An Applet for the Investigation of Simpson’s Paradox by Kady Schneiter and Jürgen Symanzik. (Journal of Statistics Education, Volume 21, Number 1 (2013))
Simpson’s paradox is best illustrated by the University of California, Berkeley sex discrimination case. Taken in the aggregate, admissions to the graduate school appeared to greatly favor men. Taken by department, no department discriminated against women and most favored admission of women. Same data, different level of examination. That is Simpson’s paradox.
Abstract:
This article describes an applet that facilitates investigation of Simpson’s Paradox in the context of a number of real and hypothetical data sets. The applet builds on the Baker-Kramer graphical representation for Simpson’s Paradox. The implementation and use of the applet are explained. This is followed by a description of how the applet has been used in an introductory statistics class and a discussion of student responses to the applet.
From Wikipedia on Simpson’s Paradox:
In probability and statistics, Simpson’s paradox, or the Yule–Simpson effect, is a paradox in which a trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data. This result is often encountered in social-science and medical-science statistics,[1] and is particularly confounding when frequency data are unduly given causal interpretations.[2] Simpson’s Paradox disappears when causal relations are brought into consideration.
A cautionary tale about the need to understand data sets and how combining them may impact outcomes of statistical analysis.