Introduction to Chi-Square Statistics – Apply It 1

  • Calculate and describe the value of a chi-square statistics in context of a real-world problem
  • Write a null and alternative hypothesis for a chi-square test

3 animated people. One is standing reading a book gesturing to a white board that says "education". 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.

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[1] 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 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: Asian American, African American, 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 four groups.

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.

Class of 2019 Applicants

Top 10% Academic Index

 Class of 2019

 Admitted Students

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%

  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). “Exhibit A: Expert report of 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.pdf
  2. Lesson adapted from Skew The Script (skewthescript.org)