The Functioning of Single-Case Randomization Tests With and Without Random Assignment

The authors used Monte Carlo methods to examine the Type I error rates for randomization tests applied to single-case data arising from ABAB designs involving random, systematic, or response-guided assignment of interventions. Six randomization tests were examined (permuting blocks of 1, 2, 3, or 5 observations, and randomly selecting intervention triplets so that each phase has at least 3 or 5 observations). When the design included randomization, the Type I error rate was controlled. When the design was systematic or guided by the absolute value of the slope, the tests permuting blocks tended to be liberal with positive autocorrelation, whereas those based on the random selection of intervention triplets tended to be conservative across levels of autocorrelation.