{"id":1381,"date":"2023-06-22T02:20:46","date_gmt":"2023-06-22T02:20:46","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-learn-it-5\/"},"modified":"2024-03-01T00:54:35","modified_gmt":"2024-03-01T00:54:35","slug":"pair-wise-comparisons-for-anova-learn-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-learn-it-5\/","title":{"raw":"Pair-wise Comparisons for ANOVA \u2013 Learn It 5","rendered":"Pair-wise Comparisons for ANOVA \u2013 Learn It 5"},"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;Complete an ANOVA hypothesis test for pair-wise comparisons&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 pair-wise comparisons for ANOVA<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13057,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>Tukey method<\/h3>\r\n<p>One method for controlling for a family-wise error rate is the <strong>Tukey method<\/strong> for all pair-wise comparisons (formally Tukey-Kramer method).<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>This method adjusts the length of the confidence interval (to ensure an overall level of confidence) and the P-value (to ensure an overall significance level for all pair-wise comparisons).<\/p>\r\n<\/section>\r\n<p>Let's look at our study about studying the efficacy of new statistics teaching methods. Recall that you randomly assign [latex]20[\/latex] students to each of the four different methods: [latex]A[\/latex], [latex]B[\/latex], [latex]C[\/latex], and [latex]D[\/latex]. You test their knowledge on the midterm to compare the differences between the teaching methods.<\/p>\r\n<ul>\r\n\t<li>Table A presents the P-values and confidence intervals that are unadjusted for multiple comparisons.<\/li>\r\n\t<li>Table B presents the adjusted confidence intervals using the Tukey method.<\/li>\r\n<\/ul>\r\n<p><strong>Table A<\/strong>: Unadjusted for multiple comparisons*<\/p>\r\n<p><img class=\"alignnone size-large wp-image-1399\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193425\/Picture1.png\" alt=\"\" width=\"1024\" height=\"284\" \/><\/p>\r\n<p class=\"student12ptnumberlist2\" style=\"margin-left: .25in; text-indent: 0in;\">*Note: These P-values and confidence intervals are slightly different than those derived from conducting separate two-sample t-tests.<\/p>\r\n<p class=\"student12ptnumberlist2\" style=\"margin-left: .25in; text-indent: -.25in;\"><strong>Table B<\/strong>: Tukey method used to adjust for multiple comparisons<\/p>\r\n<p><img class=\"alignnone size-full wp-image-1401\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22022045\/Picture1-1.png\" alt=\"\" width=\"936\" height=\"378\" \/><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2250[\/ohm2_question]<\/section>\r\n<p>Note that the difference between the methods for Group [latex]C[\/latex] and Group [latex]B[\/latex] [latex](\\mu_C-\\mu_B)[\/latex] is not considered because it would provide the same information. Similarly, [latex]\\mu_C-\\mu_A[\/latex],etc. are not needed.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2252[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete an ANOVA hypothesis test for pair-wise comparisons&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 pair-wise comparisons for ANOVA<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13057,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:10}\">Calculate a confidence interval and p-value for pair-wise comparisons and explain what it means<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<h3>Tukey method<\/h3>\n<p>One method for controlling for a family-wise error rate is the <strong>Tukey method<\/strong> for all pair-wise comparisons (formally Tukey-Kramer method).<\/p>\n<p>&nbsp;<\/p>\n<p>This method adjusts the length of the confidence interval (to ensure an overall level of confidence) and the P-value (to ensure an overall significance level for all pair-wise comparisons).<\/p>\n<\/section>\n<p>Let&#8217;s look at our study about studying the efficacy of new statistics teaching methods. Recall that you randomly assign [latex]20[\/latex] students to each of the four different methods: [latex]A[\/latex], [latex]B[\/latex], [latex]C[\/latex], and [latex]D[\/latex]. You test their knowledge on the midterm to compare the differences between the teaching methods.<\/p>\n<ul>\n<li>Table A presents the P-values and confidence intervals that are unadjusted for multiple comparisons.<\/li>\n<li>Table B presents the adjusted confidence intervals using the Tukey method.<\/li>\n<\/ul>\n<p><strong>Table A<\/strong>: Unadjusted for multiple comparisons*<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-1399\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193425\/Picture1.png\" alt=\"\" width=\"1024\" height=\"284\" \/><\/p>\n<p class=\"student12ptnumberlist2\" style=\"margin-left: .25in; text-indent: 0in;\">*Note: These P-values and confidence intervals are slightly different than those derived from conducting separate two-sample t-tests.<\/p>\n<p class=\"student12ptnumberlist2\" style=\"margin-left: .25in; text-indent: -.25in;\"><strong>Table B<\/strong>: Tukey method used to adjust for multiple comparisons<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1401\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22022045\/Picture1-1.png\" alt=\"\" width=\"936\" height=\"378\" \/><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2250\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2250&theme=lumen&iframe_resize_id=ohm2250&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Note that the difference between the methods for Group [latex]C[\/latex] and Group [latex]B[\/latex] [latex](\\mu_C-\\mu_B)[\/latex] is not considered because it would provide the same information. Similarly, [latex]\\mu_C-\\mu_A[\/latex],etc. are not needed.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2252\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2252&theme=lumen&iframe_resize_id=ohm2252&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":31,"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\/1381"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1381\/revisions"}],"predecessor-version":[{"id":5814,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1381\/revisions\/5814"}],"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\/1381\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1381"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1381"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1381"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}