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) 1) What is the null hypothesis for the above comparison? 2) What do the numbers listed in the MS column represent? 3) What would happen in the ANOVA table if you were to add a constant to each of the observed values given above Why? 4) State carefully the conclusions based on the global test. Justify your conclusion 5) What conclusions can you draw from the HSD comparisons? Why would investigators use this test rather than direct comparisons between the groups?

Explanation / Answer

One-way ANOVA: Placebo, Drug B, Drug C

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 Placebo, Drug B, Drug C

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 31.19 15.593 12.20 0.000
Error 24 30.67 1.278
Total 26 61.85

Model Summary

S R-sq R-sq(adj) R-sq(pred)
1.13039 50.42% 46.29% 37.25%

Means

Factor N Mean StDev 95% CI
Placebo 9 3.556 1.014 (2.778, 4.333)
Drug B 9 5.778 1.481 (5.000, 6.555)
Drug C 9 5.889 0.782 (5.111, 6.667)

Pooled StDev = 1.13039

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Drug C 9 5.889 A
Drug B 9 5.778 A
Placebo 9 3.556 B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference SE of Adjusted
Difference of Levels of Means Difference 95% CI T-Value P-Value
Drug B - Placebo 2.222 0.533 ( 0.892, 3.552) 4.17 0.001
Drug C - Placebo 2.333 0.533 ( 1.003, 3.663) 4.38 0.001
Drug C - Drug B 0.111 0.533 (-1.219, 1.441) 0.21 0.976

Based on your F-statistic and p-value ina ANOVA, We conclude that we have evidence to reject the null hypothesis, and conclude that at least one of the means is different. Further testing could be done using multiple comparisons.

These results show that the B-Placebo and C-Placebo differences are significant (p=0.0011 and p=0.00065)

while the C-B difference is not (p=0.97).

Hope this will helpful to you :) Thanks and god bless you :)

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