An appropriate estimate of statistical power is critical for the design of intervention studies. Although the inclusion of a pretest covariate in the test of the primary outcome can increase statistical power, samples selected on the basis of pretest performance may demonstrate range restriction on the selection measure and other correlated measures. This can result in attenuated pretest–posttest correlations, reducing the variance explained by the pretest covariate. The authors investigated the implications of two potential range restriction scenarios: direct truncation on a selection measure and indirect range restriction on correlated measures. Empirical and simulated data indicated that direct range restriction on the pretest covariate greatly reduced statistical power and necessitated sample size increases of 82%–155% (dependent on selection criteria) to achieve equivalent statistical power to parameters with unrestricted samples. However, measures demonstrating indirect range restriction required much smaller sample size increases (32%–71%) under equivalent scenarios. Additional analyses manipulated the correlations between measures and pretest–posttest correlations to guide planning experiments. Results highlight the need to differentiate between selection measures and potential covariates and to investigate range restriction as a factor impacting statistical power.
Miciak, J., Taylor, W. P., Stuebing, K. K., Fletcher, J. M., & Vaughn, S. (2016). Designing intervention studies: Selected populations, range restrictions, and statistical power. Journal of Research on Educational Effectiveness, 9, 556-569.