Evaluating single-case research data: A comparison of seven statistical methods

This study examined and compared the performances of seven popular or promising techniques for analyzing between-phase differences in single-case research designs. The techniques are: (a) Owen White's binomial test on extended Phase A baseline (White & Haring, 1980), (b) D. M. White, Rusch, Kazdin, and Hartmann's Last Treatment Day technique (1989), (c) Gorsuch's trend analysis effect size (Faith, Allison, Gorman, 1996; Gorsuch, 1983), (d) Center's mean-only and mean-plus-trend models (Center, Skiba, & Casey, 1985-1986), and (e) Allison's mean-only and mean-plus-trend models (Allison Gorman, 1993; Faith et al., 1096). The techniques were assayed by applying them to a set of 50 single-case AB design (baseline and intervention) data sets, constructed to represent a range of type and degree of intervention effects. From analysis of these 50 data sets, four questions were answered about the analytic techniques: (a) How much statistical power is possessed by the more promising techniques? (b) What typical R-2 effect sizes are evidenced for graphed data sets which, according to visual analysis, show a positive intervention effect? (c) How do the five analytic techniques covary with one another? and (d) To what extent does each technique tend to produce autocorrelated residuals?