An empirical investigation of the statistical properties of generalized single-case randomization tests

Abstract

Adapting Edgington's [J. Psychol. 90 (1975) 57] randomly determined intervention start-point model, Levin and Wampold [Sch. Psychol. Quart. 14 (1999) 59] proposed a set of nonparametric randomization tests for analyzing the data from single-case designs. In the present study, the performance of Levin and Wampold's four basic tests (independent start-point general and comparative effectiveness, simultaneous start-point general and comparative effectiveness) was examined with respect to their Type I error rates and statistical power. Of Levin and Wampold's four tests, all except the independent start-point comparative effectiveness test maintained their empirical Type I error rates and had acceptable power at larger sample-size and effect-size combinations. The one-tailed comparative intervention effectiveness test for the independent start-point model was found to be too liberal, in that it did not maintain its Type I error rate. Although a two-tailed application of that test was found to be conservative at longer series lengths, it had acceptable power at larger sample-size and effect-size combinations. The results support the utility of a versatile new class of single-case designs that permit both within- and between-unit statistical assessments of intervention effectiveness.