1. Mediation: Testing the Indirect Effect
David A. Kenny

2. Mediation Webinars
Indirect Effect

3. The Mediational Model M b a c' Y X

4. The Measure of Mediation
Indirect Effect = ab

5. Strategies to Test ab = 0 Joint test of a and b Sobel test
Use the distribution of ab
Monte Carlo Method
Bootstrapping

6. Joint Test of a and b
Easy to do
Logical
Works fairly well

7. Sobel Test of Mediation
Developed in 1982 by Michael Sobel.
Sometimes called the “delta method.”
There are other related methods.
Website: quantpsy.org/sobel/sobel.htm
Assumes that ab has a normal distribution and that a and b are independent.

8. Sobel Test of Mediation
Compute the square root of a2sb2 + b2sa2 which is denoted as sab
Note that sa and sb are the standard errors of a and b, respectively; ta = a/sa and tb = b/sb.
Divide ab by sab and treat that value as a Z.
So if ab/sab greater than 1.96 in absolute value, reject the null hypothesis that the indirect effect is zero.

9. ab Large values of “ab” are more variable than small values (i.e., 0).ab
The distribution of ab is highly skewed which lowers the power of the test.

10. Assumption of Independence
Paths a and b are assumed to be independent.
They are independent when they are regression coefficients.
But not when they are from logistic regression, structural equation modeling, and most other techniques, they may not be independent.
SSSSSSSSS

11. Bootstrapping
“Nonparametric” way of computing a sampling distribution.
Re-sampling (with replacement)
Many trials (computationally intensive)
Can correct for bias for a more powerful test
Mean of the bootstrap estimate differs slightly from the estimate.
Compute a confidence interval which is asymmetric.
Slight changes because empirically derived.

12. Results of Bootstrapping
95% Bias Corrected Confidence Interval:
Lower Upper
Note that the CI is asymmetric for an estimate of Also values differ to sampling error.
(Done using the Hayes & Preacher macro from

13. Summary

14. More Mediation Webinars
Causal Assumptions
Sensitivity Analyses