Question

A pharmaceutical company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment, 88 volunteers 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 level on a Likert scale of 1 (no pain) to 10 (extreme pain) 30 minutes after taking the drug. Is there a significant difference in the mean pain level for at least one of the three drug formulations?  

(a) Is the data categorical or quantitative?

(b)   How many groups/samples of data were collected?       (For example,   if there is a sample for men and a sample for women,   that would be two groups or samples of data)

(c) If the data is  categorical, then how many possible answers are there? If the data is  quantitative, then can it be matched?  If so, for the same what?

(d)  How can I visualize the data (what is the appropriate way to graph the data)?
(e)   What type of test would you do?     (Choose from:  one proportion,  two proportions,  chi-square goodness of fit,  chi-square test for independence,  one mean,  paired means,  independent means,  ANOVA with independent samples,   ANOVA with blocked samples  )
(f)   Write the null and alternative hypotheses.  (Do not perform the test)

Answer 1

Solution

Part (a)

Data is quantitative Answer 1

[Data is ‘pain level on a Likert scale of 1 (no pain) to 10 (extreme pain) 30 minutes after taking the drug’ which is clearly measurable.]

Part (b)

Number of groups/samples of data collected: 3 groups Answer 2

[One group each to test each of three formulations of a pain relief medicine for migraine headache sufferers]

Part (c)

Since the data is  quantitative [vide Answer 1], it can be matched Answer 3

Part (d)

Appropriate way to graph the data: A simple bar diagram with 3 individual bars, height of the bar being proportional to the mean pain level for each of three formulations

Or, a multiple line graph with three line graphs, differently colored, each plotting the actual pain levels of subjects assigned to each of the 3 formulations. Answer 4

Part (e)

Type of test to do: ANOVA with independent samples Answer 5

[One way classification with unequal number of observations per group – note that 88 is not a multiple of 3 and hence equal number of observations per group is not possible]

Part (f)

Hypotheses:

Null hypothesis: H₀: α₁ = α₂ = α₃ Vs Alternative: H₁: at least one αi is different from other αi’s. Answer 6

where

xij represents the pain level reported by the jth volunteer in the ith group, j = 1,2,…,ni; i = 1,2, 3 and

the ANOVA model is: xij = µ + αi + εij, with µ = common effect, αi = effect of ith group (formulation)   and εij is the error component which is assumed to be Normally Distributed with mean 0 and variance σ².

DONE