A drug company tested three formulations of a pain relief medicine for migraine

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 a placebo or one of two different 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 (1 being most pain). http://vassarstats.net/(ANOVA One way ANOVA Independent samples) Placebo 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 What is the null hypothesis for the above comparison? What do the numbers listed in the MS column represent? What would happen in the ANOVA table if you were to add a constant to each of the observed values given above? Why? State carefully the conclusions based on the global test. Justify your conclusion What conclusions can you draw from the HSD comparisons? Why would investigators use this test rather than direct comparisons between the grou

Explanation / Answer

Part 1)

All the three population means are equal.

Part 2)

In Anova table MS contains the "average" sum of squares for the Factor and the Error.

MSB = SS(Between)/df

MSE = SS(Error)/df

Part 3)

There will be no changes in the ANOVA table if we add a constant to each of the observed values given above as the variation in data remain the same.

Part 3 )

We go to excel and then we put the data in columns and then go to data after data analysis we select the Single Factor Anova and the we select the data. We get the following Anova table.

SUMMARY

Groups

Count

Sum

Average

Variance

Column 1

9

33

3.666667

0.75

Column 2

9

52

5.777778

2.194444

Column 3

9

53

5.888889

0.611111

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

28.22222

2

14.11111

11.906

0.0003

3.403

Within Groups

28.44444

24

1.185185

Total

56.66667

26

Part 4)

Here the F test statistics is 11.906 and the p-value is .0003. The obtained p-value is less than .05 (level of significance). The null hypothesis can be rejected and there is sufficient evidence to conclude that all the population means are not equal, at least one of the mean differs.

SUMMARY

Groups

Count

Sum

Average

Variance

Column 1

9

33

3.666667

0.75

Column 2

9

52

5.777778

2.194444

Column 3

9

53

5.888889

0.611111

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

28.22222

2

14.11111

11.906

0.0003

3.403

Within Groups

28.44444

24

1.185185

Total

56.66667

26

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