LAUSR

Power analysis is the gold standard for justifying sample size in study design. Extant software for computing power (e.g., G Power by Faul, Erdfelder, Buchner, & Lang, 2009) can only accept the specification of a single effect size. Implicit in this single effect size specification is the unrealistic assumption that the inputted value is the (unknown) population value. By ignoring the uncertainty underlying the specification of population effect sizes, estimated power is locally optimal (Du & Wang, 2016). Local optimality means that power estimates are inaccurate when specified effect sizes exhibit any departure from the unknown population value. To address local optimality, researchers should explicitly quantify epistemic uncertainty of the unknown effect size that arises from a lack of knowledge (O’Hagan, 2004). Indeed, epistemic uncertainty about the effect size can be represented formally by an informative Bayesian design prior. This approach is a Bayesian-frequentist hybrid because a Bayesian design prior is used to modify power analysis for frequentist null hypothesis significance tests. We introduce a new R package, HybridPower, which allows researchers to apply the Bayesian-frequentist hybrid approach to power analysis in study design. Here, a distribution of power estimates is computed from a random sample of effect sizes drawn from a userspecified design prior. Helper functions can visualize the distribution of power estimates, and calculate the mean of the power distribution (i.e., assurance; Figure 1. Estimated power distributions by sample size for an independent samples t-test. A normal prior distribution, N(25, 7), was used for the unstandardized mean difference in reaction time (in milliseconds) for a Stroop task. Variance in each group was equal to 45. Squares, crosses, and the upper and lower dots denote the mean, median, as well as upper and lower 20th percentiles of the distribution of power estimates, respectively. CONTACT Joonsuk Park [email protected] 221 N Lazenby Hall, 1827 Neil Avenue, Columbus, OH 43210, USA. 2019 Taylor & Francis Group, LLC MULTIVARIATE BEHAVIORAL RESEARCH 2019, VOL. 54, NO. 1, 151–152 https://doi.org/10.1080/00273171.2018.1557032 O’Hagan & Stevens, 2001), which can inform the study’s sample size. Unlike a single power estimate computed from a single effect size specification, assurance is robust to local optimality. In Figure 1, power estimates obtained from the Bayesian-frequentist hybrid approach are illustrated with an example where a study is to be designed for testing a mean difference in reaction times on a Stroop task (e.g., see Williams, Mathews, & MacLeod, 1996). Currently, HybridPower can compute power for a broad class of tests including t-tests for mean differences, correlations, one-way ANOVA, and popular nonparametric procedures.