Question

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

Drug B

Drug C

4

6

6

5

8

7

4

4

6

3

5

6

2

4

7

4

6

5

3

5

6

4

8

5

4

6

5

1) Fill in the blanks

response variable =

factor =

n = number of observations =

p = number of treatments =

overall mean =

Drug A

Drug B

Drug C

sample mean

Total variation in the data (SSTO)=

Variation caused because of drugs (SST) =

Variation caused by the samples (SSE) =

2) Fill in the ANOVA table (alpha=0.05)

Source of Variation

SS

df

MS

F

p-value

F-critical

Treatments

Samples

Total

3) Based on your Anova table, write down the conclusion about Null hyphothesis (H0: µA=µB=µC)

If you reject Null, what does that mean? Write it in once sentence.

4) Build TUKEY SIMULTANOUS 95% confidence intervals for the following:

Tukey Simultamous C.I

µA-µB

µA-µC

µB-µC

Point Estimate

Standard error

df = p and n-p ----->

q alpha

Margin of error

Lower Limit

Upper Limit

5) Build Individual 95% confidence intervals for the following:

Individual C.I

µA-µB

µA-µC

µB-µC

µA

Point Estimate

Standard error

df = n-p ---- >

talpha/2

Margin of error

Lower Limit

Upper Limit

6) Based on the answers on parts 4 and 5, write down your conclusions about which drug beats which drug?

7) Create the MegaStat output and fill in the blanks by using the post-hoc analysis of MegsaStat output:

What is the p-value of comparing drug A and B

What is the p-value of comparing drug C and B

Did we find evidence that the effects of drugs B and C on pain relief are different from eachother?

Answer 1

1. a.Response variable = Pain relief score

b. Factor = The 3 types of drugs

c. No. of observations = 27

d. No. of treatments = 3

e. Overall mean = 5.111

f. Sample mean : A = 3.667 B = 5.778 C = 5.889

g. Total variation error (SSTO) = 56.67

h. Variation due to drugs (SST) = 28.22

i. Variation due ito samples (SSE) = 28.44

2. ANOVA table:

Analysis of Variance

Source DF SS MS F-Value P-Value F-critical

Treatments 2 28.22 14.111 11.91 0.000 0.051
Samples 24 28.44 1.185
Total 26 56.67

3. Our rule was: "Reject Ho if F-tabulated > F-critical. Here we see that F-tabulated > F-critical, so our hypothesis is rejected. This means that there exists statistically significant differences between the 3 drugs' effects in relieving pain.

4. Tukey simultaneous CI :

Difference Point SE of   
of Levels estimation Difference Lower limit Upper limit q-alpha P-Value M.E
dB - dA 2.111 0.513 0.830 3.392 4.11 0.001 2.108
dC - dA 2.222 0.513 0.941 3.503 4.33 0.001 2.221
dC - dB 0.111 0.513 -1.170 1.392 0.22 0.975 0.112

5. 95% CI:

Difference Point SE of   
of Levels estimation Difference Lower limit Upper limit talpha/2 P-Value M.E
dB - dA 2.111 0.513 1.052 3.170 4.11 0.001 2.108
dC - dA 2.222 0.513 1.163 3.281 4.33 0.001 2.221
dC - dB 0.111 0.513 -0.948 1.170 0.22 0.975 0.112

6. Based on the above 2 results, we can conclude that since t-observed = 0.509, we can say that there are significant differences between A&B and A&C but NOT between B&C.

7. a.The p-value between A&B is 0.001

b.The p-value between C&B is 0.975

c.We find that although there are negligible differences between the effects of B&C, those effects having high p-value signifies that the difference was due to high random causes in the sample. So we cannot conclude that there exists differences.