{"id":2533,"date":"2021-10-15T15:35:13","date_gmt":"2021-10-15T15:35:13","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2533"},"modified":"2023-12-05T09:52:41","modified_gmt":"2023-12-05T09:52:41","slug":"summary-test-of-two-variances","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-test-of-two-variances\/","title":{"raw":"Summary: Test of Two Variances","rendered":"Summary: Test of Two Variances"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A test of two variances may be one-tailed or two-tailed.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The conditions for an <em>F<\/em> test on two variances are:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">The populations from which the two samples are drawn are normally distributed.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">The two populations are independent of each other.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The test statistic is based on the assumption that the variances are equal. It is [latex]F = \\frac{(S_1)^2}{(S_2)^2}[\/latex].<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>Variance:\u00a0<\/strong>mean of the squared deviations from the mean; the square of the standard deviation. For a set of data, a deviation can be represented as [latex]x- \\overline{x}[\/latex] where [latex]x[\/latex] is a value of the data and [latex]\\overline{x}[\/latex] is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference between the sample size and one.","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A test of two variances may be one-tailed or two-tailed.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The conditions for an <em>F<\/em> test on two variances are:\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\">The populations from which the two samples are drawn are normally distributed.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">The two populations are independent of each other.<\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The test statistic is based on the assumption that the variances are equal. It is [latex]F = \\frac{(S_1)^2}{(S_2)^2}[\/latex].<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>Variance:\u00a0<\/strong>mean of the squared deviations from the mean; the square of the standard deviation. For a set of data, a deviation can be represented as [latex]x- \\overline{x}[\/latex] where [latex]x[\/latex] is a value of the data and [latex]\\overline{x}[\/latex] is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference between the sample size and one.<\/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-2533\">\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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/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":17,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2533","chapter","type-chapter","status-publish","hentry"],"part":313,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2533","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":3,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2533\/revisions"}],"predecessor-version":[{"id":4028,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2533\/revisions\/4028"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/313"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2533\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2533"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2533"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2533"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}