{"id":1373,"date":"2023-06-22T02:20:38","date_gmt":"2023-06-22T02:20:38","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-apply-it-1\/"},"modified":"2025-05-16T22:58:07","modified_gmt":"2025-05-16T22:58:07","slug":"anova-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/anova-apply-it-1\/","title":{"raw":"ANOVA - Apply It 1","rendered":"ANOVA &#8211; 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;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 class=\"textbox keyTakeaway\">\r\n<h3>steps for one-way ANOVA<\/h3>\r\n<ol>\r\n\t<li>Set up the null and alternative hypotheses.<\/li>\r\n\t<li>Check the conditions\/assumptions for the ANOVA hypothesis test.\r\n\r\n<ul>\r\n\t<li>The right types of data\u2014factor of interest should be categorical, and the response variable should be numeric and continuous<\/li>\r\n\t<li>Similar levels of variability<\/li>\r\n\t<li>Randomly assigned, independent groups<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Calculate the [latex]F[\/latex]-statistic.<\/li>\r\n\t<li>Calculate the P-value.<\/li>\r\n\t<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\r\n\t<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\r\n<\/ol>\r\n<\/section>\r\n<p><img class=\"alignleft wp-image-1371 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193420\/Picture1-12.png\" alt=\"A diagram of a healthy bone next to a diagram of a bone with osteoporosis.\" width=\"300\" height=\"208\" \/>A 1995 study 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.<\/p>\r\n<p>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. Results were recorded as percentage changes in bone density from the beginning of the study. There were 168 participants in the study (42 in each group).<\/p>\r\n<div>\r\n<p>Let's conduct the one-way ANOVA hypothesis test for this scenario. The data set for this scenario is uploaded into the ANOVA statistical tool under \u201c<strong>Osteoporosis.<\/strong>\u201d<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" width=\"100%\" height=\"1100\" 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\/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]2219[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2220[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2221[\/ohm2_question]<\/section>\r\n<p>In an ANOVA hypothesis test, it is very tempting to make assumptions based on the obvious differences in the group means, but further testing is needed to confirm and provide statistical evidence of our conclusions.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2222[\/ohm2_question]<\/section>\r\n<\/div>","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<section class=\"textbox keyTakeaway\">\n<h3>steps for one-way ANOVA<\/h3>\n<ol>\n<li>Set up the null and alternative hypotheses.<\/li>\n<li>Check the conditions\/assumptions for the ANOVA hypothesis test.\n<ul>\n<li>The right types of data\u2014factor of interest should be categorical, and the response variable should be numeric and continuous<\/li>\n<li>Similar levels of variability<\/li>\n<li>Randomly assigned, independent groups<\/li>\n<\/ul>\n<\/li>\n<li>Calculate the [latex]F[\/latex]-statistic.<\/li>\n<li>Calculate the P-value.<\/li>\n<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<\/li>\n<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\n<\/ol>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-1371 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193420\/Picture1-12.png\" alt=\"A diagram of a healthy bone next to a diagram of a bone with osteoporosis.\" width=\"300\" height=\"208\" \/>A 1995 study 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-1373-1\" href=\"#footnote-1373-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/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.<\/p>\n<p>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. Results were recorded as percentage changes in bone density from the beginning of the study. There were 168 participants in the study (42 in each group).<\/p>\n<div>\n<p>Let&#8217;s conduct the one-way ANOVA hypothesis test for this scenario. The data set for this scenario is uploaded into the ANOVA statistical tool under \u201c<strong>Osteoporosis.<\/strong>\u201d<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/anova\/\" width=\"100%\" height=\"1100\" 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\/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=\"ohm2219\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2219&theme=lumen&iframe_resize_id=ohm2219&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2220\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2220&theme=lumen&iframe_resize_id=ohm2220&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2221\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2221&theme=lumen&iframe_resize_id=ohm2221&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>In an ANOVA hypothesis test, it is very tempting to make assumptions based on the obvious differences in the group means, but further testing is needed to confirm and provide statistical evidence of our conclusions.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2222\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2222&theme=lumen&iframe_resize_id=ohm2222&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1373-1\">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-1373-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":25,"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\/1373"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1373\/revisions"}],"predecessor-version":[{"id":6849,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1373\/revisions\/6849"}],"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\/1373\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1373"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1373"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1373"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}