A study of confidence intervals for Cohen's dp in within-subject designs with new proposals

Abstract

There exist many variants of confidence intervals for Cohen's d_p in within-subject designs. Herein, we review three past proposals (Morris, 2000; Algina & Keselman, 2003, Goulet-Pelletier & Cousineau, 2018) and examine five new ones, four of which are based on the recently discovered distribution of d_p in such design. We examine each method according to their accuracy in coverage rate (desired coverage is 95% in this study), symmetry (i. e., equal rejection rates from the left and from the right), and width of the interval. It is found that the past three proposals are pseudo confidence intervals, being too liberal under some circumstances (fortunately uncommon for the methods of Morris and Algina & Keselman). Additionally, they are not asymptotically accurate. Finally, they do not have symmetrical rejection rates on the left and on the right. Four of the five new techniques are asymptotically accurate but three of these are liberal for small samples. Finally, the relation of confidence intervals with inferential statistics testing is considered.

Keywords

• standardized mean difference
• confidence interval
• within-subject design
• noncentral t distribution
• noncentral lambda distribution
• r