Biostatistics

408 CHAPTER 8 ANALYSIS OF VARIANCE
4. Refer to the urinary colony-stimulating factor data on 1500 subjects (CSFDATA). The data are the
urinary colony-stimulating factor (CSF) levels in five populations: normal subjects and subjects
with four different diseases. Each observation represents the mean colony count offour plates from a
single urine specimen from a given subject. Select a simple random sample of size 15 from each of
the five populations and perform an analysis of variance to determine if one may conclude that the
population means are different. Let a ¼ :05. Use Tukey’s HSD statistic to test for significant
differences among all possible pairs of sample means. Prepare a narrative report on the results of
your analysis. Compare your results with those of your classmates.
5. Refer to the red blood cell data on 1050 subjects (RBCDATA). Suppose that you are a
statistical consultant to a medical researcher who is interested in learning something about the
relationship between blood folate concentrations in adult females and the quality of their diet.
The researcher has available three populations of subjects: those whose diet quality is rated as
good, those whose diets are fair, and those with poor diets. For each subject there is also
available her red blood cell (RBC) folate value (in mg=liter of red cells). Draw a simple random
sample of size 10 from each population and determine whether the researcher can conclude
that the three populations differ with respect to mean RBC folate value. Use Tukey’s test to
make all possible comparisons. Let a ¼ :05 and find the p value for each test. Compare your
results with those of your classmates.
6. Refer to the serum cholesterol data on 350 subjects under three diet regimens (SERUMCHO).
A total of 347 adult males between the ages of 30 and 65 participated in a study to investigate
the relationship between the consumption of meat and serum cholesterol levels. Each subject
ate beef as his only meat for a period of 20 weeks, pork as his only meat for another period of
20 weeks, and chicken or fish as his only meat for another 20-week period. At the end of each
period serum cholesterol determinations ðmg=100mlÞ were made on each subject. Select a
simple random sample of 10 subjects from the population of 350. Use two-way analysis of
variance to determine whether one should conclude that there is a difference in population
mean serum cholesterol levels among the three diets. Let a ¼ :05. Compare your results with
those of your classmates.
REFERENCES
Methodology References
1. R. A. FISHER, The Design of Experiments, Eighth Edition, Oliver and Boyd, Edinburgh, 1966.
2. R. A. FISHER, Contributions to Mathematical Statistics, Wiley, New York, 1950.
3. R. A. FISHER, Statistical Methods for Research Workers, Fourteenth Edition, Hafner, New York, 1973.
4. KLAUS HINKELMANN and OSCAR KEMPTHORNE, Design and Analysis of Experiments, Revised Edition, Wiley, New
York, 1994.
5. DOUGLAS C. MONTGOMERY, Design and Analysis of Experiments, Fourth Edition, Wiley, New York, 1997.
6. JEROME L. MYERS and ARNOLD D. WELL, Research Design and Statistical Analysis, Earlbaum Associates,
Hillsdale, NJ, 1995.
7. JASON C. HSU, Multiple Comparisons: Theory and Methods, Chapman & Hall, New York, 1996.
8. PETER H. WESTFALL, RANDALL D. TOBIAS, DROR ROM, RUSSELL D. WOLFINGER, and YOSEF HOCHBERG, Multiple
Comparisons and Multiple Tests, SAS Publishing, Cary, NC, 2001.
9. J. W. TUKEY, “The Problem of Multiple Comparisons,” Mimeographed Monograph, Princeton University, 1953;
cited in Yosef Hochberg and Ajit C. Tamhane, Multiple Comparison Procedures, John Wiley and Sons, New
York, 1987.
10. B. J. WINER, Statistical Principles in Experimental Design, Second Edition, McGraw-Hill, New York, 1971.
11. C. Y. KRAMER, “Extension of Multiple Range Tests to Group Means with Unequal Sample Sizes,” Biometrics, 63
(1956), 307–310.