Abstract
This research paper simulated hypothesis testing of the differences of means, when the conventional assumption of independence within one of the samples had been violated. The study ran separate Monte Carlo simulations in which both samples came from uniform and normal populations. Dependence was introduced by multiplying the randomly generated scores within one sample by a predetermined factor. Then the simulation collected data on 10,000 paired samples with factors ranging from 1.0 (independence) to 2.0 (the highest level of dependence). A separate study calculated the mean autocorrelation associated with different conditions of dependence and linked this autocorrelation to the adjusted level of Type I error (α level). The results demonstrated a systematic increase in Type I error as the level of autocorrelation increased. The α level that our study found for certain levels of dependence (with n = 30) far exceeded the asymptotic level of adjusted α, suggesting that we further explore the effects of autocorrelation on conventional hypothesis testing.
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