More on Simpson’s paradox and the analysis of memory retrieval

Abstract

A common way of analyzing the statistical relation between two tests of memory is to use contingency analyses. A potential problem with such analyses is known as Simpson’s paradox. The paradox is that collapsing two or more contingency tables may have the effect that the relationship expressed in the overall contingency table differs from the relationships expressed in the original tables. The paradox arises when covariates are correlated with each of the tests. It has been claimed that the paradox has implications for the analysis of memory retrieval, and ways of solving the problem have been called for (Hintzman, 1980). In this paper, partial gamma (Davis, 1967) is suggested as one possible solution. This method can be used to compute a weighted average of the results in the original tables. The use of partial gamma is exemplified by applying it to hypothetical instances of Simpson’s paradox. © 1993, Psychonomic Society, Inc.. All rights reserved.