Testing the Intervention Effect in Single-Case Experiments: A Monte Carlo Simulation Study

This article reports on a Monte Carlo simulation study, evaluating two approaches for testing the intervention effect in replicated randomized AB designs: two-level hierarchical linear modeling (HLM) and using the additive method to combine randomization test p values (RTcombiP). Four factors were manipulated: mean intervention effect, number of cases included in a study, number of measurement occasions for each case, and between-case variance. Under the simulated conditions, Type I error rate was under control at the nominal 5% level for both HLM and RTcombiP. Furthermore, for both procedures, a larger number of combined cases resulted in higher statistical power, with many realistic conditions reaching statistical power of 80% or higher. Smaller values for the between-case variance resulted in higher power for HLM. A larger number of data points resulted in higher power for RTcombiP.