1. RStats Statistics and Research Camp 2014
Moderation and Mediation
Session 2
Todd Daniel PhD
RStats Institute

3. “So far, we have been unable to document any incidents that were sparked by a cellular telephone. In fact, many researchers have tried to ignite fuel vapors with a cell phone and failed.”
Petroleum Equipment Institute
“The wireless industry has done studies on the potential for wireless phones to create sparks…there is no documented incident where the use of a wireless phone was found to cause a fire or explosion at a gas station.”
Federal Communications Commission

4. Hmmmm… More gas station fires occur to women
Women are more likely to re-enter the car
Women are less likely to touch the car when exiting
Conclusion: static electricity not cell phones
Isn’t this more useful?

5. Grow from whether and if
Stats Tell Us What?
Stats tell us what.
In what way?
How?
By which pathway?
Under what circumstances?
Isn’t it more interesting to know how and why?
Grow from whether and if
to how and when

6. Next Steps NHST tells us whether Correlation and Regression tell us if
Mediation answers how
Moderation answers when

7. Moderation The combined effect of two variables on another
Conceptually known as moderation
In statistical terms: an interaction effect
Moderator
Predictor
Outcome

8. Example Do violent video games make teens aggressive? Participants
442 youths
IV: Number of hours spent playing video games per week
DV: Aggression
Moderator: Callous (unemotional) traits

9. Conceptual moderation model
Callous Traits
Game Playing
Aggression
If callous traits are a moderator then the strength or direction of the relationship between game playing and aggression is affected by callous (unemotional) traits.

10. Treating callous traits as categorical

11. Treating callous traits as continuous

12. The Statistical Moderation Model
Predictor
Outcome
Moderator
Predictor x Moderator

13. Centering variables
The interaction term makes the b’s for the main predictors uninterpretable in many situations
For this reason, it is common to transform the predictors using grand mean centering
Centering refers to the process of transforming a variable into deviations around a fixed point

14. Output from moderation analysis

15. Output from moderation analysis II

16. Output from moderation analysis III

17. Following up Moderation with Simple Slopes analysis

18. Simple slopes equations of the regression of aggression on video games at three levels of callous traits

19. Reporting moderation analysis

20. How do I do that?
PROCESS
Plug in for SPSS

21. Mediation Statistical Model
Mediation: when the relationship between a predictor variable and outcome variable can be explained by their relationship to a third variable (the mediator) c'
Mediator a b
Predictor
Outcome
Predictor
Outcome c
Simple Relationship
Mediated Relationship

22. Baron & Kenny, (1986)
Mediation is tested through three regression models:
Predicting the outcome from the predictor variable
Predicting the mediator from the predictor variable
Predicting the outcome from both the predictor variable and the mediator

23. Baron & Kenny, (1986) Four conditions of mediation:
The predictor must significantly predict the outcome variable.
The predictor must significantly predict the mediator.
The mediator must significantly predict the outcome variable.
The predictor variable must predict the outcome variable less strongly in model 3 than in model 1. c'
Mediator a b
Predictor
Outcome

24. Limitations of Baron & Kenny’s (1986) Approach
How much of a reduction in the relationship between the predictor and outcome is necessary to infer mediation?
people tend to look for a change in significance, which can lead to the ‘all or nothing’ thinking that p-values encourage

25. Sobel Test
An alternative is to estimate the indirect effect and its significance using the Sobel Test (Sobel, 1982)
If the Sobel test is significant, there is significant mediation

26. Effect Sizes of Mediation Kappa-squared (k2)
(Preacher & Kelley, 2011)

27. Example of a Mediation Model
Indirect Effect c'
Relationship Commitment a b
Pornography Consumption
Infidelity
Direct Effect
Analysis is conducted in PROCESS

28. Output from Mediation Analysis

29. Output from Mediation Analysis II

30. Output from Mediation Analysis III

31. Output from Mediation Analysis IV

32. Output from Mediation Analysis – Results of Sobel test

33. Reporting Mediation Analysis
There was a significant indirect effect of pornography consumption on infidelity though relationship commitment, b = 0.127, BCa CI [0.023, 0.335]. This represents a relatively small effect, κ2 = .041, 95% BCa CI [.008, .104].

34. Reporting Mediation Analysis
Model of pornography consumption as a predictor of infidelity, mediated by relationship commitment. The confidence interval for the indirect effect is a BCa bootstrapped CI based on 1000 samples.
Relationship Commitment
b = -0.47, p = .028
b = -0.27, p < .001
Pornography Consumption
Infidelity
Direct Effect, b = 0.46, p = .02
Indirect Effect, b = 0.13, 95% CI [0.02, 0.34]

35. Anything else? You can do mediation and moderation together
Conditional Process Analysis

36. Self-Efficacy Stress at Home Social Support Task Performance
197 male amateur golfers
Stress at Home
Self-Efficacy
Social Support
Task Performance
Rees & Freeman, 2009

37. Attribution Typicality of Outgroup Mbr. Interaction w/ Outgroup
Rationality of argument
Interaction w/ Outgroup
Attitude about Outgroup
Positive or Negative
Popan et al. (2010)

38. Social anxiety Race Satisfaction with Friends 172 female freshmen
White v. Non-White
Social anxiety
Parental Attachment Satisfaction
Satisfaction with Friends
Parade et al. (2010)

39. Persuasion Focus Behavioral Prime Persuasive Intent
Awareness of advertising intent
Slogan did (not) emphasize saving money
Was the advertisement
intended to persuade
Persuasion Focus
Behavioral Prime
Persuasive Intent
Advertising Tactic
Willingness to Spend $
Brand logos v. Brand logos + slogans
$0 to $500 on imaginary
shopping spree
Laran, Dalton, and Andrade (2011)

40. Take a Break

41. “Static electricity has caused fires at gas stations…for this reason, you should not re-enter your vehicle while you are refueling, since static electricity caused by friction from your clothing’s contact with the car seat can ignite the gas when you get back out of the car to complete the refueling process.”
Ohio State Bar Association website