Question

Application Exercise:
A team of researchers recruited a random sample of migraine sufferers. Before the study began at baseline, participants were asked to record the duration of headaches they experienced in a week. A few days later, all participants were asked to practice a week-long relaxation technique designed to reduce migraine headaches. A two-week off period in which the participants practiced nothing was given between the relaxation technique. Throughout the relaxation technique participants were asked to record the duration of headaches. What can be concluded with an α of 0.05?

Baseline	Week 1	Week 3
9 7 12 8 12 7 11 7 10	9 7 6 6 9 5 6 5 9	8 9 6 4 7 4 6 5 8

a) What is the appropriate test statistic?
---Select---na, one-way ANOVA, within-subjects ANOVA, two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
critical value = ____________ ; test statistic = ___________
Decision: ---Select---Reject H0 or Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = ___________ ; ---Select---na, trivial effect, small effect, medium effect, large effect

d) Make an interpretation based on the results.

-At least one week differs on the headache duration.

-None of the weeks differed on headache duration.    

e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
1 vs. 3: difference =_______________ ; significant: ---Select---Yes OR No
1 vs. 2: difference =_______________ ; significant: ---Select---Yes OR No

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
1 vs. 3: test statistic = ______________ ; significant: ---Select---Yes OR No
2 vs. 3: test statistic = ______________ ; significant: ---Select---Yes OR No

Answer 1

Solution

a) What is the appropriate test statistic?

one-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.

Using Excel we find one-way ANOVA

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Baseline	9.0000	83.0000	9.2222	4.4444
Week 1	9.0000	62.0000	6.8889	2.8611
Week 3	9.0000	57.0000	6.3333	3.2500
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	42.2963	2.0000	21.1481	6.0105	0.0077	3.4028
Within Groups	84.4444	24.0000	3.5185
Total	126.7407	26.0000

critical value =3.4028;

test statistic = 6.0105
Decision: Reject H0

d) Make an interpretation based on the results.

At least one week differs on the headache duration.