{"id":1365,"date":"2023-06-22T02:20:31","date_gmt":"2023-06-22T02:20:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/conditions-for-anova-apply-it-2\/"},"modified":"2024-03-01T00:51:11","modified_gmt":"2024-03-01T00:51:11","slug":"conditions-for-anova-apply-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/conditions-for-anova-apply-it-2\/","title":{"raw":"Conditions for ANOVA - Apply It 2","rendered":"Conditions for ANOVA &#8211; Apply It 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Identify whether conditions for a one-way ANOVA have been met<\/li>\r\n<\/ul>\r\n<\/section>\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 [latex]168[\/latex] participants in the study ([latex]42[\/latex] in each group). The data provided in the following table are based on the summary statistics in the study.<\/p>\r\n<p class=\"para\">The values represent the changes in bone density (%) for the patients within that group.<\/p>\r\n<p class=\"para\">[reveal-answer q=\"795502\"]Data Set[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"795502\"]<\/p>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>Placebo<\/td>\r\n<td>Milk<\/td>\r\n<td>Calcium Pill<\/td>\r\n<td>Calcium Pill Plus Exercise<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.46<\/td>\r\n<td>-0.02<\/td>\r\n<td>-0.2<\/td>\r\n<td>0.53<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.57<\/td>\r\n<td>-0.43<\/td>\r\n<td>-0.07<\/td>\r\n<td>0.54<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.7<\/td>\r\n<td>-0.24<\/td>\r\n<td>-0.3<\/td>\r\n<td>0.11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.61<\/td>\r\n<td>0.05<\/td>\r\n<td>-0.26<\/td>\r\n<td>0.42<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.65<\/td>\r\n<td>-0.44<\/td>\r\n<td>-0.38<\/td>\r\n<td>0.73<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.62<\/td>\r\n<td>-0.1<\/td>\r\n<td>0.01<\/td>\r\n<td>1.21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.93<\/td>\r\n<td>-0.35<\/td>\r\n<td>-0.23<\/td>\r\n<td>0.67<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.83<\/td>\r\n<td>-0.02<\/td>\r\n<td>0.11<\/td>\r\n<td>0.63<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.7<\/td>\r\n<td>-0.21<\/td>\r\n<td>0.1<\/td>\r\n<td>0.25<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.65<\/td>\r\n<td>0.31<\/td>\r\n<td>0.07<\/td>\r\n<td>0.07<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.62<\/td>\r\n<td>-0.06<\/td>\r\n<td>-0.28<\/td>\r\n<td>0.34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.92<\/td>\r\n<td>-0.4<\/td>\r\n<td>-0.19<\/td>\r\n<td>0.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.33<\/td>\r\n<td>-0.04<\/td>\r\n<td>0.02<\/td>\r\n<td>0.18<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.7<\/td>\r\n<td>-0.14<\/td>\r\n<td>-0.14<\/td>\r\n<td>-0.02<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.47<\/td>\r\n<td>-0.39<\/td>\r\n<td>-0.25<\/td>\r\n<td>0.53<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.71<\/td>\r\n<td>0.05<\/td>\r\n<td>-0.21<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.94<\/td>\r\n<td>-0.05<\/td>\r\n<td>0<\/td>\r\n<td>0.34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.47<\/td>\r\n<td>0.06<\/td>\r\n<td>-0.54<\/td>\r\n<td>0.04<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.52<\/td>\r\n<td>-0.35<\/td>\r\n<td>-0.2<\/td>\r\n<td>0.6<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.85<\/td>\r\n<td>-0.4<\/td>\r\n<td>-0.06<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.38<\/td>\r\n<td>-0.34<\/td>\r\n<td>-0.27<\/td>\r\n<td>0.35<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.76<\/td>\r\n<td>-0.3<\/td>\r\n<td>0.06<\/td>\r\n<td>-0.45<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.71<\/td>\r\n<td>-0.35<\/td>\r\n<td>-0.14<\/td>\r\n<td>-0.26<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.77<\/td>\r\n<td>-0.2<\/td>\r\n<td>-0.33<\/td>\r\n<td>0.33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.73<\/td>\r\n<td>-0.38<\/td>\r\n<td>-0.4<\/td>\r\n<td>-0.05<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.67<\/td>\r\n<td>-0.27<\/td>\r\n<td>-0.21<\/td>\r\n<td>-0.12<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.68<\/td>\r\n<td>0.3<\/td>\r\n<td>-0.23<\/td>\r\n<td>0.51<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.67<\/td>\r\n<td>-0.29<\/td>\r\n<td>-0.38<\/td>\r\n<td>0.29<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.68<\/td>\r\n<td>-0.25<\/td>\r\n<td>-0.43<\/td>\r\n<td>0.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.52<\/td>\r\n<td>-0.1<\/td>\r\n<td>-0.27<\/td>\r\n<td>0.39<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.18<\/td>\r\n<td>-0.34<\/td>\r\n<td>0.1<\/td>\r\n<td>0.38<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.8<\/td>\r\n<td>-0.36<\/td>\r\n<td>-0.21<\/td>\r\n<td>-0.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.99<\/td>\r\n<td>-0.22<\/td>\r\n<td>-0.34<\/td>\r\n<td>0.36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.49<\/td>\r\n<td>-0.06<\/td>\r\n<td>-0.13<\/td>\r\n<td>0.39<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.81<\/td>\r\n<td>-0.26<\/td>\r\n<td>-0.18<\/td>\r\n<td>0.58<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.8<\/td>\r\n<td>-0.27<\/td>\r\n<td>0<\/td>\r\n<td>-0.07<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.66<\/td>\r\n<td>0.1<\/td>\r\n<td>-0.37<\/td>\r\n<td>0.37<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.84<\/td>\r\n<td>0.03<\/td>\r\n<td>0.07<\/td>\r\n<td>0.61<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.83<\/td>\r\n<td>-0.18<\/td>\r\n<td>0.19<\/td>\r\n<td>0.04<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.86<\/td>\r\n<td>-0.25<\/td>\r\n<td>-0.42<\/td>\r\n<td>0.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.31<\/td>\r\n<td>-0.2<\/td>\r\n<td>-0.17<\/td>\r\n<td>-0.34<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>-0.82<\/td>\r\n<td>-0.37<\/td>\r\n<td>-0.47<\/td>\r\n<td>0.47<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p>[\/hidden-answer]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2183[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2185[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2186[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Identify whether conditions for a one-way ANOVA have been met<\/li>\n<\/ul>\n<\/section>\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 [latex]168[\/latex] participants in the study ([latex]42[\/latex] in each group). The data provided in the following table are based on the summary statistics in the study.<\/p>\n<p class=\"para\">The values represent the changes in bone density (%) for the patients within that group.<\/p>\n<p class=\"para\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q795502\">Data Set<\/button><\/p>\n<div id=\"q795502\" class=\"hidden-answer\" style=\"display: none\">\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td>Placebo<\/td>\n<td>Milk<\/td>\n<td>Calcium Pill<\/td>\n<td>Calcium Pill Plus Exercise<\/td>\n<\/tr>\n<tr>\n<td>-0.46<\/td>\n<td>-0.02<\/td>\n<td>-0.2<\/td>\n<td>0.53<\/td>\n<\/tr>\n<tr>\n<td>-0.57<\/td>\n<td>-0.43<\/td>\n<td>-0.07<\/td>\n<td>0.54<\/td>\n<\/tr>\n<tr>\n<td>-0.7<\/td>\n<td>-0.24<\/td>\n<td>-0.3<\/td>\n<td>0.11<\/td>\n<\/tr>\n<tr>\n<td>-0.61<\/td>\n<td>0.05<\/td>\n<td>-0.26<\/td>\n<td>0.42<\/td>\n<\/tr>\n<tr>\n<td>-0.65<\/td>\n<td>-0.44<\/td>\n<td>-0.38<\/td>\n<td>0.73<\/td>\n<\/tr>\n<tr>\n<td>-0.62<\/td>\n<td>-0.1<\/td>\n<td>0.01<\/td>\n<td>1.21<\/td>\n<\/tr>\n<tr>\n<td>-0.93<\/td>\n<td>-0.35<\/td>\n<td>-0.23<\/td>\n<td>0.67<\/td>\n<\/tr>\n<tr>\n<td>-0.83<\/td>\n<td>-0.02<\/td>\n<td>0.11<\/td>\n<td>0.63<\/td>\n<\/tr>\n<tr>\n<td>-0.7<\/td>\n<td>-0.21<\/td>\n<td>0.1<\/td>\n<td>0.25<\/td>\n<\/tr>\n<tr>\n<td>-0.65<\/td>\n<td>0.31<\/td>\n<td>0.07<\/td>\n<td>0.07<\/td>\n<\/tr>\n<tr>\n<td>-0.62<\/td>\n<td>-0.06<\/td>\n<td>-0.28<\/td>\n<td>0.34<\/td>\n<\/tr>\n<tr>\n<td>-0.92<\/td>\n<td>-0.4<\/td>\n<td>-0.19<\/td>\n<td>0.32<\/td>\n<\/tr>\n<tr>\n<td>-0.33<\/td>\n<td>-0.04<\/td>\n<td>0.02<\/td>\n<td>0.18<\/td>\n<\/tr>\n<tr>\n<td>-0.7<\/td>\n<td>-0.14<\/td>\n<td>-0.14<\/td>\n<td>-0.02<\/td>\n<\/tr>\n<tr>\n<td>-0.47<\/td>\n<td>-0.39<\/td>\n<td>-0.25<\/td>\n<td>0.53<\/td>\n<\/tr>\n<tr>\n<td>-0.71<\/td>\n<td>0.05<\/td>\n<td>-0.21<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>-0.94<\/td>\n<td>-0.05<\/td>\n<td>0<\/td>\n<td>0.34<\/td>\n<\/tr>\n<tr>\n<td>-0.47<\/td>\n<td>0.06<\/td>\n<td>-0.54<\/td>\n<td>0.04<\/td>\n<\/tr>\n<tr>\n<td>-0.52<\/td>\n<td>-0.35<\/td>\n<td>-0.2<\/td>\n<td>0.6<\/td>\n<\/tr>\n<tr>\n<td>-0.85<\/td>\n<td>-0.4<\/td>\n<td>-0.06<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>-0.38<\/td>\n<td>-0.34<\/td>\n<td>-0.27<\/td>\n<td>0.35<\/td>\n<\/tr>\n<tr>\n<td>-0.76<\/td>\n<td>-0.3<\/td>\n<td>0.06<\/td>\n<td>-0.45<\/td>\n<\/tr>\n<tr>\n<td>-0.71<\/td>\n<td>-0.35<\/td>\n<td>-0.14<\/td>\n<td>-0.26<\/td>\n<\/tr>\n<tr>\n<td>-0.77<\/td>\n<td>-0.2<\/td>\n<td>-0.33<\/td>\n<td>0.33<\/td>\n<\/tr>\n<tr>\n<td>-0.73<\/td>\n<td>-0.38<\/td>\n<td>-0.4<\/td>\n<td>-0.05<\/td>\n<\/tr>\n<tr>\n<td>-0.67<\/td>\n<td>-0.27<\/td>\n<td>-0.21<\/td>\n<td>-0.12<\/td>\n<\/tr>\n<tr>\n<td>-0.68<\/td>\n<td>0.3<\/td>\n<td>-0.23<\/td>\n<td>0.51<\/td>\n<\/tr>\n<tr>\n<td>-0.67<\/td>\n<td>-0.29<\/td>\n<td>-0.38<\/td>\n<td>0.29<\/td>\n<\/tr>\n<tr>\n<td>-0.68<\/td>\n<td>-0.25<\/td>\n<td>-0.43<\/td>\n<td>0.32<\/td>\n<\/tr>\n<tr>\n<td>-0.52<\/td>\n<td>-0.1<\/td>\n<td>-0.27<\/td>\n<td>0.39<\/td>\n<\/tr>\n<tr>\n<td>-0.18<\/td>\n<td>-0.34<\/td>\n<td>0.1<\/td>\n<td>0.38<\/td>\n<\/tr>\n<tr>\n<td>-0.8<\/td>\n<td>-0.36<\/td>\n<td>-0.21<\/td>\n<td>-0.32<\/td>\n<\/tr>\n<tr>\n<td>-0.99<\/td>\n<td>-0.22<\/td>\n<td>-0.34<\/td>\n<td>0.36<\/td>\n<\/tr>\n<tr>\n<td>-0.49<\/td>\n<td>-0.06<\/td>\n<td>-0.13<\/td>\n<td>0.39<\/td>\n<\/tr>\n<tr>\n<td>-0.81<\/td>\n<td>-0.26<\/td>\n<td>-0.18<\/td>\n<td>0.58<\/td>\n<\/tr>\n<tr>\n<td>-0.8<\/td>\n<td>-0.27<\/td>\n<td>0<\/td>\n<td>-0.07<\/td>\n<\/tr>\n<tr>\n<td>-0.66<\/td>\n<td>0.1<\/td>\n<td>-0.37<\/td>\n<td>0.37<\/td>\n<\/tr>\n<tr>\n<td>-0.84<\/td>\n<td>0.03<\/td>\n<td>0.07<\/td>\n<td>0.61<\/td>\n<\/tr>\n<tr>\n<td>-0.83<\/td>\n<td>-0.18<\/td>\n<td>0.19<\/td>\n<td>0.04<\/td>\n<\/tr>\n<tr>\n<td>-0.86<\/td>\n<td>-0.25<\/td>\n<td>-0.42<\/td>\n<td>0.5<\/td>\n<\/tr>\n<tr>\n<td>-0.31<\/td>\n<td>-0.2<\/td>\n<td>-0.17<\/td>\n<td>-0.34<\/td>\n<\/tr>\n<tr>\n<td>-0.82<\/td>\n<td>-0.37<\/td>\n<td>-0.47<\/td>\n<td>0.47<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2183\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2183&theme=lumen&iframe_resize_id=ohm2183&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2185\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2185&theme=lumen&iframe_resize_id=ohm2185&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2186\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2186&theme=lumen&iframe_resize_id=ohm2186&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":19,"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\/1365"}],"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\/1365\/revisions"}],"predecessor-version":[{"id":5805,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1365\/revisions\/5805"}],"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\/1365\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1365"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1365"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1365"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1365"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}