Comparison of Paired T-Test and Wilcoxon Signed Rank Test for Various Change Measures in Pre-Post Designs: A Simulation Study

Objective: In a pre-post design, most commonly used change measure is simple difference (D), but percent change (PC) and symmetrized percent change (SPC) are not. We aimed to determine whether paired t-test and Wilcoxon signed rank test are suitable for PC and SPC according to type I-error and the power by a simulation. Material and Methods: Simulation study was performed by using normally distributed random numbers. Two samples which were called pre and post treatment measures with replacement were taken from a standard normal population which included 10.000 observations. Three different sample size, two different correlation degree, two different standard deviation and two different effect sizes were investigated for the purposes in simulation study. Results: The actual type-I error probabilities of paired t-test for PC were higher than nominal level except variances of pre and post measurements were near to homogenous. But they were observed significantly different from its nominal level in all test combinations for SPC. Actual type-I error of WSR for PC and SPC were found different from 5% when sample size is lower than 20. The powers of t-test and WSR test for PC and SPC were also low or moderate level in the simulation conditions. Conclusion: PC and SPC measures should only be used for descriptive purposes until appropriate test will found.