Simpson’s Paradox and Discrimination

Readers of the News Blog will have encountered an example of Simpson’s paradox in a previous blog, applied first to base-ball strikers’ averages and then to the beguilingly appealing issue of Standardised Mortality Rates. Prof. Tony Belli, director of the NIHR Surgical Reconstruction and Microbiology Research Centre in Birmingham, recently drew the CLAHRC WM Director’s attention to another fascinating example; this time arising from discrimination cases in American courts.[1] [2] You will remember that Simpson’s paradox can arise by aggregating data across strata where the strata vary in size and where outcome rates differ across strata. The departments of English and History attract large numbers of applicants, a high proportion of whom are women, and rejection rates are high. Mathematics and Physics, by contrast, attract fewer applicants, a high proportion of whom are male, and rejection rates are low. Simple aggregation, ignoring the interaction between acceptance rates and applicant numbers, results in the mistaken conclusion that there is discrimination against women, rather than the correct conclusion that women favour popular subjects with high rejection rates. To avoid this problem it is necessary to use a method of aggregation based on weighted averages of strata specific estimates.

— Richard Lilford, CLAHRC WM Director


  1. Borhani H. Bias in Measuring Bias. American Bar Association Labour and Employment Section’s Annual CLE. Washington D.C. November 4–7 2009.
  2. Bickel PJ, Hammel EA, O’Connell JW. Sex Bias in Graduate Admissions: Data from Berkeley. Science. 1975. 187(4175): 398-404.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s