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STAT461 Homework #5
due Monday, 2/11
1. In Lab 5, Problem 5:
(a) What are the Tukey, Bonferroni, and Scheff′e critical values. Which one will produce the
most powerful procedure (most likely to reject H0)?
(b) Using the Bonferroni approach, which pairs of means are significantly different? List the
group means in order from least to greatest, and underline any that are not significantly
different.
(c) When would one prefer to use Bonferroni’s approach over Scheff′e’s approach? When
would one prefer to use Scheff′e’s approach over Bonferroni’s approach?
2. The bioactivity of four different drugs for treating a particular illness was compared in a study.
The treatment averages are as follows: y1. = 66.10, y2. = 65.75, y3. = 62.63 , y4. = 63.85.
The sample size within each group was n = 7. A partial ANOVA table is provided below:
Source SS df MS F
Drug 56.10
Error 62.12
Total
(a) From the ANOVA table, find the value of the F test statistic. Is this significant evidence
that the population mean bioactivity levels are different among the four drugs.
(b) We wish to make all pairwise comparisons between the four treatments. How many
possible pairwise comparisons are there?
(c) Without adjustment for multiplicity, what would the critical value be for an individual
pairwise comparison? Use α = .05.
(d) If the desired FWER is 0.05, what would Tukey’s critical value be in this situation?
Also, find Bonferroni’s and Scheff′e’s critical values.
(e) Using each of the three approaches in (d) above, which pairs of means are significantly
different? Hint: Since the sample sizes are equal, you don’t have to compute the test
statistic every time. Using the Tukey critical value as an example,
(f) Comment on any differences in the results in parts (c), (d) and (e). Which is the most
appropriate procedure in this case?