In political science and related disciplines in the social and behavioral sciences, there exists an unfortunate de facto divide between qualitative and quantitative empirical research. Sometimes this divide is purely a function of training and disciplinary socialization, but often it reflects a valid dispute over the philosophical foundations of inquiry. I argue here that the Bayesian approach to quantitative empirical modeling is an amenable starting point for building a rapprochement between qualitative and quantitative research, and I introduce as an example a straightforward model that allows for the Bayesian estimation of the difference between means of very small samples with unknown and possibly unequal variances. I then extend this approach to consider nonnormal variates, informative priors, and a multivariate test of the difference of means useful for the researcher who is interested in determining whether two small samples are different on several dimensions simultaneously.