Mediation analysis investigates how certain variables mediate the effect of predictors on outcome variables. Existing studies of mediation models have been limited to normal theory maximum likelihood (ML) or least squares with normally distributed data. Because real data in the social and behavioral sciences are seldom normally distributed and often contain outliers, classical methods can result in biased and inefficient estimates, which lead to inaccurate or unreliable test of the meditated effect. The authors propose two approaches for better mediation analysis. One is to identify cases that strongly affect test results of mediation using local influence methods and robust methods. The other is to use robust methods for parameter estimation, and then test the mediated effect based on the robust estimates. Analytic details of both local influence and robust methods particular for mediation models were provided and one real data example was given. We first used local influence and robust methods to identify influential cases. Then, for the original data and the data with the identified influential cases removed, the mediated effect was tested using two estimation methods: normal theory ML and the robust method, crossing two tests of mediation: the Sobel (1982) test using information-based standard error (z I ) and sandwich-type standard error (z SW ). Results show that local influence and robust methods rank the influence of cases similarly, while the robust method is more objective. The widely used z I statistic is inflated when the distribution is heavy-tailed. Compared to normal theory ML, the robust method provides estimates with smaller standard errors and more reliable test.