This tutorial discusses two programs for computing (1) p-values and (2) confidence intervals for the indirect effect. Both programs are intended to be easy-to-use, do not require commercial statistical software, do not require editing of SPSS or SAS syntax, and do not require the raw data. The user only needs to input information that one would normally need to obtain anyway if performing mediational analysis using traditional methods (e.g., regression coefficients, standard errors, degrees of freedom, and t-statistics).
Within each program, there are two computational methods - one method where sampling distributions are based in-part on posterior (and t) distributions (appropriate for regression models), and a second method where normal approximations are used in place of posterior distributions (appropriate for larger samples or methods where such normal approximations are used, such as structural equation models).
P-values are computed by the partial posterior method. In Biesanz et al (2010), the partial posterior approach had high power relative to traditional approaches, power on par with the modern approaches just described, and adequately controlled Type I error rates. Furthermore, the partial posterior provides a single p-value interpretable in the same way as one would interpret the p-value from Sobel’s test. The use of normal approximations in adapting the partial posterior method to structural equation models also performed well at sample sizes above 100 in a recent simulation study (Falk & Biesanz, 2015, Structural Equation Modeling).
Confidence intervals are available from the hierarchical Bayesian and Monte Carlo methods. In Biesanz et al (2010), the hierarchical Bayesian method provided coverage rates for the indirect effect that outperformed both the distribution of the product method and the BCa bootstrap. The Monte Carlo method performs similarly to the hierarchical Bayesian method and distribution of the product method at large sample sizes. The Monte Carlo method is also appropriate for confidence intervals in structural equation models as it allows for a correlation between the two paths in the model (which is not necessarily 0 in models that contain latent variables).