The Power of Randomization Tests for Single-Case Phase Designs

Monte Carlo methods were used to estimate the power of randomization tests used with single-case designs involving the random assignment of treatments to phases. The design studied involved 2 treatments and 6 phases. The power was studied for 6 standardized effect sizes (0, .2, .5, .8, 1.1, and 1.4), 4 levels of autocorrelation (1st order autocorrelation coefficients of -.3, 0, .3, and .6), and 5 different phase lengths (4, 5, 6, 7, and 8 observations). Power was estimated for each condition by simulating 10,000 experiments. The results showed an adequate level of power (> .80) when effect sizes were large (1.1 and 1.4), phase lengths exceeded 5, and autocorrelation was not negative.