{"id":2447,"date":"2021-10-14T15:56:38","date_gmt":"2021-10-14T15:56:38","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2447"},"modified":"2022-04-22T00:09:05","modified_gmt":"2022-04-22T00:09:05","slug":"summary-test-of-independence","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-test-of-independence\/","title":{"raw":"Summary: Test of Independence","rendered":"Summary: Test of Independence"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The null hypothesis is that there is no association between the two categorical variables. The alternative hypothesis is that there is an association between the two categorical variables.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The degrees of freedom is [latex](r \u2013 1)(c \u2013 1)[\/latex], where [latex]r[\/latex] is the number of rows in the contingency table and c is the number of columns in the contingency table.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The expected count for each cell is found by taking the row total times the column total and dividing by the grand total.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The expected counts need to be 5 or more to conduct a chi-square test and are NOT rounded to the nearest whole number.<\/li>\r\n \t<li>The chi-square test statistic is the sum of [latex]\\frac{(\\mathrm{Observed} \\ - \\ \\mathrm{Expected})^2}{\\mathrm{Expected}}[\/latex] for each cell in the contingency table.<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>Chi-square test of independence:\u00a0<\/strong>a type of hypotheses test to determine if there is an association between two categorical variables\r\n\r\n<strong>Contingency Table:\u00a0<\/strong>a table that displays sample values for two different factors that may be dependent or contingent on one another; it facilitates determining conditional probabilities","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The null hypothesis is that there is no association between the two categorical variables. The alternative hypothesis is that there is an association between the two categorical variables.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The degrees of freedom is [latex](r \u2013 1)(c \u2013 1)[\/latex], where [latex]r[\/latex] is the number of rows in the contingency table and c is the number of columns in the contingency table.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The expected count for each cell is found by taking the row total times the column total and dividing by the grand total.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The expected counts need to be 5 or more to conduct a chi-square test and are NOT rounded to the nearest whole number.<\/li>\n<li>The chi-square test statistic is the sum of [latex]\\frac{(\\mathrm{Observed} \\ - \\ \\mathrm{Expected})^2}{\\mathrm{Expected}}[\/latex] for each cell in the contingency table.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>Chi-square test of independence:\u00a0<\/strong>a type of hypotheses test to determine if there is an association between two categorical variables<\/p>\n<p><strong>Contingency Table:\u00a0<\/strong>a table that displays sample values for two different factors that may be dependent or contingent on one another; it facilitates determining conditional probabilities<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2447\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2447","chapter","type-chapter","status-publish","hentry"],"part":293,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2447","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2447\/revisions"}],"predecessor-version":[{"id":3937,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2447\/revisions\/3937"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/293"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2447\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2447"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2447"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2447"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2447"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}