Running head: VIOLATING THE ASSUMPTION OF INDEPENDECE 95 Million t tests: The Empirical Findings when the Assumption of Independence has Been Violated in the Two-Sample t Test

A Monte Carlo computer simulation was used to evaluate the effect on the Type I error rate when the assumption of independence was not met in the two-sample t test. It was shown that when there is a positive correlation within groups the nominal alpha level is considerably smaller than the probability of the Type I error rate. This study used five values of ! and 19 different "’s, computing 1,000,000 t’s for each of the 95 combinations used in the empirically generated critical value table provided. The critical values in the table are derived from distributions with a known ! and ". It is believed when the independence assumption is violated in scientific research, use of empirically generated critical values that match the characteristics within groups will be more appropriate then using the t table, which is of course based on the assumption of independence.