
Floods: Using the data in Exercise 22, perform the Tukey—Kramer test to determine which pairs of

To find: The pairs of means which are different by Tukey-Kramer test.
Answer to Problem 24E
The pairs of means which are different by Tukey-Kramer test are
Explanation of Solution
Given information:
The value of
Channel Type | Drainage Time | |||
1 | 41.4 | 43.4 | 50.0 | 41.2 |
2 | 38.7 | 48.3 | 51.1 | 38.3 |
3 | 32.6 | 33.7 | 34.8 | 22.5 |
4 | 26.3 | 30.9 | 33.3 | 23.8 |
5 | 44.9 | 47.2 | 48.5 | 37.1 |
Calculation:
The sample size
The sample size are
The total number in all the samples combined is,
From the given data the sample means are,
Further solve,
Further solve,
The grand mean is,
The value of
The standard of deviation of sample 1 is,
The value of
The standard of deviation of sample 2 is,
The value of
The standard of deviation of sample 3 is,
The value of
The standard of deviation of sample 4 is,
The value of
The standard of deviation of sample 5 is,
The treatment sum of squares is,
The error sum square is,
The degree of freedom for treatment sum of square is,
The degree of freedom for error sum of square is,
The treatment mean sum of square is,
The error mean sum of square is,
The mean of 1 and 2 sample is,
The mean of 1 and 3 sample is,
The mean of 1 and 4 sample is,
The mean of 1 and 5 sample is,
The mean of 2 and 3 sample is,
The mean of 2 and 4 sample is,
The mean of 2 and 5 sample is,
The mean of 3 and 4 sample is,
The mean of 3 and 5 sample is,
The mean of 4 and 5 sample is,
The critical value q for the student zed range distribution at
The comparison of pairwise test statistic values with critical values is shown in table below.
Means | Test statistic | Critical value | Decision |
1,2 | 0.0382 | 5.56 | Do not reject null hypothesis. |
1,3 | 5.0065 | 5.56 | Do not reject null hypothesis. |
1,4 | 5.8951 | 5.56 | reject null hypothesis |
1,5 | 0.1624 | 5.56 | Do not reject null hypothesis. |
2,3 | 5.0447 | 5.56 | Do not reject null hypothesis. |
2,4 | 5.9333 | 5.56 | reject null hypothesis. |
2,5 | 0.1242 | 5.56 | Do not reject null hypothesis |
3,4 | 0.8886 | 5.56 | Do not reject null hypothesis. |
3,5 | 5.1689 | 5.56 | Do not reject null hypothesis. |
4,5 | 6.0575 | 5.56 | reject null hypothesis.. |
Therefore, the pairs of means which are different by Tukey-Kramer test are
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