The conditional power of randomization tests for single-case effect sizes in designs with randomized treatment order:...

The conditional power (CP) of the randomization test (RT) was investigated in a simulation study in which three different single-case effect size (ES) measures were used as the test statistics: the mean difference (MD), the percentage of nonoverlapping data (PND), and the nonoverlap of all pairs (NAP). Furthermore, we studied the effect of the experimental design on the RT's CP for three different single-case designs with rapid treatment alternation: the completely randomized design (CRD), the randomized block design (RBD), and the restricted randomized alternation design (RRAD). As a third goal, we evaluated the CP of the RT for three types of simulated data: data generated from a standard normal distribution, data generated from a uniform distribution, and data generated from a first-order autoregressive Gaussian process. The results showed that the MD and NAP perform very similarly in terms of CP, whereas the PND performs substantially worse. Furthermore, the RRAD yielded marginally higher power in the RT, followed by the CRD and then the RBD. Finally, the power of the RT was almost unaffected by the type of the simulated data. On the basis of the results of the simulation study, we recommend at least 20 measurement occasions for single-case designs with a randomized treatment order that are to be evaluated with an RT using a 5% significance level. Furthermore, we do not recommend use of the PND, because of its low power in the RT.