{"id":1383,"date":"2023-06-22T02:20:48","date_gmt":"2023-06-22T02:20:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-apply-it-1\/"},"modified":"2025-05-16T23:01:46","modified_gmt":"2025-05-16T23:01:46","slug":"pair-wise-comparisons-for-anova-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/pair-wise-comparisons-for-anova-apply-it-1\/","title":{"raw":"Pair-wise Comparisons for ANOVA \u2013 Apply It 1","rendered":"Pair-wise Comparisons for ANOVA \u2013 Apply It 1"},"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<h2>What is the best treatment?<\/h2>\r\n<p><img class=\"alignleft wp-image-1415\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22022047\/2019-07_elder.jpeg\" alt=\"A woman helping an older woman with holding a cane.\" width=\"310\" height=\"174\" \/>[footnote]https:\/\/www.cdc.gov\/genomics\/disease\/osteoporosis.htm[\/footnote] The CDC states that people with osteoporosis are more likely to break bones, most often in the hip, forearm, wrist, and spine. There are steps you can take to improve your bone health and strengthen weak bones.<\/p>\r\n<p>Previously, we looked at a 1995 study that used a one-way ANOVA to compare different osteoporosis prevention strategies on the bone density of older women.[footnote]Prince, R., Devine, A., Dick, I., Criddle, A., Kerr, D., Kent, N., Randell, A. &amp; Price, R. (1995). The effects of calcium supplementation (milk powder or tablets) and exercise on bone density in postmenopausal women. Journal of Bone and Mineral Research, 10(7), 1068\u20131075.[\/footnote] The women were randomly assigned to receive either a placebo treatment, milk powder containing calcium, calcium pills, or calcium pills with an exercise program. In order to compare the groups, the researchers measured the densities of the thigh bones for each of the treatment groups after a period of two years.<\/p>\r\n<p>Through a one-way ANOVA, we found that <strong>there is a difference<\/strong> between the means of two or more of these treatments. At least one of the preventative strategies was more or less effective than the other options.<\/p>\r\n<p>Now the question is: <strong>\u201cWhat treatment works best to prevent osteoporosis?\u201d<\/strong><\/p>\r\n<p>It is tempting to use the following boxplot to determine the answer, so we need to be careful. This method does not provide statistical EVIDENCE to support your conclusion.<\/p>\r\n<p><img class=\"alignnone wp-image-1416 size-large\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193427\/Picture1-4.png\" alt=\"Four different boxplots, one for the placebo, one for milk powder, one for a calcium pill, and one for calcium pills and exercise. The data corresponding to these boxplots can be found below.\" width=\"1024\" height=\"253\" \/><\/p>\r\n<p>It is also tempting to only show the comparisons you want to show based on the boxplot. For example, only looking at comparisons including Calcium Pill Plus Exercise. This is called <strong>data snooping<\/strong> or <strong>data fishing<\/strong>. You cannot look at your results and then determine the comparisons that you want to make.<\/p>\r\n<p>So, let\u2019s investigate the difference in the treatment options for all pair-wise comparisons at the family-wise [latex]5\\%[\/latex] significance level.<\/p>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Choose the \u201cFrom Textbook\u201d option and select the data set \u201cOsteoporosis.\u201d<br \/>\r\n<strong>Step 2: <\/strong>Select the option to perform \u201cPairwise Comparisons and Confidence Intervals.\u201d<br \/>\r\n<strong>Step 3: <\/strong>Select a confidence level of 95%.<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" width=\"100%\" height=\"900\" frameborder=\"no\"><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" 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]2269[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2270[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2271[\/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<h2>What is the best treatment?<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1415\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/22022047\/2019-07_elder.jpeg\" alt=\"A woman helping an older woman with holding a cane.\" width=\"310\" height=\"174\" \/><a class=\"footnote\" title=\"https:\/\/www.cdc.gov\/genomics\/disease\/osteoporosis.htm\" id=\"return-footnote-1383-1\" href=\"#footnote-1383-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> The CDC states that people with osteoporosis are more likely to break bones, most often in the hip, forearm, wrist, and spine. There are steps you can take to improve your bone health and strengthen weak bones.<\/p>\n<p>Previously, we looked at a 1995 study that used a one-way ANOVA to compare different osteoporosis prevention strategies on the bone density of older women.<a class=\"footnote\" title=\"Prince, R., Devine, A., Dick, I., Criddle, A., Kerr, D., Kent, N., Randell, A. &amp; Price, R. (1995). The effects of calcium supplementation (milk powder or tablets) and exercise on bone density in postmenopausal women. Journal of Bone and Mineral Research, 10(7), 1068\u20131075.\" id=\"return-footnote-1383-2\" href=\"#footnote-1383-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a> The women were randomly assigned to receive either a placebo treatment, milk powder containing calcium, calcium pills, or calcium pills with an exercise program. In order to compare the groups, the researchers measured the densities of the thigh bones for each of the treatment groups after a period of two years.<\/p>\n<p>Through a one-way ANOVA, we found that <strong>there is a difference<\/strong> between the means of two or more of these treatments. At least one of the preventative strategies was more or less effective than the other options.<\/p>\n<p>Now the question is: <strong>\u201cWhat treatment works best to prevent osteoporosis?\u201d<\/strong><\/p>\n<p>It is tempting to use the following boxplot to determine the answer, so we need to be careful. This method does not provide statistical EVIDENCE to support your conclusion.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1416 size-large\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193427\/Picture1-4.png\" alt=\"Four different boxplots, one for the placebo, one for milk powder, one for a calcium pill, and one for calcium pills and exercise. The data corresponding to these boxplots can be found below.\" width=\"1024\" height=\"253\" \/><\/p>\n<p>It is also tempting to only show the comparisons you want to show based on the boxplot. For example, only looking at comparisons including Calcium Pill Plus Exercise. This is called <strong>data snooping<\/strong> or <strong>data fishing<\/strong>. You cannot look at your results and then determine the comparisons that you want to make.<\/p>\n<p>So, let\u2019s investigate the difference in the treatment options for all pair-wise comparisons at the family-wise [latex]5\\%[\/latex] significance level.<\/p>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Choose the \u201cFrom Textbook\u201d option and select the data set \u201cOsteoporosis.\u201d<br \/>\n<strong>Step 2: <\/strong>Select the option to perform \u201cPairwise Comparisons and Confidence Intervals.\u201d<br \/>\n<strong>Step 3: <\/strong>Select a confidence level of 95%.<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" width=\"100%\" height=\"900\" frameborder=\"no\"><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2269\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2269&theme=lumen&iframe_resize_id=ohm2269&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2270\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2270&theme=lumen&iframe_resize_id=ohm2270&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2271\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2271&theme=lumen&iframe_resize_id=ohm2271&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1383-1\">https:\/\/www.cdc.gov\/genomics\/disease\/osteoporosis.htm <a href=\"#return-footnote-1383-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1383-2\">Prince, R., Devine, A., Dick, I., Criddle, A., Kerr, D., Kent, N., Randell, A. &amp; Price, R. (1995). The effects of calcium supplementation (milk powder or tablets) and exercise on bone density in postmenopausal women. Journal of Bone and Mineral Research, 10(7), 1068\u20131075. <a href=\"#return-footnote-1383-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":32,"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\/1383"}],"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\/1383\/revisions"}],"predecessor-version":[{"id":6853,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1383\/revisions\/6853"}],"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\/1383\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1383"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1383"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1383"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}