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Mediation analysis is increasingly common in the social and behavioral sciences contexts in which Educational Statisticians practice. This type of analysis goes beyond establishing that a relationship between variables exists by trying to explain how or why the variables are related. However, to date the empirical studies of methods to test simple mediation models have only examined results for normal distributions. The current study will detail results for multiple nonnormal distributions and introduce new methods for testing simple mediation. Results for N=100 indicate that a novel method avoids the pitfalls of existing methods, with power, confidence interval coverage rate, and bias on par with the best of the existing methods, without compromising control of the Type I error rate.