From a Sampling Precision Perspective, Skewness Is a Friend and Not an Enemy!

Abstract

Two recent publications in Educational and Psychological Measurement advocated that researchers consider using the a priori procedure. According to this procedure, the researcher specifies, prior to data collection, how close she wishes her sample mean(s) to be to the corresponding population mean(s), and the desired probability of being that close. A priori equations provide the necessary sample size to meet specifications under the normal distribution. Or, if sample size is taken as given, a priori equations provide the precision with which estimates of distribution means can be made. However, there is currently no way to perform these calculations under the more general family of skew-normal distributions. The present research provides the necessary equations. In addition, we show how skewness can increase the precision with which locations of distributions can be estimated. This conclusion, based on the perspective of improving sampling precision, contrasts with a typical argument in favor of performing transformations to normalize skewed data for the sake of performing more efficient significance tests.