ABSTRACT
An unusual phenomenon occurs so frequently in the analysis of multiway contingency tables that it has been given the label of “Simpson’s Paradox” (Simpson, 1951; Yule, 1903). Basically, various relations that appear to be present when data are conditioned on the levels of one variable, either disappear or change “direction” when aggregation occurs over the levels of the conditioning variable. A well-known real-life example is the Berkeley sex bias case applicable to graduate school (Bickel, Hammel, & O’Connell, 1975). The table below shows the aggregate admission figures for the fall of 1973:
Number of applicants Percent admitted
Men 8442 44 Women 4321 35
Given these data, there appears to be a primae facie case for bias because a lower percentage of women than men is admitted.
