{"id":1371,"date":"2023-06-22T02:20:37","date_gmt":"2023-06-22T02:20:37","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-learn-it-3\/"},"modified":"2025-05-16T22:57:12","modified_gmt":"2025-05-16T22:57:12","slug":"anova-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-learn-it-3\/","title":{"raw":"ANOVA - Learn It 3","rendered":"ANOVA &#8211; Learn It 3"},"content":{"raw":"<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<h2>[latex]F[\/latex]-Distribution<\/h2>\r\n<p>Recall that hypothesis testing for two means is based on the [latex]t[\/latex]-Distribution, and we calculate the test statistic, [latex]t[\/latex]. Additionally, the [latex]t[\/latex]-Distribution is symmetric, centered at the mean [latex]0[\/latex]. Thus, when conducting a [latex]t[\/latex]-test, we have positive [latex]t[\/latex]-values and negative [latex]t[\/latex]-values.<\/p>\r\n<section class=\"textbox proTip\">ANOVA is based on the [latex]F[\/latex]-Distribution, so we will be calculating the [latex]F[\/latex]-statistic.<\/section>\r\n<p>Let's utilize our statistical tool to explore the [latex]F[\/latex]-Distribution and its value.<\/p>\r\n<p>Enter the degrees of freedom from our fertilizer scenario into the [latex]F[\/latex]-Distribution Statistical Tool below.<\/p>\r\n<div align=\"center\">\r\n<table style=\"width: 245px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 61.1797px;\"><strong>Source<\/strong><\/td>\r\n<td style=\"width: 101.82px;\"><strong>Degrees of Freedom (df)<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 61.1797px;\">Group<\/td>\r\n<td style=\"width: 101.82px;\">2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 61.1797px;\">Error<\/td>\r\n<td style=\"width: 101.82px;\">9<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 61.1797px;\">Total<\/td>\r\n<td style=\"width: 101.82px;\">11<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" width=\"100%\" height=\"800\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2206[\/ohm2_question]<\/section>\r\n<p>As we just saw, the [latex]F[\/latex]-statistic is the ratio of the variation <em>between<\/em> groups (MSGroup) to the variation <em>within<\/em> groups (MSError). Larger values of the [latex]F[\/latex]-statistic (greater than <span class=\"AM\" title=\"1\">[latex]1[\/latex]<\/span>) would imply that the variation between groups is larger than the variation within groups.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2207[\/ohm2_question]<\/section>\r\n<p>When there is a greater difference among the group means, the [latex]F[\/latex]-statistic will be larger; when there is a smaller difference among the group means, the [latex]F[\/latex]-statistic will be smaller.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2208[\/ohm2_question]<\/section>","rendered":"<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<h2>[latex]F[\/latex]-Distribution<\/h2>\n<p>Recall that hypothesis testing for two means is based on the [latex]t[\/latex]-Distribution, and we calculate the test statistic, [latex]t[\/latex]. Additionally, the [latex]t[\/latex]-Distribution is symmetric, centered at the mean [latex]0[\/latex]. Thus, when conducting a [latex]t[\/latex]-test, we have positive [latex]t[\/latex]-values and negative [latex]t[\/latex]-values.<\/p>\n<section class=\"textbox proTip\">ANOVA is based on the [latex]F[\/latex]-Distribution, so we will be calculating the [latex]F[\/latex]-statistic.<\/section>\n<p>Let&#8217;s utilize our statistical tool to explore the [latex]F[\/latex]-Distribution and its value.<\/p>\n<p>Enter the degrees of freedom from our fertilizer scenario into the [latex]F[\/latex]-Distribution Statistical Tool below.<\/p>\n<div style=\"margin: auto;\">\n<table style=\"width: 245px;\">\n<tbody>\n<tr>\n<td style=\"width: 61.1797px;\"><strong>Source<\/strong><\/td>\n<td style=\"width: 101.82px;\"><strong>Degrees of Freedom (df)<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 61.1797px;\">Group<\/td>\n<td style=\"width: 101.82px;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 61.1797px;\">Error<\/td>\n<td style=\"width: 101.82px;\">9<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 61.1797px;\">Total<\/td>\n<td style=\"width: 101.82px;\">11<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" width=\"100%\" height=\"800\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/fdist\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2206\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2206&theme=lumen&iframe_resize_id=ohm2206&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>As we just saw, the [latex]F[\/latex]-statistic is the ratio of the variation <em>between<\/em> groups (MSGroup) to the variation <em>within<\/em> groups (MSError). Larger values of the [latex]F[\/latex]-statistic (greater than <span class=\"AM\" title=\"1\">[latex]1[\/latex]<\/span>) would imply that the variation between groups is larger than the variation within groups.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2207\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2207&theme=lumen&iframe_resize_id=ohm2207&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>When there is a greater difference among the group means, the [latex]F[\/latex]-statistic will be larger; when there is a smaller difference among the group means, the [latex]F[\/latex]-statistic will be smaller.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2208\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2208&theme=lumen&iframe_resize_id=ohm2208&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":23,"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\/1371"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1371\/revisions"}],"predecessor-version":[{"id":6847,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1371\/revisions\/6847"}],"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\/1371\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1371"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1371"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1371"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}