We propose a new Bayesian approach to predict the unobserved potential outcome for a treated unit in order to draw causal inferences on individual treatment effects with binary outcomes. Building on the canonical method of difference, we show that even with n=4, small-n studies can have similar false positive rates to those of large-n randomized control trials under reasonable assumptions. Our method allows for the replicability and credibility of small-n studies to be assessed on the same standards as large-n research and shows that well-constructed comparative studies can compare favorably to many large-n studies. Our methods are applied to an analysis of the effect on independencef for Guinea of Sékou Touré’s public opposition to de Gaulle’s proposed constitution for France and its colonies in 1958.