Feb 1

3:30 pm

## Two Statistical Vignettes: Simpson\'s Paradox and Shaved Dice

### Michael Perlman

Seminar

University of Washington - Department of Statistics

1. Simpson's Paradox occurs for events A, B, and C if A and B are positively correlated given B, positively correlated given not-B, but are negatively correlated in the aggregate. If a 2x2x2 table is chosen "at random," what is the probability that it will exhibit Simpson's Paradox?

2. Persi Diaconis has fascinated audiences at all levels with the following question: If one face of a standard gaming die is shaved uniformly by a specified fraction s, express the new face probabilities as a function of s. This apparently simple problem appears to be intractable. However, this leads to an interesting statistical question: if the shaved dice are thrown in pairs, as typical in the game of craps, what is the most efficient die design for accurate estimation of the new face probabilities?