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

  2. “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 https://www.youtube.com/watch?v=AIlsJPNMQss

  3. 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?

  4. Stats Tell Us What? Stats tell us what. In what way? How? By which pathway? Under what circumstances? Grow from whether and if to how and when

  5. Next Steps • NHST tells us whether • Correlation and Regression tell us if • Mediationanswers how • Moderationanswers when

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

  7. 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

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

  9. Treating callous traits as categorical

  10. Treating callous traits as continuous

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

  12. 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 • Centeringrefers to the process of transforming a variable into deviations around a fixed point

  13. Output from moderation analysis

  14. Output from moderation analysis II

  15. Output from moderation analysis III

  16. Following up Moderation with Simple Slopes analysis

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

  18. Reporting moderation analysis

  19. How do I do that? PROCESS www.afhayes.com Plug in for SPSS

  20. 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) Mediator c a b Predictor Predictor Outcome Outcome c' Simple Relationship Mediated Relationship

  21. 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

  22. 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. Mediator a b Predictor Outcome c'

  23. 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

  24. 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

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

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

  27. Output from Mediation Analysis

  28. Output from Mediation Analysis II

  29. Output from Mediation Analysis III

  30. Output from Mediation Analysis IV

  31. Output from Mediation Analysis – Results of Sobel test

  32. 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].

  33. 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 Direct Effect, b = 0.46, p = .02 Indirect Effect, b = 0.13, 95% CI [0.02, 0.34] Pornography Consumption Infidelity

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

  35. 197 male amateur golfers Stress at Home Self-Efficacy Social Support Task Performance Rees & Freeman, 2009

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

  37. 172 female freshmen White v. Non-White Race Social anxiety Parental Attachment Satisfaction Satisfaction with Friends Parade et al. (2010)

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

  39. Take a Break

  40. “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