Question

1) A researcher would like to determine if relaxation training affects the number of headaches for chronic headache sufferers. For a week prior to training, each participant records the number of headaches suffered. Participants then receive relaxation training and for the week following training the number of headaches is again measured. The data are as follows: before: 6, 5, 3, 3, 6, 2, 4, 4 and after: 4, 1, 3, 1, 2, 1, 3, 2.

a. Do the results indicate a significant difference? Use a two-tailed test with α = .05. State the null hypothesis and the tcritical you will use to evaluate the null hypothesis.

b. Compute Cohen’s d and r2 to measure the size of the effect. Conclude with a separate summary statement for each measure of effect size that is appropriate for publication in a scientific journal.

Answer 1

SOLUTION 1A]

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ ≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region: Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=7.

Hence, it is found that the critical value for this two-tailed test is tc​=2.365, for α=0.05 and df=7.

The rejection region for this two-tailed test is R={t:∣t∣>2.365}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis: Since it is observed that ∣t∣=4>tc​=2.365, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0052, and since p=0.0052<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is different than μ2​, at the 0.05 significance level.

b] COhen's d= 2/1.414= 1.41 EFFECT SIZE IS LARGE

This means that if two groups' means don't differ by 1.41 standard deviations or more, the difference is trivial, even if it is statistically significant.

r^2= t^2/t^2+df

= (4)^2/(4)^2+7

= 16/23

=0.7 THIS IS ALSO LARGE