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REVIEW QUESTIONS AND EXERCISES 371
• m mean of population (or the grand mean)
• n number of blocks
• n x sample size
• s 2 variance
• SSX sum-of-squares (where X: A among,
Bl block, T total, Tr treatment, W within)
• t i treatment effect
• X xxx measurement
REVIEW QUESTIONS AND EXERCISES
1. Define analysis of variance.
2. Describe the completely randomized design.
3. Describe the randomized block design.
4. Describe the repeated measures design.
5. Describe the factorial experiment as used in the completely randomized design.
6. What is the purpose of Tukey’s HSD test
7. What is an experimental unit
8. What is the objective of the randomized complete block design
9. What is interaction
10. What is a mean square
11. What is an ANOVA table
12. For each of the following designs describe a situation in your particular field of interest where the
design would be an appropriate experimental design. Use real or realistic data and do the appropriate
analysis of variance for each one:
(a) Completely randomized design
(b) Randomized complete block design
(c) Completely randomized design with a factorial experiment
(d) Repeated measures designs
13. Werther et al. (A -26) examined the b-leucocyte count 1*10 9 >L2 in 51 subjects 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 the 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 the average,
leucocyte counts differ among the five categories Let a = .01 and find the p value. Use
Tukey’s procedure to test for significant differences between individual pairs of sample means.