This document summarizes a lecture on mediation analysis. It discusses two main approaches: the standard approach using regression models and path analysis. For the standard approach, three regression models are run to test the direct and indirect effects of an independent variable on a dependent variable through a proposed mediator. For path analysis, paths are drawn between variables to represent these relationships and specific paths are tested. An example is provided of stereotype threat affecting IQ scores through working memory capacity. The results support full mediation according to the standard approach and path analysis.

1. Statistics One
Lecture 14
Mediation
1

2. Two segments
• Standard approach
• Path analysis
2

3. Lecture 14 ~ Segment 1
Mediation: Standard approach
3

4. Mediation
• Mediation and moderation may sounds alike
but they are quite different
– Moderation (Lecture 13)
– Mediation (Lecture 14)
– Both demonstrated in R (Lab 7)
4

5. Mediation
Mediator
5

6. An example
• X: Experimental manipulation
– Stereotype threat
• Y: Behavioral outcome
– IQ score
• M: Mediator (Mechanism)
– Working memory capacity (WMC)
6

7. Mediation
• A mediation analysis is typically conducted
to better understand an observed effect of
an IV on a DV or a correlation between X
and Y
• Why, and how, does stereotype threat influence IQ
test performance?
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8. Mediation
• If X and Y are correlated then we can use
regression to predict Y from X
• Y = B0 + B1X + e
8

9. Mediation
• If X and Y are correlated BECAUSE of the
mediator M, then (X à M à Y):
• Y = B0 + B1M + e
&
• M = B0 + B1X + e
9

10. Mediation
• If X and Y are correlated BECAUSE of the
mediator M, and:
• Y = B0 + B1M + B2X + e
• What will happen to the predictive value of X
• In other words, will B2 be significant?
10

11. Mediation
• A mediator variable (M) accounts for some or
all of the relationship between X and Y
– Some: Partial mediation
– All: Full mediation
11

12. Mediation
• CAUTION!
– Correlation does not imply causation!
– In other words, there is a BIG difference between
statistical mediation and true causal mediation
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13. How to test for mediation
• Run three regression models
• lm(Y ~ X)
• lm(M ~ X)
• lm(Y ~ X + M)
13

14. How to test for mediation
• Run three regression models
• lm(Y ~ X)
– Regression coefficient for X should be significant
• lm(M ~ X)
– Regression coefficient for X should be significant
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15. How to test for mediation
• Run three regression models
• lm(Y ~ X + M)
– Regression coefficient for M should be significant
– Regression coefficient for X?
15

16. Back to the example
• X: Experimental manipulation
– Stereotype threat
• Y: Behavioral outcome
– IQ score
• M: Mediator (Mechanism)
– Working memory capacity (WMC)
16

17. Simulated experiment & data
• Students randomly assigned to one of two
experimental conditions
– Threat
– Control
• Students completed a working memory task
• Students completed an IQ test
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18. Results
18

19. Results
Control group
Threat group
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20. Interpretation
• Full mediation
– The direct effect is no longer significant after
adding the mediator into the regression
equation
– The Sobel test is significant
20

21. END SEGMENT
21

22. Lecture 14 ~ Segment 2
Mediation: Path analysis approach
22

23. Mediation
• Mediation analyses are typically illustrated
using “path models”
• Rectangles: Observed variables (X, Y, M)
• Circles: Unobserved variables (e)
• Triangles: Constants
• Arrows: Associations (more on these later)
23

24. Path model
• Y = B0 + B1X + e
1
X
B1
B0
Y
1
e
24

25. Path model with a mediator
X
1
B0
B1
M
Y
1
1
e
e
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26. Path model with a mediator
• To avoid confusion, let’s label the paths
• a: Path from X to M
• b: Path from M to Y
• c: Direct path from X to Y (before including M)
• c’: Direct path from X to Y (after including M)
• Note: (a*b) is known as the indirect path
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27. Path model
1
X
c
B0
Y
1
e
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28. Path model with a mediator
1
B0
c’
X
Y
a
1
e
b
M
1
e
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29. How to test for mediation
• Three regression equations can now be rewritten with new notation:
• Y = B0 + c(X) + e
• Y = B0 + c’(X) + b(M) + e
• M = B0 + a(X) + e
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30. How to test for mediation
• The Sobel test
z = (Ba* Bb) / SQRT[(Ba2 * SEb2) + (Bb2 * SEa2)]
– The null hypothesis
• The indirect effect is zero
• (Ba*Bb) = 0
30

31. Results
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32. Path model
1
Threat
-11.00
97.32
IQ
1
e
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33. Path model with a mediator
Threat
1
56.00
-2.41
IQ
-11.42
1
e
.75
WMC
1
e
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34. Mediation: Final comments
• Here we used path analysis to *illustrate*
the mediation analysis
• It is also possible to test for mediation using
a statistical procedure called:
– Structural Equation Modeling (SEM)
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35. END SEGMENT
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36. END LECTURE 14
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