Question

A veterinarian is studying three different medications that could be used in the prevention of heartworm in young puppies. She has acquired for study four different litters of cocker spaniels, and three puppies were randomly selected from each litter. The three selected puppies from a litter were then randomly assigned to one of the three treatments. The data below represents the number of months after a single treatment before the initial onset of heartworm in the puppies for this randomized block design. The veterinarian determined that each of the treatment groups has an approximately normal distribution

Formula	Litter 1	Litter 2	Litter 3	Litter 4
A	3.3	3.6	4.1	4.1
B	3.2	3.2	3.9	3.8
C	2.3	2.9	3.5	3.5

a) Construct the ANOVA table for this experiment.

b) Test the equality of the mean time to onset of heartworm for the three different medications at a 5% level of significance. Your answer should show assumptions, hypotheses, and conclusions

c) Using the 95% Tukey-Kramer procedure, determine which of the treatment means are significantly different.

Answer 1

b) the mean time to onset of heart worm for the three different medications are the same

vs

the alternative that atleast one treatment shows significantly different times.

The assumptions made before proceeding to ANOVA analysis are

1) Samples should be independent.

2) The independent samples have variances almost equal

3) The residuals are approximately normal.The veteranian determined that each of the treatment groups has an approximately normal distribution

All the three assumptions are met.Hence we have the ANOVA table below

a)

The pvalue indicates that we fail to reject the null hypothesis as the p value >0.05. Hence None of the three treatments are statistically significant. Hence there is no need for the post hoc analysis in c)