Regression analysis in comparative research suffers from two distinct
problems of statistical inference. First, because the data constitute
all the available observations from a population, conventional inferen
ce based on the long-run behavior of a repeatable data mechanism is no
t appropriate. Second, the small and collinear data sets of comparativ
e research yield imprecise estimates of the effects of explanatory var
iables. We describe a Bayesian approach to statistical inference that
provides a unified solution to these two problems. This approach is il
lustrated in a comparative analysis of unionization.