{"id":314,"date":"2021-07-14T15:59:12","date_gmt":"2021-07-14T15:59:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-f-distribution-and-one-way-anova\/"},"modified":"2022-04-24T02:29:17","modified_gmt":"2022-04-24T02:29:17","slug":"why-it-matters-f-distribution-and-one-way-anova","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/why-it-matters-f-distribution-and-one-way-anova\/","title":{"raw":"Why It Matters: F Distribution and One-Way ANOVA","rendered":"Why It Matters: F Distribution and One-Way ANOVA"},"content":{"raw":"<h2>How can we analyze means if we have more than two populations to compare?<\/h2>\r\n<div>\r\n<div class=\"media-body\">\r\n\r\nOften data is gathered across several groups and we wish to make inferences about the population means for those groups. Rather than conducting multiple hypothesis tests to compare two means, an Analysis of Variance (or ANOVA) is conducted. This requires a new statistic, known as the F statistic, and a new distribution, known as the F distribution. For example, based on these boxplots for the GPAs of a random sample of students at four colleges, do we think the mean GPAs are different at these colleges? Although we can see differences within the plots, an ANOVA would need to be done to completely answer this question.\r\n\r\n<img class=\"aligncenter wp-image-2663 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/11205003\/Picture15.png\" alt=\"Four parallel boxplots are shown. The boxplots are labeled from the bottom to the top as College A, College B, College C and College D. The boxplots for College A and B are similar, but College A has a slightly higher maximum (about 3.3) and third quartile (about 3.1) than College B. The distribution of GPAs of College C shows 50% of students with GPAs between about 2.4 and 2.6 and 50% of GPAs between about 2.6 and 4.0. The distribution of GPAs of College D has the highest median of all the colleges at about 3.2. The minimum and maximum GPA\u2019s of College D are about 2.25 and 3.8, respectively.\" width=\"546\" height=\"429\" \/>\r\n\r\n<\/div>\r\n<\/div>","rendered":"<h2>How can we analyze means if we have more than two populations to compare?<\/h2>\n<div>\n<div class=\"media-body\">\n<p>Often data is gathered across several groups and we wish to make inferences about the population means for those groups. Rather than conducting multiple hypothesis tests to compare two means, an Analysis of Variance (or ANOVA) is conducted. This requires a new statistic, known as the F statistic, and a new distribution, known as the F distribution. For example, based on these boxplots for the GPAs of a random sample of students at four colleges, do we think the mean GPAs are different at these colleges? Although we can see differences within the plots, an ANOVA would need to be done to completely answer this question.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2663 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/07\/11205003\/Picture15.png\" alt=\"Four parallel boxplots are shown. The boxplots are labeled from the bottom to the top as College A, College B, College C and College D. The boxplots for College A and B are similar, but College A has a slightly higher maximum (about 3.3) and third quartile (about 3.1) than College B. The distribution of GPAs of College C shows 50% of students with GPAs between about 2.4 and 2.6 and 50% of GPAs between about 2.6 and 4.0. The distribution of GPAs of College D has the highest median of all the colleges at about 3.2. The minimum and maximum GPA\u2019s of College D are about 2.25 and 3.8, respectively.\" width=\"546\" height=\"429\" \/><\/p>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-314\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-314","chapter","type-chapter","status-publish","hentry"],"part":313,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/314\/revisions"}],"predecessor-version":[{"id":4000,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/314\/revisions\/4000"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/313"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/314\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=314"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=314"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=314"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}