Question

A randomized clinical trial of 135 youth aged 10 to 17 years diagnosed with chronic migraine were assigned to one of two treatments. One involved 10 cognitive behavioral therapy (CBT) sessions and use of the drug amitriptyline. The other involved 10 headache education sessions plus amitriptyline. Twenty weeks after treatment, the severity of migraines for each subject was assessed using the Pediatric Migraine Disability Assessment Score (PedMIDAS). Here are data on PedMIDAS scores 20 weeks post-treatment for the two groups:

Group n mean SD

CBT 71 12.2 16.0

education 64 28.5 38.8

Does this data show that there is a difference in mean PedMIDAS scores for the two treatments?

The solution must include the following parts, in order. Point form is fine.

a) First answer each of these questions:

i) Does this call for a confidence interval or a hypothesis test?

ii) Is this 1 sample or 2 samples?

iii) Is this about mean(s) or proportion(s)?

iv) If this is about mean(s), do you know the SD of the population (σ — or σ1 & σ2 )? (If this is about proportions, skip this question.)

b) What are the population parameter(s), and what are the sample statistic(s)? Provide symbols, and say what they represent in the context of the question. (For example, "µ is the mean completion time of the population, and x̄ is the mean completion time for the sample".) You may want to give the statistic values here.

c) Complete the question. Details depend on the kind of problem:

• For a confidence interval:

i) State the confidence level. (If it is not given, make a reasonable choice.)

ii) Give the formula for the margin of error (symbols only, no numbers!).

iii) Calculate the margin of error (show your work!).

iv) State the confidence interval in a complete sentence (in words!), in the context of the original problem. (You may use whichever form you prefer.)

• For a hypothesis test:

i) State the significance level (alpha). (If it is not given, make a reasonable choice.)

ii) Give the formula for the test statistic (z or t) (symbols only, no numbers!).

iii) State the null and alternative hypotheses. Use symbols, and state them in the context of the original problem. (A sketch is optional, but very useful.)

iv) Calculate the test statistic (z or t) (show your work!), and determine the p-value.

v) State your conclusion in a complete sentence (in words!), in the context of the original problem. Your conclusion should state whether or not you reject the null hypothesis, and what this says about the original question.

Answer 1

(a)

(i) Hypothesis test

(ii) Two samples

(iii) Means

(iv) We know only the sample means. We don't know the population means.

(b)

n1 = 71, n2 = 64, x1-bar = 12.2, x2-bar = 28.5, s1 = 16, s2 = 38.8   

(c)      

(i) α = 0.05 (assumed)

(ii) Pooled SD, s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)]

SE = s * √{(1 /n1) + (1 /n2)}

t = (x1-bar -x2-bar)/SE

(iii) Ho: μ1 = μ2 (the mean scores are the same for the two groups) and

Ha: μ1 ≠ μ2 (the mean scores are significantly different for the two groups)

(iv)

s = √[{(n1 - 1) s1^2 + (n2 - 1) s2^2} / (n1 + n2 - 2)] =   √(((71 - 1) * 16^2 + (64 - 1) * 38.8^2)/(71 + 64 -2)) =     29.12

SE = s * √{(1 /n1) + (1 /n2)} = 29.1176922162454 * √((1/71) + (1/64)) = 5.018855293      

t = (x1-bar -x2-bar)/SE = -3.247752535       

p- value = 0.001472539

(v) Decision: Since p- value < α, we reject Ho

Conclusion: There is sufficient evidence of a significant difference in mean PedMIDAS scores for the two treatments.

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