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

“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

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?

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

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

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

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

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.

Treating callous traits as categorical

Treating callous traits as continuous

The Statistical Moderation Model Predictor Outcome Moderator Predictor x Moderator

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

Output from moderation analysis

Output from moderation analysis II

Output from moderation analysis III

Following up Moderation with Simple Slopes analysis

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

Reporting moderation analysis

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

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

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

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

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

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

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

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

Output from Mediation Analysis

Output from Mediation Analysis II

Output from Mediation Analysis III

Output from Mediation Analysis IV

Output from Mediation Analysis – Results of Sobel test

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].

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]

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

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

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

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)

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)

Take a Break

“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