In small samples, maximum likelihood (ML) estimates of logit model coefficients have substantial bias away from zero. As a solution, we remind political scientists of Firth's (1993, Biometrika, 80, 27–38) penalized maximum likelihood (PML) estimator. Prior research has described and used PML, especially in the context of separation, but its small sample properties remain under-appreciated. The PML estimator eliminates most of the bias and, perhaps more importantly, greatly reduces the variance of the usual ML estimator. Thus, researchers do not face a bias-variance tradeoff when choosing between the ML and PML estimators—the PML estimator has a smaller bias and a smaller variance. We use Monte Carlo simulations and a re-analysis of George and Epstein (1992, American Political Science Review, 86, 323–337) to show that the PML estimator offers a substantial improvement in small samples (e.g., 50 observations) and noticeable improvement even in larger samples (e.g., 1000 observations).

Political science is gradually moving away from an exclusive focus on statistical significance and toward an emphasis on the magnitude and importance of effects. While we welcome this change, we argue that the current practice of “magnitude-and-significance,” in which researchers only interpret the magnitude of a statistically significant point estimate, barely improves the much-maligned “sign-and-significance” approach, in which researchers focus only on the statistical significance of an estimate. This exclusive focus on the point estimate hides the uncertainty behind a veil of statistical significance. Instead, we encourage researchers to explicitly account for uncertainty by interpreting the range of values contained in the confidence interval. Especially when making judgments about the importance of estimated effects, we advise researchers to make empirical claims if and only if those claims hold for the entire confidence interval.