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Why is Simpson's paradox a paradox?

Simpson's paradox is the phenomenon whereby the direction of association present within stratified tables is reversed in the marginal table. The controversy in the 1970's over apparent gender-bias in admissions to Berkeley is a well-known instance.

Simpson's paradox is well understood from a statistical perspective. However, the traditional analysis leaves open the following questions:

Why do we describe this phenomenon as paradoxical?
When is it appropriate to stratify?
In this talk I will review work by Judea Pearl and others which attempts to answer these questions by making reference to causal concepts.