Abstract

Knowing how many replicates are needed to reach a certain power of the test allows the researcher to design an efficient and sound experiment. Sample size determination, however, is not universal and mostly depends on the parameters being considered and the implementation of the experiment (i.e., randomization and local control). In many clinical studies, for instance, subjects also carries variation in the measurements and ignoring this effect may result in highly conservative tests. Moreover, randomization, which plays a central role in uncertainty measurements, may not be straightforward in clinical experiments. This study brought the split-plot design in a multivariate setting with a goal of sample size calculation that may be recommended for hypothesis testing, particularly, this study focused on interaction of two factors. Results have shown accurate estimation by GLS-backfitting algorithm and the test proposed was correctly sized (uses Bonferroni adjustment). The power of the test was affected by effect sizes (main and interaction effects), sample size, and dispersion of random error term. In general, higher sample size is needed for higher desired power and fixed level of significance, but it is also affected by factors including, but not limited to, standard deviation of random error and effect size. This study also intends to provide sample size calculator in R, aiming to make it available in RShiny, in the near future.