//One-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
> dataOneWayComparisons <- read.csv("dataset_ANOVA_OneWayComparisons.csv")
> #display the data
> dataOneWayComparisons
   Treatment StressReduction
1     mental               2
2     mental               2
3     mental               3
4     mental               4
5     mental               4
6     mental               5
7     mental               3
8     mental               4
9     mental               4
10    mental               4
11  physical               4
12  physical               4
13  physical               3
14  physical               5
15  physical               4
16  physical               1
17  physical               1
18  physical               2
19  physical               3
20  physical               3
21   medical               1
22   medical               2
23   medical               2
24   medical               2
25   medical               3
26   medical               2
27   medical               3
28   medical               1
29   medical               3
30   medical               1

> #use anova(object) to test the omnibus hypothesis
> #Is there a significant difference amongst the treatment means?
> anova(lm(StressReduction ~ Treatment, dataOneWayComparisons))
Analysis of Variance Table

Response: StressReduction
          Df Sum Sq Mean Sq F value  Pr(>F)  
Treatment  2 11.667  5.8333  5.1639 0.01262 *
Residuals 27 30.500  1.1296                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

> #omnibus test significant; 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?
> #note that no Type I error adjustment is used in this example and an alpha level of .05 is assumed
> pairwise.t.test(dataOneWayComparisons$StressReduction, dataOneWayComparisons$Treatment, p.adj = "none")

	Pairwise comparisons using t tests with pooled SD 

data:  dataOneWayComparisons$StressReduction and dataOneWayComparisons$Treatment 

         medical mental
mental   0.0039  -     
physical 0.0448  0.3022

P value adjustment method: none 

> #significant differences exist between the mental-medical and physical-medical, but not the mental-physical treatments

> #additional information
> #treatment group means derived using subset(data, condition)
> mean(subset(dataOneWayComparisons$StressReduction, dataOneWayComparisons$Treatment == "mental"))
[1] 3.5
> mean(subset(dataOneWayComparisons$StressReduction, dataOneWayComparisons$Treatment == "physical"))
[1] 3
> mean(subset(dataOneWayComparisons$StressReduction, dataOneWayComparisons$Treatment == "medical"))
[1] 2