Necessary sample sizes for specified closeness and confidence of matched data under the skew normal setting

Abstract

Previous researchers have shown how to compute a priori confidence interval (as opposed to sample-based confidence intervals) for means, assuming normal distributions (Trafimow 2017; Trafimow and MacDonald 2017); or for locations, assuming skew normal distributions (Trafimow et al. 2018). The present work extends a priori thinking to an important case not addressed previously, where the researcher is interested in the difference between means or the difference in locations across two matched samples. The proposed procedure can be used under the assumption that both samples come from normal distributions or skew normal distributions. Computer simulations support the equations presented, along with an example with real data.

Keywords:

• Skew normal
• Sampling precision
• Matched data