Reliability and statistical power: Conceptual background and practical implications

In behavioral sciences, robust phenomena having large effect sizes and related statistical power may be unreliable. This relation is in contrast with the view that both statistical power and reliability depend similarly on the measurement error. In this view, robust but unreliable phenomena can be considered as a reliability paradox. The mathematical relation and possible independence of statistical power and reliability have been discussed in the statistical literature for decades. A common misconception related to the relationship between statistical power and reliability is that absolute reliability (measurement error) is often confounded with relative reliability (ratio of the true score variance and the total score variance). The present work reviews and discusses how measurement error and individual differences influence the relative reliability and robustness of a phenomenon. It discusses why relative reliability and robustness are partly related and why they are generally independent. Following these considerations, it is summarized how measurement error and group heterogeneity can be potentially manipulated to optimize for the reliability and robustness of a measured phenomenon.