15A InClass

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’ll explore those data and the claim of racial discrimination in admissions.2 Two important notes about the data we’ll explore for this in-class activity: •Academic index ratings are internal measures of academic qualification produced by the Harvard admissions office. They’re calculated based on standardized test scores and high school grades/performance.•The 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’s 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.
Group %
Asian American 57.5%
Hispanic 3.1%
African American 0.8%
White 38.7%
Group %
Asian American 21.4%
Hispanic 12.2%
African American 11.2%
White 55.3%

Question 1

1) Would it be appropriate to conduct four two-sample z-tests for proportions to compare the admission rates for each group—Applicants vs. Admitted Students? Explain.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.T he report: Arcidiacono, P.(2018, June 15).“Exhibit A: Expert reportof Peter S. Arcidiacono.” 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

Imagine that Harvard claims: “We 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.” You would like to decide if there’s convincing evidence against this claim. Formally, the null hypothesis, 𝐻0, is that the distribution of the admitted group is the same as the distribution of the top academic applicants. The alternative hypothesis, 𝐻𝐴, is that the distribution of the admitted group is different than the distribution of the top academic applicants.

Question 2

2) In total, Harvard admitted 𝑛=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.

Group %
Asian American 57.5%
Hispanic 3.1%
African American 0.8%
White 38.7%

Question 3

3) The followingis the formula for the chi-square test statistic:𝜒2=∑(Observed−Expected)2ExpectedGroup%Expected CountsAsianAmerican57.4%Hispanic3.1%AfricanAmerican0.8%White38.7%Population of TopAcademic Applicants
Part A: Why do we square the differences between observed and expected values?
Part B: Why do we divide by the expected values?
Part C: Why do we sumup the (Observed−Expected)2Expectedquantitiesbetween all the categories?

Question 4

4)The observed counts of students actually admitted to the Class of 2019 are provided in the following table.

Group Expected Count Observed Count
Asian American 1161.202 432
Hispanic 62.713 247
African American 16.184 226
White 782.901 1118

Part A: Which groups were admitted less often than expected? Which groups were admitted more often than expected?
Part 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.
Part C: Now, let’s 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.
Part D: Add the results to get the value of the chi-square statistic. Record your answer.

Question 5

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 “Enter Data,” choose the “Contingency Table” option. Enter the relevant data and proportions and press “Submit.” Confirm that the simulation’s 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.

Question 6

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’s lawyersdefend the school’s admissions policy? Explain.