Three-Way Mixed ANOVA in Research
Slide 1
Mixed ANOVA (GLM 5)
Prof. Andy Field
Slide 2
Aims
•
What is mixed ANOVA?
•
Carrying out mixed ANOVA using
R
•
Interpretation
–
Main effects
–
Interactions
Slide 3
What Is Three-Way Mixed
ANOVA?
•
Three independent variables
–
Three-way = 3 IVs
•
Mixed:
–
1 or more independent variables use the
same participants
–
1 or more independent variables use
different participants
–
A.k.a. ‘mixed-plot design’
Slide 4
An Example: Speed Dating
•
Is personality or looks more important?
–
IV 1 (Looks): Attractive, Average, Ugly
–
IV 2 (Personality): High Charisma, Some Charisma,
Dullard
–
IV 3 (Gender): Male or Female?
•
Dependent variable (DV): P’s rating of the date
–
100% = The prospective date was perfect!
–
0% = I’d rather date my own mother
Slide 6
Effects
•
Main effects
–
We will get an
F
-ratio for the main effect of each independent variable:
•
Looks
•
Personality
•
Gender
•
Two-way interactions
•
We will get
F
-ratios for all possible interactions between pairs of variables:
•
Looks
Personality
•
Looks
Gender
•
Personality
Gender
•
Three-way interactions
•
We will get an
F
-ratio for the interaction between all three variables
•
Looks
Personality
Gender
Entering the Data
•
We need the data to be in the long format. We
can again use the
melt()
function :
speedData<-melt(dateData, id =
c("participant","gender"), measured = c("att_high","av_high", "ug_high", "att_some", "av_some",
"ug_some", "att_none", "av_none", "ug_none"))
•
The latter two labels are not helpful so we’ll
rename these columns so that we know what
they represent:
names(speedData)<-c("participant", "gender","groups", "dateRating")
Entering the Data
•
The variable
groups
is a mixture of our two
predictor variables (
looks
and
personality
).
We need to create two variables that
dissociate them.
•
Create a variable called
personality
:
speedData$personality<-gl(3, 60, labels =
c("Charismatic", "Average", "Dullard"))•
Create a variable called
looks
:
speedData$looks<-gl(3, 20, 180, labels =
c("Attractive", "Average", "Ugly"))Entering the Data
Slide 10
Contrasts
Mixed ANOVA
•
We can use the
ezANOVA()
function in much
the same way as for a repeated measures
design. The only difference is that we can add
our between-group variable (
gender
) by using
the
between = .()
option:
speedModel<-ezANOVA(data = speedData, dv =
.(dateRating), wid = .(participant), between =
.(gender), within = .(looks, personality), type = 3,
detailed = TRUE)
speedModel
Output
Slide 13
Mixed designs as a GLM
Building the Model
baseline<-lme(dateRating ~ 1, random =
~1|participant/looks/personality, data =
speedData, method = "ML")
•
Add main effects one at a time:
–
looksM<-update(baseline, .~. + looks)
–
personalityM<-update(looksM, .~. +
personality)
–
genderM<-update(personalityM, .~. + gender)
Building the Model
•
Add two-way interactions one at a time:
–
looks_gender<-update(genderM, .~. +
looks:gender)
–
personality_gender<-update(looks_gender, .~.
+ personality:gender)
–
looks_personality<-update(personality_gender,
.~. + looks:personality)
Building the model
•
Add the three-way interaction to the
model:
–
speedDateModel<-update(looks_personality, .~. +
looks:personality:gender)
•
To compare these models we can list them
in the order in which we want them
compared in the
anova()
function:
anova(baseline, looksM, personalityM, genderM,
looks_gender, personality_gender,
looks_personality, speedDateModel)
Output
Model Parameters
Slide 19
Main Effect of Gender
Slide 20
Main Effect of Looks
Slide 21
Main Effect of Charisma
Slide 22
The Gender
Looks Interaction
Slide 23
Gender
Charisma Interaction
Slide 24
The Looks
Charisma Interaction
Slide 26
Gender
Looks
Charisma Interaction
Conducting a Three-Way Mixed ANOVA in research involves analyzing the main effects and interactions of multiple independent variables using data in long format. This method allows researchers to determine the significance of various factors on the dependent variable. Learn how to interpret the results and carry out analyses using R programming. Explore examples like speed dating to understand the nuances of this statistical technique in psychological research.
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Presentation Transcript
Mixed ANOVA (GLM 5) Prof. Andy Field Slide 1
Aims What is mixed ANOVA? Carrying out mixed ANOVA using R Interpretation Main effects Interactions Slide 2
What Is Three-Way Mixed ANOVA? Three independent variables Three-way = 3 IVs Mixed: 1 or more independent variables use the same participants 1 or more independent variables use different participants A.k.a. mixed-plot design Slide 3
An Example: Speed Dating Is personality or looks more important? IV 1 (Looks): Attractive, Average, Ugly IV 2 (Personality): High Charisma, Some Charisma, Dullard IV 3 (Gender): Male or Female? Dependent variable (DV): P s rating of the date 100% = The prospective date was perfect! 0% = I d rather date my own mother Slide 4
Effects Main effects We will get an F-ratio for the main effect of each independent variable: Looks Personality Gender Two-way interactions We will get F-ratios for all possible interactions between pairs of variables: Looks Personality Looks Gender Personality Gender Three-way interactions We will get an F-ratio for the interaction between all three variables Looks Personality Gender Slide 6
Entering the Data We need the data to be in the long format. We can again use the melt() function : speedData<-melt(dateData, id = c("participant","gender"), measured = c("att_high", "av_high", "ug_high", "att_some", "av_some", "ug_some", "att_none", "av_none", "ug_none")) The latter two labels are not helpful so we ll rename these columns so that we know what they represent: names(speedData)<-c("participant", "gender", "groups", "dateRating")
Entering the Data The variable groups is a mixture of our two predictor variables (looks and personality). We need to create two variables that dissociate them. Create a variable called personality: speedData$personality<-gl(3, 60, labels = c("Charismatic", "Average", "Dullard")) Create a variable called looks: speedData$looks<-gl(3, 20, 180, labels = c("Attractive", "Average", "Ugly"))
Contrasts Slide 10
Mixed ANOVA We can use the ezANOVA() function in much the same way as for a repeated measures design. The only difference is that we can add our between-group variable (gender) by using the between = .() option: speedModel<-ezANOVA(data = speedData, dv = .(dateRating), wid = .(participant), between = .(gender), within = .(looks, personality), type = 3, detailed = TRUE) speedModel
Mixed designs as a GLM Slide 13
Building the Model baseline<-lme(dateRating ~ 1, random = ~1|participant/looks/personality, data = speedData, method = "ML") Add main effects one at a time: looksM<-update(baseline, .~. + looks) personalityM<-update(looksM, .~. + personality) genderM<-update(personalityM, .~. + gender)
Building the Model Add two-way interactions one at a time: looks_gender<-update(genderM, .~. + looks:gender) personality_gender<-update(looks_gender, .~. + personality:gender) looks_personality<-update(personality_gender, .~. + looks:personality)
Building the model Add the three-way interaction to the model: speedDateModel<-update(looks_personality, .~. + looks:personality:gender) To compare these models we can list them in the order in which we want them compared in the anova() function: anova(baseline, looksM, personalityM, genderM, looks_gender, personality_gender, looks_personality, speedDateModel)
Main Effect of Gender Slide 19
Main Effect of Looks Slide 20
Main Effect of Charisma Slide 21
The Gender Looks Interaction Slide 22
Gender Charisma Interaction Slide 23
The Looks Charisma Interaction Slide 24
Gender Looks Charisma Interaction Slide 26
