The stability of bivariate correlations: A Bayesian approach
Title: The stability of bivariate correlations: A Bayesian approach
DNr: SNIC 2022/22-1182
Project Type: SNIC Small Compute
Principal Investigator: Carl Delfin <>
Affiliation: Lunds universitet
Duration: 2022-12-04 – 2024-01-01
Classification: 10106


As sample size increases, sample correlations converge to the population correlation. At small sample sizes, however, the estimates are often unstable. Previous work based on frequentist statistics has shown that in typical circumstances in psychological research, correlations stabilize at a sample size of around 250. The Bayesian approach allows for incorporating prior knowledge, however, which could lead to stability at even smaller sample sizes. The current project simulates data from a population with a known correlation coefficient, and then estimates the sample correlation as samples are sequentially added from the population (from n = 5 to n = 500, at n = 5 intervals. This process is repeated several times, for different population correlations (ρ = 0.1, 0.2, 0.3, 0.4, 0.5), and using different prior distributions (weakly, moderately, and highly informative). The primary aims are to compare the stability and convergence of the Bayesian approach to a classic frequentist approach, and to examine the impact of different priors.