{"id":2263,"date":"2021-10-08T16:55:39","date_gmt":"2021-10-08T16:55:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2263"},"modified":"2023-12-05T09:33:14","modified_gmt":"2023-12-05T09:33:14","slug":"summary-outcomes-and-the-type-i-and-type-ii-errors","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-outcomes-and-the-type-i-and-type-ii-errors\/","title":{"raw":"Summary: Outcomes and the Type I and Type II Errors","rendered":"Summary: Outcomes and the Type I and Type II Errors"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">There are two types of errors that can happen in hypothesis testing: Type I and Type II.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A Type I error is rejecting the null hypothesis when the null hypothesis is true.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of a Type I error is called alpha, [latex]\\alpha[\/latex].<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">A Type II error is not rejecting the null hypothesis when the null hypothesis is false.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of a Type II error is called beta, [latex]\\beta[\/latex].<\/li>\r\n<\/ul>\r\nPower is the ability of a test to correctly reject a false null hypothesis.\u00a0 Power equals [latex]1 - \\beta[\/latex].\r\n<h2>Glossary<\/h2>\r\n<strong>Level of Significance of the Test: <\/strong>Probability of a Type I error (reject the null hypothesis when it is true). Notation: [latex]\\alpha[\/latex]. In hypothesis testing, the Level of Significance is called the preconceived [latex]\\alpha[\/latex] or the preset [latex]\\alpha[\/latex].\r\n\r\n<strong>Type 1 Error:\u00a0<\/strong>The decision is to reject the null hypothesis when, in fact, the null hypothesis is true.\r\n\r\n<strong>Type 2 Error:\u00a0<\/strong>The decision is not to reject the null hypothesis when, in fact, the null hypothesis is false.","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">There are two types of errors that can happen in hypothesis testing: Type I and Type II.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A Type I error is rejecting the null hypothesis when the null hypothesis is true.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of a Type I error is called alpha, [latex]\\alpha[\/latex].<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">A Type II error is not rejecting the null hypothesis when the null hypothesis is false.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The probability of a Type II error is called beta, [latex]\\beta[\/latex].<\/li>\n<\/ul>\n<p>Power is the ability of a test to correctly reject a false null hypothesis.\u00a0 Power equals [latex]1 - \\beta[\/latex].<\/p>\n<h2>Glossary<\/h2>\n<p><strong>Level of Significance of the Test: <\/strong>Probability of a Type I error (reject the null hypothesis when it is true). Notation: [latex]\\alpha[\/latex]. In hypothesis testing, the Level of Significance is called the preconceived [latex]\\alpha[\/latex] or the preset [latex]\\alpha[\/latex].<\/p>\n<p><strong>Type 1 Error:\u00a0<\/strong>The decision is to reject the null hypothesis when, in fact, the null hypothesis is true.<\/p>\n<p><strong>Type 2 Error:\u00a0<\/strong>The decision is not to reject the null hypothesis when, in fact, the null hypothesis is false.<\/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-2263\">\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\/9-key-terms\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/9-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":11,"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\/9-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-2263","chapter","type-chapter","status-publish","hentry"],"part":276,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2263","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":9,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2263\/revisions"}],"predecessor-version":[{"id":3836,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2263\/revisions\/3836"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/276"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2263\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2263"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2263"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2263"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}