Multiple Comparisons Test.
To study the effects of different kinds of vigorous exercise on physical fitness, researchers randomized 33 healthy, non-athletic, 20- to 25-year-old made volunteers into three exercise programs: swimming, running, and bicycling. After six months, a variety of measures were taken of the men's fitness levels. One such measure was forced expiratory volume (FEV1), with higher values indicating better pulmonary fitness. The results were as follows:
|
FEV1(liters)
|
|
Programs
|
Sample size
|
Sample mean
|
Sample standard deviation
|
|
Swimming
|
11
|
4.4
|
0.4
|
|
Running
|
11
|
4.2
|
0.4
|
|
Bicycling
|
11
|
3.7
|
0.5
|
The one-way ANOVA table for these data is as follows, indicating as a minimum one significant difference in mean FEV1 among the three groups.
|
Source
|
DF
|
Sum of Squares
|
Mean Square
|
F Value
|
Pr > F
|
|
Model
|
2
|
2.86
|
1.43
|
7.53
|
0.0022
|
|
Error
|
30
|
5.7
|
0.19
|
|
|
|
Corrected Total
|
32
|
8.56
|
|
|
|
Perform all pair wise comparisons among the 3 programs, using a Tukey adjustment and an overall significance level of 0.05, and then interpret all your results.