{"id":1351,"date":"2023-06-22T02:20:19","date_gmt":"2023-06-22T02:20:19","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-one-way-anova-learn-it-1\/"},"modified":"2025-05-16T22:48:58","modified_gmt":"2025-05-16T22:48:58","slug":"introduction-to-one-way-anova-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-one-way-anova-learn-it-1\/","title":{"raw":"Introduction to One-Way ANOVA \u2013 Learn It 1","rendered":"Introduction to One-Way ANOVA \u2013 Learn 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;Write a null and alternative hypothesis for 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}\">Write a null and alternative hypothesis for a one-way ANOVA hypothesis test<\/span><\/li>\r\n\t<li><span data-sheets-root=\"1\" data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the error sum of squares and group sum of squares&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:14720,&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:9}\">Discuss the error sum of squares and group sum of squares<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>One-way ANOVA<\/h2>\r\n<p>Previously, we explored hypothesis tests that allowed us to compare means from <em>two<\/em> groups\/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another.<\/p>\r\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">For hypothesis tests comparing averages between more than two groups, statisticians have developed a method called \"Analysis of Variance\" (abbreviated ANOVA).<\/span><\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>ANOVA<\/h3>\r\n<p><span style=\"font-family: 'Arial',sans-serif;\"><b>One-way ANOVA<\/b> (analysis of variance) is a statistical test for comparing and making inferences about means associated with <i>two or more groups<\/i>. The one-way ANOVA is also referred to as the <strong>one-factor ANOVA<\/strong>.<\/span><\/p>\r\n<\/section>\r\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example, an environmentalist is interested in knowing if the average amount of pollution varies in several bodies of water. A sociologist is interested in knowing if the amount of income a person earns varies according to his or her upbringing. A consumer looking for a new car might compare the average gas mileage of several models. <\/span><\/p>\r\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">Is the average amount of money spent by Olympic athletes on their training the same for all water sports (pool swimming, diving, water polo, synchronized swimming, open-water swimming)? To answer this question, we would want to compare the five means. Rather than doing separate [latex]t[\/latex]-tests for each different pair of water sports, we will do an analysis on all five means called an Analysis of Variance or ANOVA.<\/span><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2008[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for 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}\">Write a null and alternative hypothesis for a one-way ANOVA hypothesis test<\/span><\/li>\n<li><span data-sheets-root=\"1\" data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Discuss the error sum of squares and group sum of squares&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:14720,&quot;10&quot;:2,&quot;11&quot;:4,&quot;14&quot;:{&quot;1&quot;:2,&quot;2&quot;:0},&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:9}\">Discuss the error sum of squares and group sum of squares<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>One-way ANOVA<\/h2>\n<p>Previously, we explored hypothesis tests that allowed us to compare means from <em>two<\/em> groups\/populations. More specifically, we performed calculations to determine if there was evidence that the means associated with the populations were statistically different from one another.<\/p>\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">For hypothesis tests comparing averages between more than two groups, statisticians have developed a method called &#8220;Analysis of Variance&#8221; (abbreviated ANOVA).<\/span><\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>ANOVA<\/h3>\n<p><span style=\"font-family: 'Arial',sans-serif;\"><b>One-way ANOVA<\/b> (analysis of variance) is a statistical test for comparing and making inferences about means associated with <i>two or more groups<\/i>. The one-way ANOVA is also referred to as the <strong>one-factor ANOVA<\/strong>.<\/span><\/p>\n<\/section>\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">Many statistical applications in psychology, social science, business administration, and the natural sciences involve several groups. For example, an environmentalist is interested in knowing if the average amount of pollution varies in several bodies of water. A sociologist is interested in knowing if the amount of income a person earns varies according to his or her upbringing. A consumer looking for a new car might compare the average gas mileage of several models. <\/span><\/p>\n<p class=\"para\"><span style=\"font-family: 'Arial',sans-serif;\">Is the average amount of money spent by Olympic athletes on their training the same for all water sports (pool swimming, diving, water polo, synchronized swimming, open-water swimming)? To answer this question, we would want to compare the five means. Rather than doing separate [latex]t[\/latex]-tests for each different pair of water sports, we will do an analysis on all five means called an Analysis of Variance or ANOVA.<\/span><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2008\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2008&theme=lumen&iframe_resize_id=ohm2008&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":8,"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\/1351"}],"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\/1351\/revisions"}],"predecessor-version":[{"id":7144,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1351\/revisions\/7144"}],"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\/1351\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1351"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1351"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1351"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}