Sample size matters when estimating test-retest reliability of behaviour.

Intraclass correlation coefficients (ICCs) are a commonly used metric in test-retest reliability research to assess a measure's ability to quantify systematic between-subject differences. However, estimates of between-subject differences are also influenced by factors including within-subject variability, random errors, and measurement bias. Here, we use data collected from a large online sample (N = 150) to (1) quantify test-retest reliability of behavioural and computational measures of reversal learning using ICCs, and (2) use our dataset as the basis for a simulation study investigating the effects of sample size on variance component estimation and the association between estimates of variance components and ICC measures. In line with previously published work, we find reliable behavioural and computational measures of reversal learning, a commonly used assay of behavioural flexibility. Reliable estimates of between-subject, within-subject (across-session), and error variance components for behavioural and computational measures (with ± .05 precision and 80% confidence) required sample sizes ranging from 10 to over 300 (behavioural median N: between-subject = 167, within-subject = 34, error = 103; computational median N: between-subject = 68, within-subject = 20, error = 45). These sample sizes exceed those often used in reliability studies, suggesting that sample sizes larger than are commonly used for reliability studies (circa 30) are required to robustly estimate reliability of task performance measures. Additionally, we found that ICC estimates showed highly positive and highly negative correlations with between-subject and error variance components, respectively, as might be expected, which remained relatively stable across sample sizes. However, ICC estimates were weakly or not correlated with within-subject variance, providing evidence for the importance of variance decomposition for reliability studies.