The stability of bivariate correlations: A Bayesian approach

Dnr:

SNIC 2022/22-1182

Type:

SNIC Small Compute

Principal Investigator:

Carl Delfin

Affiliation:

Lunds universitet

Start Date:

2022-12-04

End Date:

2024-01-01

Primary Classification:

10106: Probability Theory and Statistics

Webpage:

- Centre Storage at NSC: 500 GiB
- Tetralith at NSC: 5 x 1000 core-h/month

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.