//Two-Way ANOVA with Unequal Sample Sizes Example
//Created by John M. Quick
//http://www.johnmquick.com
//January 22, 2011

> #read the dataset into an R variable using the read.csv(file) function
> dataTwoWayUnequalSample <- read.csv("dataset_ANOVA_TwoWayUnequalSample.csv")
> #display the data
> dataTwoWayUnequalSample
   environment instruction math
1      offline   classroom   50
2      offline   classroom   55
3      offline   classroom   70
4      offline   classroom   75
5      offline   classroom   85
6      offline   classroom   80
7      offline   classroom   90
8      offline   classroom   90
9       online   classroom   75
10      online   classroom   70
11      online   classroom   50
12      online   classroom   55
13      online   classroom   70
14      online   classroom   75
15      online   classroom   85
16      online   classroom   80
17      online   classroom   90
18      online   classroom   90
19      online   classroom   75
20      online   classroom   70
21     offline       tutor   70
22     offline       tutor   75
23     offline       tutor   80
24     offline       tutor   75
25     offline       tutor   80
26     offline       tutor   90
27      online       tutor   95
28      online       tutor   95
29      online       tutor   80
30      online       tutor   80

> #use subset(data, condition) to create subsets for each treatment group
> #offline subset
> offlineData <- subset(dataTwoWayUnequalSample, dataTwoWayUnequalSample$environment == "offline")
> #online subset
> onlineData <- subset(dataTwoWayUnequalSample, dataTwoWayUnequalSample$environment == "online")
> #classroom subset
> classroomData <- subset(dataTwoWayUnequalSample, dataTwoWayUnequalSample$instruction == "classroom")
> #tutor subset
> tutorData <- subset(dataTwoWayUnequalSample, dataTwoWayUnequalSample$instruction == "tutor")

> #use mean(data) to calculate the weighted means for each treatment group
> #offline weighted mean
> mean(offlineData$math)
[1] 76.07143
> #online weighted mean
> mean(onlineData$math)
[1] 77.1875
> #classroom weighted mean
> mean(classroomData$math)
[1] 74
> #tutor weighted mean
> mean(tutorData$math)
[1] 82

> #use anova(object) to execute the Type I SS ANOVAs
> #notice that the main effect results are different when the independent variables are ordered differently
> #environment ANOVA
> anova(lm(math ~ environment * instruction, dataTwoWayUnequalSample))
Analysis of Variance Table

Response: math
                        Df Sum Sq Mean Sq F value  Pr(>F)  
environment              1    9.3    9.30  0.0647 0.80119  
instruction              1  467.5  467.50  3.2531 0.08289 .
environment:instruction  1  153.4  153.40  1.0674 0.31104  
Residuals               26 3736.5  143.71                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

> #instruction ANOVA
> anova(lm(math ~ instruction * environment, dataTwoWayUnequalSample))
Analysis of Variance Table

Response: math
                        Df Sum Sq Mean Sq F value  Pr(>F)  
instruction              1  426.7  426.67  2.9689 0.09675 .
environment              1   50.1   50.14  0.3489 0.55984  
instruction:environment  1  153.4  153.40  1.0674 0.31104  
Residuals               26 3736.5  143.71                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

> #use mean(data) and subset(data, condition) to calculate the unweighted means for each treatment group
> #offline unweighted mean = (classroom offline mean + tutor offline mean) / 2
> (mean(subset(offlineData$math, offlineData$instruction == "classroom")) + mean(subset(offlineData$math, offlineData$instruction == "tutor"))) / 2
[1] 76.35417
> #online unweighted mean = (classroom online mean + tutor online mean) / 2
> (mean(subset(onlineData$math, onlineData$instruction == "classroom")) + mean(subset(onlineData$math, onlineData$instruction == "tutor"))) / 2
[1] 80.625
> #classroom unweighted mean = (offline classroom mean + online classroom mean) / 2
> (mean(subset(classroomData$math, classroomData$environment == "offline")) + mean(subset(classroomData$math, classroomData$environment == "online"))) / 2
[1] 74.0625
> #tutor unweighted mean = (offline tutor mean + online tutor mean) / 2
> (mean(subset(tutorData$math, tutorData$environment == "offline")) + mean(subset(tutorData$math, tutorData$environment == "online"))) / 2
[1] 82.91667

> #load the car package (install first, if necessary)
> library(car)
> #use the Anova(mod, type) function to conduct the Type III SS ANOVA
> Anova(lm(math ~ environment * instruction, dataTwoWayUnequalSample), type = "3")
Anova Table (Type III tests)

Response: math
                        Sum Sq Df  F value    Pr(>F)    
(Intercept)              44253  1 307.9336 6.218e-16 ***
environment                  2  1   0.0130    0.9099    
instruction                 54  1   0.3738    0.5462    
environment:instruction    153  1   1.0674    0.3110    
Residuals                 3736 26                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1