Hypothesis testing for one-way ANOVA.
An experiment was conducted to evaluate the effectiveness of five different weight reducing agents. A random sample of 50 males was at random divided into five equal groups, with preparation A assigned to the first group, B to the second, and so on. Each person in the experiment was given a pre-study physical and told how numerous pounds overweight he was. A comparison of the mean number of pounds overweight for the groups showed no significant differences. The study was then begun, with each group taking the prescribed preparation for a fixed period of time. Finally of the study period, weight losses were recorded. The data are given here.
|
A
|
12.4
|
10.7
|
11.9
|
11.0
|
12.4
|
12.3
|
13.0
|
12.5
|
11.2
|
13.1
|
|
B
|
9.1
|
11.5
|
11.3
|
9.7
|
13.2
|
10.7
|
10.6
|
11.3
|
11.1
|
11.7
|
|
C
|
8.5
|
11.6
|
10.2
|
10.9
|
9.0
|
9.6
|
9.9
|
11.3
|
10.5
|
11.2
|
|
D
|
8.7
|
9.3
|
8.2
|
8.3
|
9.0
|
9.4
|
9.2
|
12.2
|
8.5
|
9.9
|
|
E
|
12.7
|
13.2
|
11.8
|
11.9
|
12.2
|
11.2
|
13.7
|
11.8
|
11.5
|
11.7
|
A. Test for important differences among weight losses for the five diets, and perform all pair wise comparisons using
a. Fisher's LSD
b. Tukey's procedure
B. Which procedure in part A is most appropriate. Give reasons for your selection.