This page provides a brief tutorial for the p-value calculator described in Falk & Biesanz (2016). The program is intended to be easy-to-use, does not require commercial statistical software, does not require editing of SPSS or SAS syntax, and does 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 the 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 - a high-power alternative to Sobel’s test. 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. The calculator may be used for making inferences about indirect effects with multiple regression models (t-distribution computational method), or structural equation or certain multilevel models (see also FAQ about multilevel models) when degree of freedom approximations are not available (normal approximation). 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).
Users of the p-value calculator calculator may cite:
Falk, C.F., & Biesanz, J.C. (2016). Two cross-platform programs for inferences and interval estimation about indirect effects in mediational models. SAGE Open, 6. http://dx.doi.org/10.1177/2158244015625445
Instructions on program use
Click on the link below to download the program.
MediationPval.jar (last update: 2015-08-18)
Once downloaded, double click on the file and it will open in a new window. For some users, it may require an update/install to a new version of Java Runtime Environment: https://java.com/en/download/
This program is computationally intensive. The program has been tested under Windows XP, Windows 7, and OSX (Mac) version 10.7.3 (Lion). If you encounter any problems with the program, please report them directly to me: carl.falk@mcgill.ca
After the program loads, the next step is to enter the t-statistic and degrees of freedom for the a path in the mediational model. In the empirical example in Biesanz, Falk, and Savalei (2010), the t-statistic is 3.165 with df of 38. After that, enter the t-statistic and degrees of freedom for the b path in the mediational model. In the empirical example in Biesanz, Falk, and Savalei (2010), the t-statistic is 2.153 with df of 37. The result of these two steps is shown below. If the paths are part of a structural equation model, enter the z-statistics for the two paths, and select “Normal approximation” as the computational method (no df necessary).
Next click “Compute” and the program will get to work. Note that “Good” computational accuracy will usually take just a couple minutes and is recommended for general use. Researchers wishing a higher level of stability (e.g., p-values that vary less from run to run) for publication may use the “Excellent” computational accuracy setting, but must be prepared to be very patient.
The result of the program is now displayed below (.029), which is significant at the alpha = .05 level. Thus, the indirect effect, ab is significant in this example. Evidence consistent with mediation has been found.
Additional References
An example for writing up the results from a mediation analysis that uses the partial posterior method may be found in the following paper (end of p. 26): Human, Biesanz, Parisotto, and Dunn (2012), or in Falk & Biesanz (2016). The method using t-statistics was presented and studied by Biesanz et al. (2010), and the method using the normal approximation with structural equation models was initially studied by Falk & Biesanz (2015).
Human, L.J., Biesanz, J.C., Parisotto, K.L., & Dunn, E.W. (2012). Your best self helps reveal your true self: Positive self-presentation leads to more accurate personality impressions. Social Psychological and Personality Science, 3, 23-30. http://dx.doi.org/10.1177/1948550611407689
Biesanz, J.C., Falk, C.F., & Savalei, V. (2010). Assessing mediational models: Testing and interval estimation for indirect effects. Multivariate Behavioral Research, 45, 661-701. http://dx.doi.org/10.1080/00273171.2010.498292
Falk, C.F., & Biesanz, J.C. (2015). Inference and interval estimation methods for indirect effects with latent variable models. Structural Equation Modeling, 22, 24-38. http://dx.doi.org/10.1080/10705511.2014.935266