The biasing effects of violating the independence assumption upon the power of t test

In many areas of educational and psychological research, the t test is among the most popular statistical analysis methods. One of the assumptions for the t test is the independence of observations, which is important but rarely satisfying in real data. The power analysis for the t test also requires the independence assumption. The effects of the violation of this assumption has been extensively studied with respect to the probability of Type I error, but not regarding the power. The purpose of this study is to investigate the biasing effects of non-independence of observations on the power of the t test by means of computer simulation. In this study, the non-independence of observations is defined by the intraclass correlation coefficients within subgroups of observations. The result suggests that the magnitude of the bias can be considerable depending upon the population effect size, intraclass correlation coefficient, and the size of subgroups.