Question

Sara wanted to know if depression was greater in the Fall or Spring. So Sara measured depressive symptoms (0 – 10 with 10 being highest depression symptoms) one Fall, then again in Spring. Use a repeated-measures t-test to solved the problem using a nondirectional hypothesis and alpha of .05. Participant1: score of 7 in Fall; score of 8 in Spring Participant2: score of 5 in Fall; score of 4 in Spring Participant3: score of 9 in Fall; score of 6 in Spring Participant4: score of 5 in Fall; score of 5 in Spring Participant5: score of 9 in Fall; score of 3 in Spring Participant6: score of 3 in Fall; score of 2 in Spring Participant7: score of 9 in Fall; score of 7 in Spring Participant8: score of 4 in Fall; score of 0 in Spring Participant9: score of 9 in Fall; score of 4 in Spring

Answer 1

To perform a repeated measures t-test, or a dependent t-test, we do the following:

We find the difference in the scores of depression in fall and spring for each participants. Let that difference be D_i.

where, D_i = x_i - y_i ; x_i and y_i being the scores in fall and spring respectively.

We then find the mean of the D_i as M_d.

The hypothesis is then:

H₀ : M_d = 0 , H₁ : M_d 0

The standard deviation of the difference is :

$s_{M_{d}}=2.345$

The test statistic is :

The p-value of the test is 0.017 < 0.05.

Hence, we reject the null hypothesis and conclude on the basis of the given data that the score of depression is significantly different for fall and spring.