Data_Sheet_1_Improving the stability of bivariate correlations using informative Bayesian priors: a Monte Carlo simulation study.PDF

ObjectiveMuch 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.MethodsSimulated data from four populations with known bivariate correlations (ρ = 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.ResultsThe 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.ConclusionInformative 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.

研究目的：众多心理学研究因样本量有限和统计功效不足而遭受困扰，导致参数估计不稳定。贝叶斯方法通过将先验知识融入统计模型，为解决此问题提供了有前景的解决方案，相较于频率主义方法，可能带来更高的稳定性。研究方法：本研究采用四个已知双变量相关系数（ρ = 0.1, 0.2, 0.3, 0.4）的模拟数据集，通过从每个种群中依次增加样本（从n=10至n=500），来估计样本相关系数。研究调查并比较了三种主观定义的先验分布（弱、中、高度信息性）对频率主义模型的影响。研究结果：结果显示，双变量相关系数估计存在不稳定性，且在样本量低于100时，获得夸张或错误方向的估计风险相对较高，尤其是在样本量低于50时。然而，这种不稳定性可以通过信息性贝叶斯先验得到约束。研究结论：信息性贝叶斯先验具有显著降低样本量需求并确保获得的估计值与实际预期相符的潜力。特别是在样本量较小的研究情况下，弱信息性先验的稳定和规范效应尤为有用。更信息性的贝叶斯先验的影响取决于个人对概率的阈值以及对估计仅需正确方向还是需高精度估计（其相关区间位于较窄范围内）的目标。关于样本量需求和未来研究方向的影响讨论也在其中。