{"id":1416,"date":"2023-06-22T02:22:57","date_gmt":"2023-06-22T02:22:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-learn-it-5\/"},"modified":"2025-05-16T23:42:33","modified_gmt":"2025-05-16T23:42:33","slug":"chi-square-test-of-homogeneity-learn-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-learn-it-5\/","title":{"raw":"Chi-Square Test of Homogeneity \u2013 Learn It 5","rendered":"Chi-Square Test of Homogeneity \u2013 Learn It 5"},"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;Complete a chi-square test of homogeneity&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}\">Complete a chi-square test of homogeneity<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a chi-square test of homogeneity in context of the problem&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}\">Write the conclusion of a chi-square test of homogeneity in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>[latex]\\chi^2[\/latex], P-Value, &amp; Conclusions<\/h2>\r\n<p>As with the chi-square goodness of fit test, we compute the value of<\/p>\r\n<p style=\"text-align: center;\">[latex]\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\r\n<p>for each cell in the table, and then we obtain the value of the test statistic:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\chi^2=\\sum\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\r\n<p>Let's use technology to compute the chi-square value and the associated P-value.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><\/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<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2442[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a chi-square test of homogeneity&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}\">Complete a chi-square test of homogeneity<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a chi-square test of homogeneity in context of the problem&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}\">Write the conclusion of a chi-square test of homogeneity in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>[latex]\\chi^2[\/latex], P-Value, &amp; Conclusions<\/h2>\n<p>As with the chi-square goodness of fit test, we compute the value of<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\n<p>for each cell in the table, and then we obtain the value of the test statistic:<\/p>\n<p style=\"text-align: center;\">[latex]\\chi^2=\\sum\\dfrac{(\\text{Observed}-\\text{Expected})^2}{\\text{Expected}}[\/latex]<\/p>\n<p>Let&#8217;s use technology to compute the chi-square value and the associated P-value.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/chisquaredtest\/\" width=\"100%\" height=\"1100\" frameborder=\"no\"><\/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<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2442\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2442&theme=lumen&iframe_resize_id=ohm2442&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":23,"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\/1416"}],"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\/1416\/revisions"}],"predecessor-version":[{"id":6875,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1416\/revisions\/6875"}],"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\/1416\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1416"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1416"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1416"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}