Sample Size Estimation of Nonparametric Tests with Ordered Alternatives for Longitudinal Data in Randomized Complete Block Designs

Longitudinal studies involve repeated measurements from the same subjects or blocks over short or an extended periods of time. In longitudinal studies, usually the most important step is to decide how many experimental units to use. There are no closed form equations for determining sample size in many complex designs. Monte Carlo simulation method is an effective tool in complex designs to estimate power or sample size. This paper introduces estimating sample size for the number of blocks or experimental units based on a fixed number of treatment/time in randomized complete block designs with correlated longitudinal responses analyzed by nonparametric tests against ordered alternatives. The sample size of subjects is estimated for each test statistics by taking into account the autocorrelation structure of the error terms which form either a stationary first-order moving average or autoregressive with non-normally distributed white noise terms. An extensive sample size/power comparison among the recently proposed Modification of S test and the other two well-known nonparametric tests such as the Page test and the generalized Jonckheere test against ordered alternatives in randomized complete block designs is carried out under stationary first-order autoregressive and moving average error structures with white noise terms distributed with either Laplace or Weibull distributions. Simulation study indicates that the distribution of white noise and the error structure have an important role on sample size estimation for each nonparametric test. The Modification of S test requires large sample size in contrast to other tests for longitudinal data in the specified simulation setting.