“Make things as simple as possible, but no simpler.” A rejoinder to Scruggs and Mastropieri

Scruggs and Mastropieri (Behaviour Research and Therapy, 32, 879–883, 1994) take issue with criticisms of their PND (Percent of Nonoverlapping Data) statistic that we offered in our recent article (Allison & German, Behaviour Research and Therapy, 31, 621–631, 1993), which advocated a regressionbased method for obtaining effect sizes in single-subject studies. They contend that their PND approach has several advantages over our approach because: (1) they believe that, unlike ours, it can take advantage of the small number of observations that are typically available in single-case studies; (2) it is simple to compute; (3) it frees researchers from traditional regression assumptions of normality, homogeneity of variance, and independence of observations and residuals; and (4) it correlates with visual judgements made by experts. As we shall argue, these claims are built upon very questionable assumptions and they are very difficult to substantiate. In addition, we show that the expected value of the PND is so strongly related to sample size as to be rendered meaningless.