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In this article, we describe two new programs that compute bothp-values and confidence intervals (CI) for the indirect effect in mediational models,including (a) a p-value based on the partial posterior method, which we refer to as p3computed across the posterior distribution of the regression coefficients; (b) a variantof p3 that uses a normal approximation for the posterior distributions, p3N; (c)Hierarchical Bayesian CIs (CIHB) based on the posterior distributions of the regressioncoefficients; and (d) CIs based on the Monte Carlo method (CIMC). These programs do notrequire access to raw data as do resampling methods. Similar to Sobel’s test, p3 and p3Nconstitute a single p-value for the indirect effect while performing substantiallybetter in terms of Type I and II error rates. Furthermore, we include a memory efficientcomputational algorithm for CIHB and CIMC that allows for precision beyond that inexisting alternative implementations. The underlying programs can utilize multicoreprocessors, and their performance is tested through a simulation study. Finally, the useof these programs is illustrated with an empirical example

Two Cross-Platform Programs for Inferences and Interval Estimation About Indirect Effects in Mediational Models