The a Priori Procedure (APP) for Estimating the Cohen's Effect Size for Matched Pairs Under Skew Normal Settings

The a priori procedure (APP) provides minimum sample sizes to meet specifications for precision and confidence that, in turn, can enhance trust that the sample statistics to be obtained provide good estimates of corresponding population parameters. A recent advance by Chen et al.(3) showed how to perform the APP with respect to Cohen's d, which is the most popular effect size measure in the social sciences. However, a limitation is that Chen et al.(3) assumed normal distributions that compose only a subset of the much larger family of skew normal distributions, which are used as distributions of random errors in many economical models such as stochastic frontier models that are popular and useful models to investigate production efficiency in microeconomics, see Hung.(5) Therefore, it would be useful to generalize to skew normal distributions. We perform the mathematical derivations for the generalization and support them with simulations and worked examples. Finally, we provide a free and user-friendly computer program by which researchers can perform the APP to determine minimum sample sizes necessary to meet specifications for precision and confidence, with respect to Cohen's d, for a matched sample under the large umbrella of skew normal distributions.