{"id":766,"date":"2016-04-21T22:43:36","date_gmt":"2016-04-21T22:43:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstats1xmaster\/?post_type=chapter&#038;p=766"},"modified":"2019-05-29T22:16:05","modified_gmt":"2019-05-29T22:16:05","slug":"relationships-in-an-anova-table","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/chapter\/relationships-in-an-anova-table\/","title":{"raw":"Relationships in an ANOVA Table","rendered":"Relationships in an ANOVA Table"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<section>\r\n<ul id=\"fs-idp124304720\">\r\n \t<li>Conduct and interpret one-way ANOVA<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\n<h2>Relationships Within an ANOVA Table<\/h2>\r\n<a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-2.56.05-PM.png\"><img class=\"aligncenter wp-image-474\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215047\/Screen-Shot-2015-06-04-at-2.56.05-PM.png\" alt=\"Basic ANOVA Table\" width=\"579\" height=\"126\" \/><\/a>\r\n\r\nAbove is a basic ANOVA table. How are the cells in this table related? Let\u2019s look at the first two columns of data S.S. and d.f. :\r\n\r\n<a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-2.58.46-PM.png\"><img class=\"aligncenter wp-image-476\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215049\/Screen-Shot-2015-06-04-at-2.58.46-PM.png\" alt=\"Basic ANOVA Table. SS and df columns highlighted.\" width=\"582\" height=\"126\" \/><\/a>\r\n\r\nNotice how the first two cells add up to the total below it in the columns highlighted above. (i.e. 5272.015 + 5763 = 11035.015)\r\n\r\nNow let\u2019s move onto the third column M.S. . In this case, we need to look at the rows which the cells belong to:\r\n\r\n<a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-3.00.37-PM.png\"><img class=\"aligncenter wp-image-477\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215051\/Screen-Shot-2015-06-04-at-3.00.37-PM.png\" alt=\"Basic ANOVA Table with SS, df and MS columns highlighted\" width=\"567\" height=\"122\" \/><\/a>\r\n\r\nNotice how the values in the third column are the quotient of the prior two cells (i.e. 5272.015 \u00f7 5 = 1054.403)\r\n\r\nThis leaves us with our last column F.\r\n\r\n<a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-3.01.50-PM.png\"><img class=\"aligncenter wp-image-478\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215053\/Screen-Shot-2015-06-04-at-3.01.50-PM.png\" alt=\"Basic ANOVA Table with MS and F columns highlighted\" width=\"563\" height=\"116\" \/><\/a>\r\n\r\nThis again is a division problem. (i.e. 1054.403 \u00f7 113 = 9.331)\r\n\r\nThe relationships work for every ANOVA table. However, you may not be given the same elements as you are in this table. In this case, you may have to work backwards and solve for the other missing cells.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<section>\n<ul id=\"fs-idp124304720\">\n<li>Conduct and interpret one-way ANOVA<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<h2>Relationships Within an ANOVA Table<\/h2>\n<p><a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-2.56.05-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-474\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215047\/Screen-Shot-2015-06-04-at-2.56.05-PM.png\" alt=\"Basic ANOVA Table\" width=\"579\" height=\"126\" \/><\/a><\/p>\n<p>Above is a basic ANOVA table. How are the cells in this table related? Let\u2019s look at the first two columns of data S.S. and d.f. :<\/p>\n<p><a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-2.58.46-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-476\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215049\/Screen-Shot-2015-06-04-at-2.58.46-PM.png\" alt=\"Basic ANOVA Table. SS and df columns highlighted.\" width=\"582\" height=\"126\" \/><\/a><\/p>\n<p>Notice how the first two cells add up to the total below it in the columns highlighted above. (i.e. 5272.015 + 5763 = 11035.015)<\/p>\n<p>Now let\u2019s move onto the third column M.S. . In this case, we need to look at the rows which the cells belong to:<\/p>\n<p><a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-3.00.37-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-477\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215051\/Screen-Shot-2015-06-04-at-3.00.37-PM.png\" alt=\"Basic ANOVA Table with SS, df and MS columns highlighted\" width=\"567\" height=\"122\" \/><\/a><\/p>\n<p>Notice how the values in the third column are the quotient of the prior two cells (i.e. 5272.015 \u00f7 5 = 1054.403)<\/p>\n<p>This leaves us with our last column F.<\/p>\n<p><a href=\"https:\/\/courses.candelalearning.com\/introstats1xmaster\/wp-content\/uploads\/sites\/635\/2015\/06\/Screen-Shot-2015-06-04-at-3.01.50-PM.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-478\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21215053\/Screen-Shot-2015-06-04-at-3.01.50-PM.png\" alt=\"Basic ANOVA Table with MS and F columns highlighted\" width=\"563\" height=\"116\" \/><\/a><\/p>\n<p>This again is a division problem. (i.e. 1054.403 \u00f7 113 = 9.331)<\/p>\n<p>The relationships work for every ANOVA table. However, you may not be given the same elements as you are in this table. In this case, you may have to work backwards and solve for the other missing cells.<\/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-766\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Statistics . <strong>Authored by<\/strong>: Barbara Illowski, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\">http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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>: Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44<\/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":21,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Statistics \",\"author\":\"Barbara Illowski, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/30189442-6998-4686-ac05-ed152b91b9de@17.44\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-766","chapter","type-chapter","status-publish","hentry"],"part":733,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/766","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/766\/revisions"}],"predecessor-version":[{"id":1832,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/766\/revisions\/1832"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/parts\/733"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapters\/766\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/media?parent=766"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/pressbooks\/v2\/chapter-type?post=766"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/contributor?post=766"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ntcc-introstats1\/wp-json\/wp\/v2\/license?post=766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}