12.54 A dandruff study.

Analysis of variance methods are often used in clinical trials where the goal is to assess the

effectiveness of one or more treatments for a particular medical condition. One such study compared three treatments for dandruff and a placebo. The treatments were 1% pyrithione zinc shampoo (PyrI), the same shampoo but with instructions to shampoo two times (PyrII), 2% ketoconazole shampoo (Keto), and a placebo shampoo (Placebo). After six weeks of treatment, eight sections of the scalp were examined and given a score that measured the amount of scalp flaking on a 0 to 10 scale. The response variable was the sum of these eight scores. An analysis of the baseline flaking measure indicated that randomization of patients to treatments was successful in that no differences were found between the groups. At baseline there were 112 subjects in each of the three treatment groups and 28 subjects in the Placebo group. During the clinical trial, 3 dropped out from the PyrII group and 6 from the Keto group. No patients dropped out of the other two groups.

DANDRUFF

(a) Find the mean, standard deviation, and standard error for the subjects in each group. Summarize these, along with the sample sizes, in a table and make a graph of the means.

(b) Run the analysis of variance on these data. Write a short summary of the results and your

conclusion. Be sure to include the hypotheses tested, the test statistic with degrees of freedom, and theP-value.

Pyrl	Keto	Placebo
17	17	30
16	17	29
18	17	31
17	15	31
18	14	29
16	16	29
17	16	28
20	17	29
17	15	26
17	15	29
15	16	29
18	17	28
17	17	31
17	16	30
17	16	28
15	15	28
17	16	30
16	17	31
20	16	31
17	15	31
17	18	28
17	17	32
18	16	32
18	17	29
17	15	28
18	15	26
18	16	29
19	15	31
16	18
17	16
18	16
20	18
19	16
18	16
19	17
17	16
19	15
15	15
19	16
18	17
19	16
16	18
19	18
17	16
18	17
17	15
16	15
16	16
17	16
18	14
17	15
17	17
15	16
18	15
19	17
17	16
18	16
18	15
18	16
18	14
18	17
20	16
16	16
18	15
19	16
15	16
18	16
16	16
16	17
17	15
19	16
15	16
17	16
18	15
17	17
18	16
18	17
17	16
18	16
16	16
17	16
17	18
17	15
17	17
17	16
17	15
17	15
18	15
18	16
17	17
17	15
18	15
18	14
18	16
18	17
17	16
17	16
17	15
17	17
18	17
16	17
19	16
19	16
17	17
19	15
17	16
15
16
18
18
17
17
17
17
18
19
16
18
18
16
18
19
19
17
19
18
17
18
16
19
16
16
19
17
19
14
17
18
17
19
18
16
16
15
16
18
16
14
18
17
17
17
16
18
19
16
16
16
17
17
19
18
19
18
18
17
16
18
19
14
16
18
16
16
15
19
17
19
17
20
16
16
17
16
16
16
16
16
18
19
17
17
15
17
19
17
20
17
19
15
17
18
16
17
18
17
16
16
17
18
18
18
16
16
18
17
21
17
19
16
17