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The conditional power (CP) of the randomization test (RT) was investigated in a simulation study using three different single-case effect size (ES) measures as the test statistic: the mean difference (MD), the Percentage of Nonoverlapping Data (PND), and the Nonoverlap of All Pairs (NAP). Other factors included in the study were three types of randomized single-case alternation designs and three types of simulated data patterns. The MD and NAP performed very similar in terms of CP whereas the PND performed substantially worse. The CP was influenced by the employed type of single-case design but not by the type of data pattern. Recommendations regarding the minimum amount of measurement occasions for sufficient statistical power in SCEs using alternation designs are provided.