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STAT680 Applied Statistics

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Question:

A clinical trial was conducted to evaluate the effectiveness of three treatment creams (Cream 1 - 3) for fever blisters. Twenty-four patients were randomly divided into four groups of equal size. Each group of six (6) patients were then allocated to be treated with one of the four creams (Cream 1-3 and plus a control group labelled Cream 4). The data recorded are the number of days [Days] from initial appearance of the blisters until healing is complete. (Data source: Kleinbaum, D.G., Kupper, L.L. and Muller, K.E., 1988 ).

Note: Mainly need to be done by hand but may make use of R/RStudio when possible.
a) Comment on two main interesting features of the blister data based on the boxplot of the data below.
b) Suggest an appropriate analysis (or model) for this data for comparing the four treatment groups (creams).
c) Suppose we wish to perform a one-way ANOVA for the blister data. Using the descriptive statistics below to complete the ANOVA table shown on next page. Also show, in details, how each item, such as SST, is computed. (Note that you may need first to work out the overall/grand mean based on the treatment/Cream group means given below.)
Cream i (1-4) n mean sd
 1 6 5.000 1.265
 2 6 4.333 1.033
 3 6 5.167 1.472
 4 6 7.500 1.643 

d) Based on the results in your completed ANOVA table above in part c, test if there is any difference in average number of days until healing across the four cream groups. Remember to state null and alternative hypotheses, give the test statistic value and associated degrees of freedom, p-value or range of it, and draw your conclusion (assuming that all relevant assumptions are ok for this part).
e) If one wishes to carry out multiple pairwise comparisons of all the four creams (including the control group) at an overall 5% significance level, 
i) what is the total number of these comparisons
ii) what are the significance level for each individual comparison (test) if using Bonferroni approach and the relevant t critical value in this case? (Do NOT carry out the tests.)
f) If someone wants to find out if there is any difference in average number of days until healing between the three real treatment creams (Cream 1-3) as a whole and the control group (Cream 4), form an appropriate contrast to evaluate and test the difference. Remember to state null and alternative hypotheses, give the test statistic value and associated degrees of freedom, the evidence for rejecting or not rejecting the null hypothesis, and give a conclusion that includes a relevant 95% confidence interval. (Note: Means and sample sizes by Cream group are presented in part c.)

g) In the case that only the normality assumption of an ANOVA model is violated, explain which non-parametric procedure may be considered. (Do NOT carry out this procedure!)
h) What would you suggest to try if both normality and equal variance assumptions are violated Why.
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