{"id":2514,"date":"2021-10-15T12:32:40","date_gmt":"2021-10-15T12:32:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2514"},"modified":"2023-12-05T09:51:20","modified_gmt":"2023-12-05T09:51:20","slug":"summary-one-way-anova","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-one-way-anova\/","title":{"raw":"Summary: One-Way ANOVA","rendered":"Summary: One-Way ANOVA"},"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 all the group population means are the same. The alternative hypothesis is that at least one pair of means is different.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A one-way ANOVA uses variances to help determine if the means are equal or not.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">To perform a one-way ANOVA certain assumptions must be met:\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">Each population from which a sample is taken is assumed to be normal.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">All samples are randomly selected and independent.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">The populations are assumed to have equal standard deviations or variances.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">The factor is a categorical variable. (In the introductory example, type of swimming is the factor).<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"2\">The response is a numerical variable. (In the introductory example, the amount of money is a numerical variable).<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Glossary<\/h2>\r\n<strong>One-Way ANOVA:\u00a0<\/strong>a method of testing whether or not the means of three or more populations are equal; The test statistic for analysis of variance is the <em>F<\/em>-ratio.\r\n\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\">The null hypothesis is that all the group population means are the same. The alternative hypothesis is that at least one pair of means is different.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A one-way ANOVA uses variances to help determine if the means are equal or not.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">To perform a one-way ANOVA certain assumptions must be met:\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\">Each population from which a sample is taken is assumed to be normal.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">All samples are randomly selected and independent.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">The populations are assumed to have equal standard deviations or variances.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">The factor is a categorical variable. (In the introductory example, type of swimming is the factor).<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\">The response is a numerical variable. (In the introductory example, the amount of money is a numerical variable).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<p><strong>One-Way ANOVA:\u00a0<\/strong>a method of testing whether or not the means of three or more populations are equal; The test statistic for analysis of variance is the <em>F<\/em>-ratio.<\/p>\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-2514\">\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\/13-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/13-key-terms<\/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":8,"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\/13-key-terms\",\"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-2514","chapter","type-chapter","status-publish","hentry"],"part":313,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2514","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\/2514\/revisions"}],"predecessor-version":[{"id":4009,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2514\/revisions\/4009"}],"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\/2514\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2514"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2514"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2514"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2514"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}