Wertheretal et al. examined the β-leucocyte count (/ L)  in 51subjects with colorectal cancer and 19 healthy controls. The cancer patients were also classified into Dukes’s classification (A,B,C) for colorectal cancer that gives doctors a guide to the risk, following surgery, of cancer coming back or spreading to other parts of the body. An additional category (D) identified patients with disease that had not been completely resected. The results are displayed in the following table. Perform an analysis of these data in which you identify the sources of variability and specify the degrees of freedom for each. Do these data provide sufficient evidence to indicate that, on average, leucocyte counts differ among the five categories? Let α=0.01 . Write the null and alternative hypotheses of this study. Test the claim using the ANOVA Table. If you reject the null hypothesis, interpret your results using multiple comparison test Bonferroni. What assumptions must be made in part (b)? Are they satisfied?

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Wertheretal et al. examined the β-leucocyte count (/ L)  in 51subjects with colorectal cancer and 19 healthy controls. The cancer patients were also classified into Dukes’s classification (A,B,C) for colorectal cancer that gives doctors a guide to the risk, following surgery, of cancer coming back or spreading to other parts of the body. An additional category (D) identified patients with disease that had not been completely resected. The results are displayed in the following table. Perform an analysis of these data in which you identify the sources of variability and specify the degrees of freedom for each. Do these data provide sufficient evidence to indicate that, on average, leucocyte counts differ among the five categories? Let α=0.01 .

Write the null and alternative hypotheses of this study.

Test the claim using the ANOVA Table.

If you reject the null hypothesis, interpret your results using multiple comparison test Bonferroni.

What assumptions must be made in part (b)? Are they satisfied?

Healthy
A
D
6.0
7.7
10.4
8.0
9.5
6.3
7.8
5.6
6.7
7.8
5.1
6.1
7.0
9.3
5.7
6.2
9.6
8.2
6.6
8.0
10.4
5.5
9.0
9.3
9.6
4.4
5.8
8.4
7.2
13.7
7.4
4.0
8.1
5.2
6.3
7.0
5.4
8.0
9.8
7.3
5.6
6.5
6.2
6.2
5.3
9.1
10.1
2.6
11.0
9.3
6.3
10.9
9.4
6.1
10.6
6.5
5.3
5.2
5.4
5.4
7.9
7.6
5.2
7.6
9.2
4.3
5.8
4.9
7.0
7.3
4.9
6.9
4.3
5.6
5.1
Source: Data provided courtesy of Kim Werther, M.D., Ph.D.
Transcribed Image Text:Healthy A D 6.0 7.7 10.4 8.0 9.5 6.3 7.8 5.6 6.7 7.8 5.1 6.1 7.0 9.3 5.7 6.2 9.6 8.2 6.6 8.0 10.4 5.5 9.0 9.3 9.6 4.4 5.8 8.4 7.2 13.7 7.4 4.0 8.1 5.2 6.3 7.0 5.4 8.0 9.8 7.3 5.6 6.5 6.2 6.2 5.3 9.1 10.1 2.6 11.0 9.3 6.3 10.9 9.4 6.1 10.6 6.5 5.3 5.2 5.4 5.4 7.9 7.6 5.2 7.6 9.2 4.3 5.8 4.9 7.0 7.3 4.9 6.9 4.3 5.6 5.1 Source: Data provided courtesy of Kim Werther, M.D., Ph.D.
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