Question

Problem 1. A drug company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment 27 volunteers were selected and 9 were randomly assigned to one of three drug formulations. The subjects were instructed to take the drug during their next migraine headache episode and to report their pain on a scale of 1 to 10 (10 being most pain).

             Drug A 4 5 4 3 2 4 3 4 4

             Drug B 6 8 4 5 4 6 5 8 6

             Drug C 6 7 6 6 7 5 6 5 5

You can read in data into R by the following R code.

pain = c(4, 5, 4, 3, 2, 4, 3, 4, 4, 6, 8, 4, 5, 4, 6, 5, 8, 6, 6, 7, 6, 6, 7, 5, 6, 5, 5)

drug = c(rep("A",9), rep("B",9), rep("C",9))

migraine = data.frame(pain,drug)

a). Make a boxplot to have a visual check.

b). Compute SST, SSG. SSE directly by definition

c). Compute F value directly by definition

d). Find p-value directly by definition

e). Conduct ANOVA test by R function aov.

f). Make your conclusion.

Applied stats 2 r code questions

Answer 1

a). Make a boxplot to have a visual check.

b). Compute SST, SSG. SSE directly by definition

SST = 56.66

SSG = 28.22

SSE = 28.44

c). Compute F value directly by definition

F = 11.91

d). Find p-value directly by definition

p-value = 0.000256

e). Conduct ANOVA test by R function aov.

The R output is:

The R code is:

pain = c(4, 5, 4, 3, 2, 4, 3, 4, 4, 6, 8, 4, 5, 4, 6, 5, 8, 6, 6, 7, 6, 6, 7, 5, 6, 5, 5)
drug = c(rep("A",9), rep("B",9), rep("C",9))
migraine = data.frame(pain,drug)
boxplot(pain)
aov(pain~drug)
ANOVA1 = aov(pain~drug)
summary(ANOVA1)

f). Make your conclusion.

Since the p-value (0.000256) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference between the groups.