Nonparametric statistical tests for single-case systematic and randomized ABAB…AB and alternating treatment intervention designs: new developments, new directions.

In this four-investigation Monte Carlo simulation study, we examined the properties of nonparametric randomization and permutation statistical tests applied to single-case ABAB…AB and alternating treatment designs based on either systematically alternating or randomly determined phase assignments. Contrary to previous admonitions, when appropriately conceptualized nonparametric tests were conducted the systematic designs maintained Type I error rates at or less than their nominal values whenever either no or positive autocorrelation was present in the series. Statistical power for all designs varied as a function of both the number of phases and the number of observations per phase. It was concluded that to increase methodological rigor and statistical precision in the face of autocorrelation, (a) whenever possible, researchers should adopt a randomization scheme in assigning the orders in which the A and B phases are administered and (b) in situations where randomized phase assignment is not feasible, researchers should adopt a systematic phase assignment scheme consisting of individually alternating A and B observations, with a cost of sacrificing some degree of statistical power. Implications for single-case intervention research in school psychology are discussed.