Multiple Comparisons Test.
To study the effects of different kinds of vigorous exercise on physical fitness, researchers randomized 33 healthy, nonathletic, 20 to 25yearold 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 (FEV_{1}), with higher values indicating better pulmonary fitness. The results were as follows:
FEV_{1}(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 oneway 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.