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RStats Statistics and Research Camp 2014
Moderation and Mediation
Session 2
Todd Daniel PhDRStats Institute
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“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 Commissionhttps://www.youtube.com/watch?v=AIlsJPNMQss
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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?
Slide 5
Stats Tell Us What?
Stats tell us what.
How? In what way?
By which pathway?
Under what circumstances? Grow from whether and if
to how and when
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Next Steps
• NHST tells us whether• Correlation and Regression tell us if• Mediation answers how• Moderation answers when
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Moderation
• The combined effect of two variables on another – Conceptually known as moderation– In statistical terms: an interaction
effect
Predictor Outcome
Moderator
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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
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Conceptual moderation model
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.
Game Playing
Aggression
Callous Traits
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Treating callous traits as categorical
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Treating callous traits as continuous
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The Statistical Moderation Model
Predictor
OutcomeModerator
Predictor x Moderator
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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
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Output from moderation analysis
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Output from moderation analysis II
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Output from moderation analysis III
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Following up Moderation with Simple Slopes analysis
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Simple slopes equations of the regression of aggression on video games at three levels of callous traits
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Reporting moderation analysis
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Mediation Statistical Model
c'
Mediatora b
Predictor OutcomePredictor Outcomec
Simple RelationshipMediated Relationship
Mediation: when the relationship between a predictor variable and
outcome variable can be explained by their relationship to a third
variable (the mediator)
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Baron & Kenny, (1986)
• Mediation is tested through three regression models:1. Predicting the outcome from the
predictor variable2. Predicting the mediator from the
predictor variable3. Predicting the outcome from both
the predictor variable and the mediator
Slide 23
Baron & Kenny, (1986)
Four conditions of mediation: 1. The predictor must significantly predict the
outcome variable.2. The predictor must significantly predict the
mediator.3. The mediator must significantly predict the
outcome variable.4. The predictor variable must predict the
outcome variable less strongly in model 3 than in model 1.
c'
Mediatora b
Predictor Outcome
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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
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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
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Effect Sizes of Mediation Kappa-squared (k2)
(Preacher & Kelley, 2011)
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Example of a Mediation Model
Analysis is conducted in PROCESS
c'
Relationship Commitment
a b
Pornography Consumption Infidelity
Indirect Effect
Direct Effect
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Output from Mediation Analysis
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Output from Mediation Analysis II
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Output from Mediation Analysis III
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Output from Mediation Analysis IV
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Output from Mediation Analysis – Results of Sobel test
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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].
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Reporting Mediation Analysis
Relationship Commitment
Pornography Consumption Infidelity
Direct Effect, b = 0.46, p = .02Indirect Effect, b = 0.13, 95% CI [0.02, 0.34]
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.
b = -0.47, p = .028 b = -0.27, p < .001
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Anything else?• You can do
mediation and moderation together
• Conditional Process Analysis
Slide 36 Rees & Freeman, 2009
Self-Efficacy
Social SupportTask
Performance
Stress at Home
197 male amateur golfers
Slide 37 Popan et al. (2010)
Typicality of Outgroup
Mbr.Attribution
Rationality of argument
Interaction w/ Outgroup
Attitude about Outgroup
Positive or Negative
Slide 38 Parade et al. (2010)
Social anxiety
Parental Attachment Satisfaction
Satisfaction with Friends
172 female freshmen
Race
White v. Non-White
Slide 39 Laran, Dalton, and Andrade (2011)
Persuasive Intent
Advertising Tactic
Willingness to Spend $
Behavioral Prime
Persuasion Focus
Awareness of advertising intent
Brand logos v. Brand logos + slogans
Was the advertisement intended to persuade
Slogan did (not) emphasize saving money
$0 to $500 on imaginary shopping spree
Slide 40
Take a Break
Slide 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
