu_order":34,"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":"learn_it","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\/1427"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1427\/revisions"}],"predecessor-version":[{"id":6884,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1427\/revisions\/6884"}],"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\/1427\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1427"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1427"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1427"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1427"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}