Clarifying the reliability paradox: poor test-retest reliability attenuates group differences

Cognitive sciences are grappling with the reliability paradox: measures that robustly produce within-group effects tend to have low test-retest reliability, rendering them unsuitable for studying individual differences. Despite the growing awareness of this paradox, its full extent remains underappreciated. Specifically, most research focuses exclusively on how reliability affects correlational analyses of individual differences, while largely ignoring its effects on studying group differences. Moreover, by conflating within- and between-group effects, some studies erroneously suggest that poor reliability does not pose problems for studying group differences. This brief report aims to clarify this misunderstanding through simple data simulations. To make the argument more intuitive, we consider two illustrative cases: comparing patients versus controls and comparing two groups formed by a median split. We demonstrate that reliability attenuates observed group differences just as much as it attenuates individual differences. Given that dichotomizing/grouping continuous data - which is implicit in many group differences analyses - leads to a loss of statistical power, low reliability proves to be even more problematic for studying group differences. While here we focused on cognitive sciences and psychiatry, our findings are quite general and could inform many other areas of research, including education, sex, gender, age, race, ethnicity, etc.