{"id":1356,"date":"2023-06-22T02:20:23","date_gmt":"2023-06-22T02:20:23","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-one-way-anova-apply-it-3\/"},"modified":"2025-05-16T22:50:59","modified_gmt":"2025-05-16T22:50:59","slug":"introduction-to-one-way-anova-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-one-way-anova-apply-it-3\/","title":{"raw":"Introduction to One-Way ANOVA \u2013 Apply It 3","rendered":"Introduction to One-Way ANOVA \u2013 Apply It 3"},"content":{"raw":"<section>\r\n<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a one-way ANOVA hypothesis test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Write a null and alternative hypothesis for a one-way ANOVA hypothesis test<\/span><\/li>\r\n\t<li><span data-sheets-root=\"1\" data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the error sum of squares and group sum of squares&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:14720,&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:9}\">Discuss the error sum of squares and group sum of squares<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<\/section>\r\n<h2>Sum of Squares<\/h2>\r\n<p>The test statistic and P-value are calculated by considering the <em>ratio<\/em> of variation<em> within <\/em>each of the groups to the variation <em>between<\/em> each of the groups. That is, when the variation <em>between<\/em> each of the groups is significantly greater than the variation <em>within<\/em> each of the groups, we will reject the null hypothesis and conclude that at least two of the means are different. However, when there is a significant amount of variation <em>within<\/em> groups, relative to the variation <em>between<\/em> groups, we will have less evidence of a difference and may fail to reject the null hypothesis.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>sum of squares<\/h3>\r\n<p>The statistic measuring the variation <em>within<\/em> the groups is the <strong>error sum of squares<\/strong>. This is calculated by summing the variation <em>within<\/em> each of the groups. The variation <em>within<\/em> each of the groups is visualized in the boxplot by the size of the box and in the dotplot as the spread of the dots within each group.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>A statistic measuring the variation <em>between<\/em> the groups is the <strong>group sum of squares<\/strong>. This is calculated by summing the variation <em>between<\/em> each of the group means and the grand mean (i.e., the mean of all the data values).<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2018[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2019[\/ohm2_question]<\/section>","rendered":"<section>\n<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a one-way ANOVA hypothesis test&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Write a null and alternative hypothesis for a one-way ANOVA hypothesis test<\/span><\/li>\n<li><span data-sheets-root=\"1\" data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the error sum of squares and group sum of squares&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:14720,&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:9}\">Discuss the error sum of squares and group sum of squares<\/span><\/li>\n<\/ul>\n<\/section>\n<\/section>\n<h2>Sum of Squares<\/h2>\n<p>The test statistic and P-value are calculated by considering the <em>ratio<\/em> of variation<em> within <\/em>each of the groups to the variation <em>between<\/em> each of the groups. That is, when the variation <em>between<\/em> each of the groups is significantly greater than the variation <em>within<\/em> each of the groups, we will reject the null hypothesis and conclude that at least two of the means are different. However, when there is a significant amount of variation <em>within<\/em> groups, relative to the variation <em>between<\/em> groups, we will have less evidence of a difference and may fail to reject the null hypothesis.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>sum of squares<\/h3>\n<p>The statistic measuring the variation <em>within<\/em> the groups is the <strong>error sum of squares<\/strong>. This is calculated by summing the variation <em>within<\/em> each of the groups. The variation <em>within<\/em> each of the groups is visualized in the boxplot by the size of the box and in the dotplot as the spread of the dots within each group.<\/p>\n<p>&nbsp;<\/p>\n<p>A statistic measuring the variation <em>between<\/em> the groups is the <strong>group sum of squares<\/strong>. This is calculated by summing the variation <em>between<\/em> each of the group means and the grand mean (i.e., the mean of all the data values).<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2018\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2018&theme=lumen&iframe_resize_id=ohm2018&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2019\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2019&theme=lumen&iframe_resize_id=ohm2019&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":13,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1348,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1356"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1356\/revisions"}],"predecessor-version":[{"id":6839,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1356\/revisions\/6839"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1348"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1356\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1356"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1356"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1356"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}