Homework SourseThree group of six guinea pigs each were injected respective
Three group of six guinea pigs each were injected, respectively, with 0.5 milligram, 1.0 milligram and 1.5 milligrams of a new tranquilizer, and the following are the numbers of minutes it took them to fall asleep.
Using an appropriate nonparametric method, test the null hypothesis that difference in dosage have no effect. Use 0.05 level of significance.
Solution
Null hypothesis: the three medians are equal
Alternate hypothesis: At least on pair of medians are not equal
No.
Label
Data
Rank
1
0.5mg
21
12.5
2
0.5mg
23
15.5
3
0.5mg
19
8.5
4
0.5mg
24
17
5
0.5mg
25
18
6
0.5mg
23
15.5
7
1.0mg
19
8.5
8
1.0mg
21
12.5
9
1.0mg
20
10.5
10
1.0mg
18
7
11
1.0mg
22
14
12
1.0mg
20
10.5
13
1.5mg
15
5.5
14
1.5mg
10
1
15
1.5mg
13
3
16
1.5mg
14
4
17
1.5mg
11
2
18
1.5mg
15
5.5
Kruskal-Wallis Rank Test for Differences in Medians
Data
Level of Significance
0.05
Group
Sample Size
Sum of Ranks
Mean Ranks
0.5mg
6
87
14.5
Intermediate Calculations
1.0mg
6
63
10.5
Sum of Squared Ranks/Sample Size
1996.5
1.5mg
6
21
3.5
Sum of Sample Sizes
18
Number of Groups
3
Test Result
H Test Statistic
13.0526
Critical Value
5.991
p-Value
0.0015
Reject the null hypothesis
Calculated chi square value =13.0526 > 5.991 the table value at0.05 level of significance.
The null hypothesis is rejected.
We conclude that difference in dosage has an effect.
| No. | Label | Data | Rank |
| 1 | 0.5mg | 21 | 12.5 |
| 2 | 0.5mg | 23 | 15.5 |
| 3 | 0.5mg | 19 | 8.5 |
| 4 | 0.5mg | 24 | 17 |
| 5 | 0.5mg | 25 | 18 |
| 6 | 0.5mg | 23 | 15.5 |
| 7 | 1.0mg | 19 | 8.5 |
| 8 | 1.0mg | 21 | 12.5 |
| 9 | 1.0mg | 20 | 10.5 |
| 10 | 1.0mg | 18 | 7 |
| 11 | 1.0mg | 22 | 14 |
| 12 | 1.0mg | 20 | 10.5 |
| 13 | 1.5mg | 15 | 5.5 |
| 14 | 1.5mg | 10 | 1 |
| 15 | 1.5mg | 13 | 3 |
| 16 | 1.5mg | 14 | 4 |
| 17 | 1.5mg | 11 | 2 |
| 18 | 1.5mg | 15 | 5.5 |
