{"id":1398,"date":"2023-06-22T02:22:42","date_gmt":"2023-06-22T02:22:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-1\/"},"modified":"2024-02-08T22:18:34","modified_gmt":"2024-02-08T22:18:34","slug":"introduction-to-chi-square-statistics-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/introduction-to-chi-square-statistics-apply-it-1\/","title":{"raw":"Introduction to Chi-Square Statistics \u2013 Apply It 1","rendered":"Introduction to Chi-Square Statistics \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;Calculate and describe the value of a chi-square statistics in context of a real-world 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;:9}\">Calculate and describe the value of a chi-square statistics in context of a real-world problem<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a chi-square 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;:9}\">Write a null and alternative hypothesis for a chi-square test<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p><img class=\"alignright wp-image-1448\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193804\/Education-amico.png\" alt=\"3 animated people. One is standing reading a book gesturing to a white board that says &quot;education&quot;. Another is sitting on a large pile of books on a computer. The third is sitting in a wheelchair holding a tablet. There are various education themed animations surrounding them.\" width=\"301\" height=\"301\" \/><\/p>\r\n<p>In 2014, Harvard was sued by a group of Asian American applicants who were not selected for admission. They claimed racial discrimination. The public release of court documents provided unprecedented access to admissions data[footnote]The data in this lesson were reconstructed from parts of the plaintiff report, in which the defense and plaintiffs generally agreed on the findings. The report: Arcidiacono, P. (2018, June 15). \u201cExhibit A: Expert report of Peter S. Arcidiacono.\u201d Students for Fair Admissions, Inc. v. Harvard. https:\/\/samv91khoyt2i553a2t1s05i-wpengine.netdna-ssl.com\/wp-content\/uploads\/2018\/06\/Doc-415-1-Arcidiacono-Expert-Report.pdf[\/footnote] from a prominent private university. Today, we\u2019ll explore those data and the claim of racial discrimination in admissions.[footnote]Lesson adapted from Skew The Script (skewthescript.org)[\/footnote]<\/p>\r\n<div>\r\n<p>Two important notes about the data we\u2019ll explore for this activity:<\/p>\r\n<ul>\r\n\t<li>Academic index ratings are internal measures of academic qualification produced by the Harvard admissions office. They\u2019re calculated based on standardized test scores and high school grades\/performance.<\/li>\r\n\t<li>The data only display information for four racial groups: Asian American, African American, Hispanic, and White. Other groups (Native American, Mixed Race, etc.) and international students were not included in the court\u2019s main analysis. Percentages are calculated just out of these four groups.<\/li>\r\n<\/ul>\r\n<p>Data on the top academic applicants to Harvard (top 10% in academic index ratings) and on the students who were actually admitted to the Class of 2019 are summarized in the following tables.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td style=\"text-align: center;\">\r\n<p style=\"text-align: left;\"><strong>Class of 2019 Applicants<\/strong><\/p>\r\n<p><strong>Top 10% Academic Index<\/strong><\/p>\r\n<\/td>\r\n<td style=\"text-align: center;\">\r\n<p style=\"text-align: left;\"><strong>\u00a0Class of 2019<\/strong><\/p>\r\n<p><strong>\u00a0Admitted Students<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Group<\/strong><\/td>\r\n<td><strong>%<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Asian American<\/td>\r\n<td>57.5%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Hispanic<\/td>\r\n<td>3.1%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>African American<\/td>\r\n<td>0.8%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>White<\/td>\r\n<td>38.7%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/td>\r\n<td>\r\n<div align=\"center\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Group<\/strong><\/td>\r\n<td><strong>%<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Asian American<\/td>\r\n<td>21.4%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Hispanic<\/td>\r\n<td>12.2%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>African American<\/td>\r\n<td>11.2%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>White<\/td>\r\n<td>55.3%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2340[\/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;Calculate and describe the value of a chi-square statistics in context of a real-world 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;:9}\">Calculate and describe the value of a chi-square statistics in context of a real-world problem<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a chi-square 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;:9}\">Write a null and alternative hypothesis for a chi-square test<\/span><\/li>\n<\/ul>\n<\/section>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-1448\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193804\/Education-amico.png\" alt=\"3 animated people. One is standing reading a book gesturing to a white board that says &quot;education&quot;. Another is sitting on a large pile of books on a computer. The third is sitting in a wheelchair holding a tablet. There are various education themed animations surrounding them.\" width=\"301\" height=\"301\" \/><\/p>\n<p>In 2014, Harvard was sued by a group of Asian American applicants who were not selected for admission. They claimed racial discrimination. The public release of court documents provided unprecedented access to admissions data<a class=\"footnote\" title=\"The data in this lesson were reconstructed from parts of the plaintiff report, in which the defense and plaintiffs generally agreed on the findings. The report: Arcidiacono, P. (2018, June 15). \u201cExhibit A: Expert report of Peter S. Arcidiacono.\u201d Students for Fair Admissions, Inc. v. Harvard. https:\/\/samv91khoyt2i553a2t1s05i-wpengine.netdna-ssl.com\/wp-content\/uploads\/2018\/06\/Doc-415-1-Arcidiacono-Expert-Report.pdf\" id=\"return-footnote-1398-1\" href=\"#footnote-1398-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> from a prominent private university. Today, we\u2019ll explore those data and the claim of racial discrimination in admissions.<a class=\"footnote\" title=\"Lesson adapted from Skew The Script (skewthescript.org)\" id=\"return-footnote-1398-2\" href=\"#footnote-1398-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<div>\n<p>Two important notes about the data we\u2019ll explore for this activity:<\/p>\n<ul>\n<li>Academic index ratings are internal measures of academic qualification produced by the Harvard admissions office. They\u2019re calculated based on standardized test scores and high school grades\/performance.<\/li>\n<li>The data only display information for four racial groups: Asian American, African American, Hispanic, and White. Other groups (Native American, Mixed Race, etc.) and international students were not included in the court\u2019s main analysis. Percentages are calculated just out of these four groups.<\/li>\n<\/ul>\n<p>Data on the top academic applicants to Harvard (top 10% in academic index ratings) and on the students who were actually admitted to the Class of 2019 are summarized in the following tables.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: center;\">\n<p style=\"text-align: left;\"><strong>Class of 2019 Applicants<\/strong><\/p>\n<p><strong>Top 10% Academic Index<\/strong><\/p>\n<\/td>\n<td style=\"text-align: center;\">\n<p style=\"text-align: left;\"><strong>\u00a0Class of 2019<\/strong><\/p>\n<p><strong>\u00a0Admitted Students<\/strong><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Group<\/strong><\/td>\n<td><strong>%<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Asian American<\/td>\n<td>57.5%<\/td>\n<\/tr>\n<tr>\n<td>Hispanic<\/td>\n<td>3.1%<\/td>\n<\/tr>\n<tr>\n<td>African American<\/td>\n<td>0.8%<\/td>\n<\/tr>\n<tr>\n<td>White<\/td>\n<td>38.7%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/td>\n<td>\n<div style=\"margin: auto;\">\n<table>\n<tbody>\n<tr>\n<td><strong>Group<\/strong><\/td>\n<td><strong>%<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Asian American<\/td>\n<td>21.4%<\/td>\n<\/tr>\n<tr>\n<td>Hispanic<\/td>\n<td>12.2%<\/td>\n<\/tr>\n<tr>\n<td>African American<\/td>\n<td>11.2%<\/td>\n<\/tr>\n<tr>\n<td>White<\/td>\n<td>55.3%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2340\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2340&theme=lumen&iframe_resize_id=ohm2340&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1398-1\">The data in this lesson were reconstructed from parts of the plaintiff report, in which the defense and plaintiffs generally agreed on the findings. The report: Arcidiacono, P. (2018, June 15). \u201cExhibit A: Expert report of Peter S. Arcidiacono.\u201d Students for Fair Admissions, Inc. v. Harvard. https:\/\/samv91khoyt2i553a2t1s05i-wpengine.netdna-ssl.com\/wp-content\/uploads\/2018\/06\/Doc-415-1-Arcidiacono-Expert-Report.pdf <a href=\"#return-footnote-1398-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1398-2\">Lesson adapted from Skew The Script (skewthescript.org) <a href=\"#return-footnote-1398-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":9,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1388,"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\/1398"}],"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\/1398\/revisions"}],"predecessor-version":[{"id":5492,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1398\/revisions\/5492"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1388"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1398\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1398"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1398"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1398"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}