//Two-Way ANOVA with Pairwise Comparisons Example
//Created by John M. Quick
//http://www.johnmquick.com
//January 16, 2011

> #read the dataset into an R variable using the read.csv(file) function
> dataTwoWayComparisons <- read.csv("dataset_ANOVA_TwoWayComparisons.csv")
> #display the data
> dataTwoWayComparisons
   Treatment   Age StressReduction
1     mental young              10
2     mental young               9
3     mental young               8
4     mental   mid               7
5     mental   mid               6
6     mental   mid               5
7     mental   old               4
8     mental   old               3
9     mental   old               2
10  physical young               9
11  physical young               8
12  physical young               7
13  physical   mid               6
14  physical   mid               5
15  physical   mid               4
16  physical   old               3
17  physical   old               2
18  physical   old               1
19   medical young               8
20   medical young               7
21   medical young               6
22   medical   mid               5
23   medical   mid               4
24   medical   mid               3
25   medical   old               2
26   medical   old               1
27   medical   old               0

> #use anova(object) to test the omnibus hypothesis
> #Are main effects or interaction effects present in the independent variables?
> anova(lm(StressReduction ~ Treatment * Age, dataTwoWayComparisons))
Analysis of Variance Table

Response: StressReduction
              Df Sum Sq Mean Sq   F value   Pr(>F)    
Treatment      2     18       9         9 0.001953 ** 
Age            2    162      81        81    1e-09 ***
Treatment:Age  4      0       0 2.250e-30 1.000000    
Residuals     18     18       1                       
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

> #omnibus test significant with no interaction effect; continue to pairwise comparisons

> #use pairwise.t.test(x, g, p.adj) to test the pairwise comparisons between the treatment group means
> #What significant differences are present amongst the treatment means?
> pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Treatment, p.adj = "none")
Pairwise comparisons using t tests with pooled SD 

data:  dataTwoWayComparisons$StressReduction and dataTwoWayComparisons$Treatment 

         medical mental
mental   0.13    -     
physical 0.45    0.45  

P value adjustment method: none

> #use pairwise.t.test(x, g, p.adj) to test the pairwise comparisons between the age group means
> #What significant differences are present amongst the age group means?
> pairwise.t.test(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons$Age, p.adj = "none")
Pairwise comparisons using t tests with pooled SD 

data:  dataTwoWayComparisons$StressReduction and dataTwoWayComparisons$Age 

      mid     old    
old   2.5e-05 -      
young 2.5e-05 2.3e-10

P value adjustment method: none 

> #no statistically significant differences exist between the treatment group means
> #all of the age group means are significantly different from one another

> #additional information
> #treatment group means derived using subset(data, condition)
> mean(subset(dataTwoWayComparisons$StressReduction, dataTwoWayComparisons $Treatment == "mental"))
6
> mean(subset(dataTwoWayComparisons $StressReduction, dataTwoWayComparisons $Treatment == "physical"))
5
> mean(subset(dataTwoWayComparisons $StressReduction, dataTwoWayComparisons $Treatment == "medical"))
4
> #age group means derived using subset(data, condition)
> mean(subset(dataTwoWayComparisons $StressReduction, dataTwoWayComparisons $Age == "young"))
8
> mean(subset(dataTwoWayComparisons $StressReduction, dataTwoWayComparisons $Age == "mid"))
5
> mean(subset(dataTwoWayComparisons $StressReduction, dataTwoWayComparisons $Age == "old"))
2