An Improved Effect Size for Single-Case Research: Nonoverlap of All Pairs

Abstract

Nonoverlap of All Pairs (NAP), an index of data overlap between phases in single-case research, is demonstrated and field tested with 200 published AB contrasts. NAP is a novel application of an established effect size known in various forms as Area Under the Curve (AUC), the Common Language Effect Size (CL), the Probability of Superiority (PS), the Dominance Statistic (DS), Mann-Whitney’s U, and Sommers D, among others. NAP was compared with 3 other non-overlap-based indices: PND (percent of nonoverlapping data), PEM (percent of data points exceeding the median), and PAND (percent of all nonoverlapping data), as well as Pearson’s R 2. Five questions were addressed about NAP: (a) typical NAP values, (b) its ability to discriminate among typical single-case research results, (c) its power and precision (confidence interval width), (d) its correlation with the established effect size index, R 2, and (e) its relationship with visual judgments. Results were positive, the new index equaling or outperforming the other overlap indices on most criteria.