Homogeneity of Subpopulations and Simpson's Paradox

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Abstract
Pooling of information from subpopulations achieves data compactification, but some characteristics of the data are lost in the process. The greatest danger in amalgamating contingency tables is the possibility of a resulting paradox. Many such have been noted since 1903, when Yule first noticed this phenomenon. We note three types of paradoxes. The definition of homogeneity proposed here is a sufficient condition to avoid Yule's Reversal Paradox. We look at interpretations of this definition and some examples. We also explore the connection of this definition with Lindley and Novick's necessary condition for the paradox.

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