{"id":5483,"date":"2022-09-14T09:04:30","date_gmt":"2022-09-14T09:04:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5483"},"modified":"2022-10-02T14:31:13","modified_gmt":"2022-10-02T14:31:13","slug":"15a-inclass","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/15a-inclass\/","title":{"raw":"15A InClass","rendered":"15A InClass"},"content":{"raw":"
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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 data1 from a prominent private university. Today, we\u2019ll explore those data and the claim of racial discrimination in admissions.2 Two important notes about the data we\u2019ll explore for this in-class activity: \u2022Academic 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.\u2022The data only display information for four racial groups: AsianAmerican, AfricanAmerican, 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 fourgroups.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.<\/div>\r\n<\/div>\r\n
<\/div>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group<\/strong><\/td>\r\n%<\/strong><\/td>\r\n<\/tr>\r\n
Asian American<\/td>\r\n57.5%<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n3.1%<\/td>\r\n<\/tr>\r\n
African American<\/td>\r\n0.8%<\/td>\r\n<\/tr>\r\n
White<\/td>\r\n38.7%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group<\/strong><\/td>\r\n%<\/strong><\/td>\r\n<\/tr>\r\n
Asian American<\/td>\r\n21.4%<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n12.2%<\/td>\r\n<\/tr>\r\n
African American<\/td>\r\n11.2%<\/td>\r\n<\/tr>\r\n
White<\/td>\r\n55.3%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
\r\n
\r\n

Question 1<\/h3>\r\n1) Would it be appropriate to conduct four two-sample z-tests for proportions to compare the admission rates for each group\u2014Applicants vs. Admitted Students? Explain.1<\/sup> The data in this lesson were reconstructed from parts of the plaintiff report, in which the defense and plaintiffs generally agreed on the findings.T he report: Arcidiacono, P.(2018, June 15).\u201cExhibit A: Expert reportof 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.pdf2Lesson adapted from Skew The Script (skewthescript.org)Source:Plaintiff report, Table B.5.7 Source:Harvard Gazette\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
Imagine that Harvard claims: \u201cWe only accept the top academic applicants and we treat those applicants equally. Our admitted class is as good as a random sample from the distribution of top academic applicants.\u201d You would like to decide if there\u2019s convincing evidence against this claim. Formally, the null hypothesis, \ud835\udc3b0, is that the distribution of the admitted group is the same as the distribution of the top academic applicants. The alternative hypothesis, \ud835\udc3b\ud835\udc34, is that the distribution of the admitted group is different than the distribution of the top academic applicants.<\/div>\r\n
\r\n
\r\n

Question 2<\/h3>\r\n2) In total, Harvard admitted \ud835\udc5b=2023 applicants from these racial groups to the Class of 2019. How many would you expect to admit from each group if it was a random samplefrom the pool of top academic applicants?Fill in the expected counts in the following table.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group<\/strong><\/td>\r\n%<\/strong><\/td>\r\n<\/tr>\r\n
Asian American<\/td>\r\n57.5%<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n3.1%<\/td>\r\n<\/tr>\r\n
African American<\/td>\r\n0.8%<\/td>\r\n<\/tr>\r\n
White<\/td>\r\n38.7%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n

Question 3<\/h3>\r\n3) The followingis the formula for the chi-square test statistic:\ud835\udf122=\u2211(Observed\u2212Expected)2ExpectedGroup%Expected CountsAsianAmerican57.4%Hispanic3.1%AfricanAmerican0.8%White38.7%Population of TopAcademic Applicants\r\nPart A: Why do we square the differences between observed and expected values?\r\nPart B: Why do we divide by the expected values?\r\nPart C: Why do we sumup the (Observed\u2212Expected)2Expectedquantitiesbetween all the categories?\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 4<\/h3>\r\n4)The observed counts of students actually admitted to the Class of 2019 are provided in the following table.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Group<\/strong><\/td>\r\nExpected Count<\/strong><\/td>\r\nObserved Count<\/strong><\/td>\r\n<\/td>\r\n<\/tr>\r\n
Asian American<\/td>\r\n1161.202<\/td>\r\n432<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Hispanic<\/td>\r\n62.713<\/td>\r\n247<\/td>\r\n<\/td>\r\n<\/tr>\r\n
African American<\/td>\r\n16.184<\/td>\r\n226<\/td>\r\n<\/td>\r\n<\/tr>\r\n
White<\/td>\r\n782.901<\/td>\r\n1118<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nPart A: Which groups were admitted less often than expected? Which groups were admitted more often than expected?\r\nPart B: Without performing any calculations, do you believe the observed and expected counts are different enoughto refute the claim that admitted students are essentially a random sample from the pool of top academic applicants? Explain.\r\nPart C: Now, let\u2019s calculate the value of the chi-square statistic to quantify the overall distance between the observed and expected counts.Fill in the final columnof the previous table.\r\nPart D: Add the results to get the value of the chi-square statistic. Record your answer.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
\r\n
\r\n
\r\n

Question 5<\/h3>\r\n5) To assess what our chi-square value tells us about the distancebetween the expected and observed values, we turn to the chi-square distribution, assuming the conditions of using the chi-square distribution aremet (we will talk aboutthese conditions in next activity).Goto the DCMPChi-Square Testtool at https:\/\/dcmathpathways.shinyapps.io\/ChiSquaredTest\/.Select the Goodness of Fittab. Under \u201cEnter Data,\u201d choose the \u201cContingency Table\u201d option. Enter the relevant data and proportions and press \u201cSubmit.\u201d Confirm that the simulation\u2019s chi-square test statistic matches the one you calculated in Part D of Question 4. Then, comment on what the calculatedprobability(P-value)suggestsabout the claim that the admitted students are essentially a random sample from the pool of top academic applicants.\r\n\r\n<\/div>\r\n
\r\n

Question 6<\/h3>\r\n6) In addition to relatively high academic ratings, the plaintiff report also found thatAsian American applicants tended to receive better extracurricular ratings from Harvard(on average)compared to the other racial groups. Imagine that the plaintiffs argued thatthis evidence, along with your previous calculations,proves racial discrimination. How might Harvard\u2019s lawyersdefend the school\u2019s admissions policy? Explain.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"
\n
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 data1 from a prominent private university. Today, we\u2019ll explore those data and the claim of racial discrimination in admissions.2 Two important notes about the data we\u2019ll explore for this in-class activity: \u2022Academic 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.\u2022The data only display information for four racial groups: AsianAmerican, AfricanAmerican, 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 fourgroups.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.<\/div>\n<\/div>\n
<\/div>\n\n\n\n\n\n\n\n
Group<\/strong><\/td>\n%<\/strong><\/td>\n<\/tr>\n
Asian American<\/td>\n57.5%<\/td>\n<\/tr>\n
Hispanic<\/td>\n3.1%<\/td>\n<\/tr>\n
African American<\/td>\n0.8%<\/td>\n<\/tr>\n
White<\/td>\n38.7%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n\n\n\n\n\n\n\n
Group<\/strong><\/td>\n%<\/strong><\/td>\n<\/tr>\n
Asian American<\/td>\n21.4%<\/td>\n<\/tr>\n
Hispanic<\/td>\n12.2%<\/td>\n<\/tr>\n
African American<\/td>\n11.2%<\/td>\n<\/tr>\n
White<\/td>\n55.3%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n
\n

Question 1<\/h3>\n

1) Would it be appropriate to conduct four two-sample z-tests for proportions to compare the admission rates for each group\u2014Applicants vs. Admitted Students? Explain.1<\/sup> The data in this lesson were reconstructed from parts of the plaintiff report, in which the defense and plaintiffs generally agreed on the findings.T he report: Arcidiacono, P.(2018, June 15).\u201cExhibit A: Expert reportof 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.pdf2Lesson adapted from Skew The Script (skewthescript.org)Source:Plaintiff report, Table B.5.7 Source:Harvard Gazette<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
Imagine that Harvard claims: \u201cWe only accept the top academic applicants and we treat those applicants equally. Our admitted class is as good as a random sample from the distribution of top academic applicants.\u201d You would like to decide if there\u2019s convincing evidence against this claim. Formally, the null hypothesis, \ud835\udc3b0, is that the distribution of the admitted group is the same as the distribution of the top academic applicants. The alternative hypothesis, \ud835\udc3b\ud835\udc34, is that the distribution of the admitted group is different than the distribution of the top academic applicants.<\/div>\n
\n
\n

Question 2<\/h3>\n

2) In total, Harvard admitted \ud835\udc5b=2023 applicants from these racial groups to the Class of 2019. How many would you expect to admit from each group if it was a random samplefrom the pool of top academic applicants?Fill in the expected counts in the following table.<\/p>\n\n\n\n\n\n\n\n
Group<\/strong><\/td>\n%<\/strong><\/td>\n<\/tr>\n
Asian American<\/td>\n57.5%<\/td>\n<\/tr>\n
Hispanic<\/td>\n3.1%<\/td>\n<\/tr>\n
African American<\/td>\n0.8%<\/td>\n<\/tr>\n
White<\/td>\n38.7%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n
\n
\n

Question 3<\/h3>\n

3) The followingis the formula for the chi-square test statistic:\ud835\udf122=\u2211(Observed\u2212Expected)2ExpectedGroup%Expected CountsAsianAmerican57.4%Hispanic3.1%AfricanAmerican0.8%White38.7%Population of TopAcademic Applicants
\nPart A: Why do we square the differences between observed and expected values?
\nPart B: Why do we divide by the expected values?
\nPart C: Why do we sumup the (Observed\u2212Expected)2Expectedquantitiesbetween all the categories?<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

Question 4<\/h3>\n

4)The observed counts of students actually admitted to the Class of 2019 are provided in the following table.<\/p>\n\n\n\n\n\n\n\n
Group<\/strong><\/td>\nExpected Count<\/strong><\/td>\nObserved Count<\/strong><\/td>\n<\/td>\n<\/tr>\n
Asian American<\/td>\n1161.202<\/td>\n432<\/td>\n<\/td>\n<\/tr>\n
Hispanic<\/td>\n62.713<\/td>\n247<\/td>\n<\/td>\n<\/tr>\n
African American<\/td>\n16.184<\/td>\n226<\/td>\n<\/td>\n<\/tr>\n
White<\/td>\n782.901<\/td>\n1118<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Part A: Which groups were admitted less often than expected? Which groups were admitted more often than expected?
\nPart B: Without performing any calculations, do you believe the observed and expected counts are different enoughto refute the claim that admitted students are essentially a random sample from the pool of top academic applicants? Explain.
\nPart C: Now, let\u2019s calculate the value of the chi-square statistic to quantify the overall distance between the observed and expected counts.Fill in the final columnof the previous table.
\nPart D: Add the results to get the value of the chi-square statistic. Record your answer.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
\n

Question 5<\/h3>\n

5) To assess what our chi-square value tells us about the distancebetween the expected and observed values, we turn to the chi-square distribution, assuming the conditions of using the chi-square distribution aremet (we will talk aboutthese conditions in next activity).Goto the DCMPChi-Square Testtool at https:\/\/dcmathpathways.shinyapps.io\/ChiSquaredTest\/.Select the Goodness of Fittab. Under \u201cEnter Data,\u201d choose the \u201cContingency Table\u201d option. Enter the relevant data and proportions and press \u201cSubmit.\u201d Confirm that the simulation\u2019s chi-square test statistic matches the one you calculated in Part D of Question 4. Then, comment on what the calculatedprobability(P-value)suggestsabout the claim that the admitted students are essentially a random sample from the pool of top academic applicants.<\/p>\n<\/div>\n

\n

Question 6<\/h3>\n

6) In addition to relatively high academic ratings, the plaintiff report also found thatAsian American applicants tended to receive better extracurricular ratings from Harvard(on average)compared to the other racial groups. Imagine that the plaintiffs argued thatthis evidence, along with your previous calculations,proves racial discrimination. How might Harvard\u2019s lawyersdefend the school\u2019s admissions policy? Explain.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":23592,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-5483","chapter","type-chapter","status-publish","hentry"],"part":5479,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5483","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/23592"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5483\/revisions"}],"predecessor-version":[{"id":5599,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5483\/revisions\/5599"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/5479"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5483\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5483"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5483"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5483"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}