{"id":1370,"date":"2023-06-22T02:20:36","date_gmt":"2023-06-22T02:20:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-learn-it-2\/"},"modified":"2025-05-16T22:56:42","modified_gmt":"2025-05-16T22:56:42","slug":"anova-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-learn-it-2\/","title":{"raw":"ANOVA - Learn It 2","rendered":"ANOVA &#8211; Learn It 2"},"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;Perform 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}\">Complete a one-way ANOVA hypothesis test<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a one-way ANOVA hypothesis test in context of the problem&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 the conclusion of a one-way ANOVA hypothesis test in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<\/section>\r\n<h2>Mean Square<\/h2>\r\n<div align=\"left\">\r\n<p><span style=\"font-size: 1rem; text-align: initial;\">When performing a formal hypothesis test for a one-way ANOVA, the mean square values are used to calculate the value of our test statistic; thus, they impact the P-value we get.\u00a0\u00a0<\/span><\/p>\r\n<\/div>\r\n<p>As noted in the previous table, the mean square for error and mean square for group are calculated by taking each of the sum of square values and dividing them by the degrees of freedom associated with the respective source (i.e., Group or Error).<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>mean square<\/h3>\r\n<p style=\"text-align: center;\">[latex]\\text{Mean Square for Error (MSError)}=\\dfrac{\\text{Error sum of squares}}{\\text{degrees of freedom (Error)}}=\\dfrac{SSE}{N-k}[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{Mean Square for Group (MSGroup)}=\\dfrac{\\text{Group sum of squares}}{\\text{degrees of freedom (Group)}}=\\dfrac{SSG}{k-1}[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2191[\/ohm2_question]<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>F-statistic<\/h3>\r\n<p>The test statistic that we use to complete the appropriate hypothesis test for a one-way ANOVA is calculated with the ratio below:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{F-Statistic}=\\dfrac{\\text{MSGroup}}{\\text{MSError}}=\\dfrac{\\text{Variation BETWEEN groups}}{\\text{Variation WITHIN groups}}[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2192[\/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;Perform 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}\">Complete a one-way ANOVA hypothesis test<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the conclusion of a one-way ANOVA hypothesis test in context of the problem&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 the conclusion of a one-way ANOVA hypothesis test in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<\/section>\n<h2>Mean Square<\/h2>\n<div style=\"text-align: left;\">\n<p><span style=\"font-size: 1rem; text-align: initial;\">When performing a formal hypothesis test for a one-way ANOVA, the mean square values are used to calculate the value of our test statistic; thus, they impact the P-value we get.\u00a0\u00a0<\/span><\/p>\n<\/div>\n<p>As noted in the previous table, the mean square for error and mean square for group are calculated by taking each of the sum of square values and dividing them by the degrees of freedom associated with the respective source (i.e., Group or Error).<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>mean square<\/h3>\n<p style=\"text-align: center;\">[latex]\\text{Mean Square for Error (MSError)}=\\dfrac{\\text{Error sum of squares}}{\\text{degrees of freedom (Error)}}=\\dfrac{SSE}{N-k}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Mean Square for Group (MSGroup)}=\\dfrac{\\text{Group sum of squares}}{\\text{degrees of freedom (Group)}}=\\dfrac{SSG}{k-1}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2191\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2191&theme=lumen&iframe_resize_id=ohm2191&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox keyTakeaway\">\n<h3>F-statistic<\/h3>\n<p>The test statistic that we use to complete the appropriate hypothesis test for a one-way ANOVA is calculated with the ratio below:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{F-Statistic}=\\dfrac{\\text{MSGroup}}{\\text{MSError}}=\\dfrac{\\text{Variation BETWEEN groups}}{\\text{Variation WITHIN groups}}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2192\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2192&theme=lumen&iframe_resize_id=ohm2192&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":22,"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":"learn_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\/1370"}],"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\/1370\/revisions"}],"predecessor-version":[{"id":6846,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1370\/revisions\/6846"}],"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\/1370\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1370"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1370"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1370"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}