Homework SourseFour treatments were compared using a completely randomized
Four treatments were compared using a completely randomized design. The data are shown here:
Table 1.
Treatment
1 2 3 4
124 147 141 117
167 121 144 128
135 136 139 102
160 114 162 119
159 129 155 128
144 117 150 123
133 109
Do the data provide sufficient evidence to indicate a di fference in location for at least two of the
population distributions? Test using the Kruskal-Wallis H test with alpha = 0.05.
Solution
Do the data provide sufficient evidence to indicate a di fference in location for at least two of the
population distributions? Test using the Kruskal-Wallis H test with alpha = 0.05.
No.
Label
Data
Rank
1
T1
124
9
2
T1
167
26
3
T1
135
14
4
T1
160
24
5
T1
159
23
6
T1
144
18.5
7
T1
133
13
8
T2
147
20
9
T2
121
7
10
T2
136
15
11
T2
114
3
12
T2
129
12
13
T2
117
4.5
14
T2
109
2
15
T3
141
17
16
T3
144
18.5
17
T3
139
16
18
T3
162
25
19
T3
155
22
20
T3
150
21
21
T4
117
4.5
22
T4
128
10.5
23
T4
102
1
24
T4
119
6
25
T4
128
10.5
26
T4
123
8
Kruskal-Wallis Rank Test for Differences in Medians
Data
Level of Significance
0.05
Group
Sample Size
Sum of Ranks
Mean Ranks
T1
7
127.5
18.2143
Intermediate Calculations
T2
7
63.5
9.0714
Sum of Squared Ranks/Sample Size
5551.774
T3
6
119.5
19.9167
Sum of Sample Sizes
26
T4
6
40.5
6.7500
Number of Groups
4
Test Result
H Test Statistic
13.9021
Critical Value
7.8147
p-Value
0.0030
Reject the null hypothesis
DF=3
Calculated test value 13.9021 > 7.8147 the table value.
The null hypothesis is rejected
The data provide sufficient evidence to indicate a difference in location for at least two of the
population distributions.
| No. | Label | Data | Rank |
| 1 | T1 | 124 | 9 |
| 2 | T1 | 167 | 26 |
| 3 | T1 | 135 | 14 |
| 4 | T1 | 160 | 24 |
| 5 | T1 | 159 | 23 |
| 6 | T1 | 144 | 18.5 |
| 7 | T1 | 133 | 13 |
| 8 | T2 | 147 | 20 |
| 9 | T2 | 121 | 7 |
| 10 | T2 | 136 | 15 |
| 11 | T2 | 114 | 3 |
| 12 | T2 | 129 | 12 |
| 13 | T2 | 117 | 4.5 |
| 14 | T2 | 109 | 2 |
| 15 | T3 | 141 | 17 |
| 16 | T3 | 144 | 18.5 |
| 17 | T3 | 139 | 16 |
| 18 | T3 | 162 | 25 |
| 19 | T3 | 155 | 22 |
| 20 | T3 | 150 | 21 |
| 21 | T4 | 117 | 4.5 |
| 22 | T4 | 128 | 10.5 |
| 23 | T4 | 102 | 1 |
| 24 | T4 | 119 | 6 |
| 25 | T4 | 128 | 10.5 |
| 26 | T4 | 123 | 8 |
