Improving the stability of bivariate correlations using informative Bayesian priors: a Monte Carlo simulation study.

Abstract

Much of psychological research has suffered from small sample sizes and low statistical power, resulting in unstable parameter estimates. The Bayesian approach offers a promising solution by incorporating prior knowledge into statistical models, which may lead to improved stability compared to a frequentist approach. Simulated data from four populations with known bivariate correlations ( = 0.1, 0.2, 0.3, 0.4) was used to estimate the sample correlation as samples were sequentially added from the population, from n = 10 to n = 500. The impact of three different, subjectively defined prior distributions (weakly, moderately, and highly informative) was investigated and compared to a frequentist model. The results show that bivariate correlation estimates are unstable, and that the risk of obtaining an estimate that is exaggerated or in the wrong direction is relatively high, for sample sizes for below 100, and considerably so for sample sizes below 50. However, this instability can be constrained by informative Bayesian priors. Informative Bayesian priors have the potential to significantly reduce sample size requirements and help ensure that obtained estimates are in line with realistic expectations. The combined stabilizing and regularizing effect of a weakly informative prior is particularly useful when conducting research with small samples. The impact of more informative Bayesian priors depends on one's threshold for probability and whether one's goal is to obtain an estimate merely in the correct direction, or to obtain a high precision estimate whose associated interval falls within a narrow range. Implications for sample size requirements and directions for future research are discussed.