Links to specific topics

Saturday, June 18, 2011

Testing the significance of mediating effects with WarpPLS using the Preacher & Hayes approach

This post refers to the use of WarpPLS to test a mediating effect using what is often referred to as the Preacher and Hayes approach. This approach employs the Sobel's standard error method (for a recent discussion, see: Kock, 2013). You can also test mediating effects directly with WarpPLS, using indirect and total effect outputs:

Previously I also discussed on this blog the classic approach proposed by Baron & Kenny (1986) to test the significance of mediating effects with WarpPLS.

An approach that is an alternative to Baron & Kenny's (1986) approach has been proposed by Preacher & Hayes (2004) to test the significance of mediating effects. This approach has been further extended by Hayes & Preacher (2010) for nonlinear relationships.

These approaches are implemented through an Excel spreadsheet available from the “Resources” area of the site, under “Excel files”. The spreadsheet, which implements the Sobel's standard error method, can be used with coefficients generated based on linear and nonlinear analyses.

The Excel spreadsheet above takes as inputs coefficients generated by WarpPLS, including path coefficients and their standard errors. The formulas used in it are discussed in a recent publication (Kock, 2013). The outputs are Sobel’s standard errors, product path coefficients, as well as T and P values, for mediating effects.


Baron, R.M., & Kenny, D.A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality & Social Psychology, 51(6), 1173-1182.

Hayes, A.F., & Preacher, K.J. (2010). Quantifying and testing indirect effects in simple mediation models when the constituent paths are nonlinear. Multivariate Behavioral Research, 45(4), 627-660.

Kock, N. (2013). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM. Laredo, Texas: ScriptWarp Systems.

Preacher, K.J., & Hayes, A.F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36 (4), 717-731.


Anonymous said...

Hi. Prof. Kock.
I have questions.

I am testing multi-group analysis in you excel sheet.
I think that fomular of the pooled standard error is a little strange.
Is there a reason for (n1-1)^2 & (n2-1)^2 instead of (n1-1) & (n2-1).

Are p-values for the two-tailed test in warpPLS?

I'll wait for your answer. :)
Thank you.

Ned Kock said...

Hi Jiyoung.

You have the second product term on the right, which counterbalances the squaring. By the way, the equation in our article (linked below) is slightly different from the one provided by Keil et al. (2000). The latter has a small error. This error has been corrected in our article and our spreadsheet.

Kock, N. (2014). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM. International Journal of e-Collaboration, 10(3), 1-13.

The pooled standard error method and the (arguably simpler) Satterthwaite method should yield fairly similar results in most cases. The Satterthwaite method is often seen also as a more conservative method, since it does not assume equality of standard errors between groups.

Regarding P values, see the article below. For the reasons explained in this article, WarpPLS generates one-tailed values. As you’ll see in the article, two-tailed values can be easily obtained by multiplying the one-tailed values by 2.

Kock, N. (2015). One-tailed or two-tailed P values in PLS-SEM? International Journal of e-Collaboration, 11(2), 1-7.