{"id":1421,"date":"2023-06-22T02:23:02","date_gmt":"2023-06-22T02:23:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-independence-learn-it-2\/"},"modified":"2023-10-20T20:46:21","modified_gmt":"2023-10-20T20:46:21","slug":"chi-square-test-of-independence-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-independence-learn-it-2\/","title":{"raw":"Chi-Square Test of Independence \u2013 Learn It 2","rendered":"Chi-Square Test of Independence \u2013 Learn It 2"},"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 independence&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 independence<\/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 independence 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 independence in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>In the test of independence, we consider one population and two categorical variables.<\/p>\r\n<p>The mechanics of performing a chi-square test of independence are the same as those for the chi-square test of homogeneity.<\/p>\r\n<p>The first step of any hypothesis test is to write its hypotheses.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>the null and alternative hypotheses<\/h3>\r\n<p>The null and alternative hypotheses for chi-square test of independence are the following:<\/p>\r\n<ul>\r\n\t<li>[latex]H_0[\/latex]: The two variables of interest are independent.<\/li>\r\n\t<li>[latex]H_A[\/latex]: The two variables of interest are not independent.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>As usual, the null hypothesis is a statement of no change in that if the two variables are independent in the population, knowing the value of one variable does not change the likelihood that the second variable will have a particular value.<\/p>\r\n<p>Sometimes the null and alternative hypotheses are written with slightly different wording, but they are equivalent to the previous wording:<\/p>\r\n<ul>\r\n\t<li>[latex]H_0[\/latex]: The two variables of interest are not associated.<\/li>\r\n\t<li>[latex]H_A[\/latex]: The two variables of interest are associated.<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2870[\/ohm2_question]<\/section>\r\n<p>The second step in a hypothesis test is to check the conditions for the hypothesis test.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>conditions for [latex]\\chi^2[\/latex] test of independence<\/h3>\r\n<ol>\r\n\t<li>The data represent the counts for two categorical variables measured for individuals in one sample from one population.<\/li>\r\n\t<li>Independence\/Randomness Condition:\u00a0The sample from our population should be independent, random sample or independent sample that can be considered representative of the population.<\/li>\r\n\t<li>Large Sample Size Condition: The sample size must be large enough so that the expected count in each cell is at least five.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2883[\/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 independence&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 independence<\/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 independence 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 independence in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<p>In the test of independence, we consider one population and two categorical variables.<\/p>\n<p>The mechanics of performing a chi-square test of independence are the same as those for the chi-square test of homogeneity.<\/p>\n<p>The first step of any hypothesis test is to write its hypotheses.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>the null and alternative hypotheses<\/h3>\n<p>The null and alternative hypotheses for chi-square test of independence are the following:<\/p>\n<ul>\n<li>[latex]H_0[\/latex]: The two variables of interest are independent.<\/li>\n<li>[latex]H_A[\/latex]: The two variables of interest are not independent.<\/li>\n<\/ul>\n<\/section>\n<p>As usual, the null hypothesis is a statement of no change in that if the two variables are independent in the population, knowing the value of one variable does not change the likelihood that the second variable will have a particular value.<\/p>\n<p>Sometimes the null and alternative hypotheses are written with slightly different wording, but they are equivalent to the previous wording:<\/p>\n<ul>\n<li>[latex]H_0[\/latex]: The two variables of interest are not associated.<\/li>\n<li>[latex]H_A[\/latex]: The two variables of interest are associated.<\/li>\n<\/ul>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2870\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2870&theme=lumen&iframe_resize_id=ohm2870&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The second step in a hypothesis test is to check the conditions for the hypothesis test.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>conditions for [latex]\\chi^2[\/latex] test of independence<\/h3>\n<ol>\n<li>The data represent the counts for two categorical variables measured for individuals in one sample from one population.<\/li>\n<li>Independence\/Randomness Condition:\u00a0The sample from our population should be independent, random sample or independent sample that can be considered representative of the population.<\/li>\n<li>Large Sample Size Condition: The sample size must be large enough so that the expected count in each cell is at least five.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2883\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2883&theme=lumen&iframe_resize_id=ohm2883&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":28,"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\/1421"}],"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\/1421\/revisions"}],"predecessor-version":[{"id":3955,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1421\/revisions\/3955"}],"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\/1421\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1421"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1421"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1421"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}