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3. Measuring effect size for two-factor ANOVA It is projected that approximately 580,000 veterans will take advantage of the GI Bill for the 21st Century.

3. Measuring effect size for two-factor ANOVA

It is projected that approximately 580,000 veterans will take advantage of the GI Bill for the 21st Century. Boots to Books is a course for all veterans, current military members, and their family members, friends, and supporters. The goal of Boots to Books is to assist deployed, postdeployed, and veteran students in making a positive transition from military to civilian life or from deployment to postdeployment life, including the acquisition of college survival skills.

Posttraumatic stress disorder (PTSD) is quite common among combat veterans. Suppose that a researcher wants to revise the Boots to Books course in order to reduce the effects of PTSD. She recruits a group of combat veterans and collects data on the length of time they were in the military (factor A) and the potential components of the revised course (community service, physical activity, journaling, and meditation: factor B). She then assigns them one of the four components. The study will evaluate which components of the program are the most effective for reducing PTSD symptoms.

The results of the hypothetical study are summarized in the following data matrix. Each cell reports the average (M), the total (T), and the sum of squares (SS) of the symptom score (X) on the Clinician-Administered PTSD Scale (CAPS) of 10 veterans. Veterans are grouped according to the number of years they served in the military.

Factor B: Program Component

Community Service Physical Activity Journaling Meditation
M = 48.5 M = 48.5 M = 53 M = 54
1-2 T = 485 T = 485 T = 530 T = 540 TROW1ROW1= 2,040
SS = 52.5 SS = 52.5 SS = 240 SS = 210
M = 49.5 M = 49.5 M = 48.5 M = 48.5
Factor A: Years in Military 3-4 T = 495 T = 495 T = 485 T = 485 TROW2ROW2= 1,960 X = 301,175
SS = 62.5 SS = 112.50 SS = 52.5 SS = 52.5
M = 50.5 M = 50.5 M = 49.5 M = 49
>4 T = 505 T = 505 T = 495 T = 490 TROW3ROW3= 1,995
SS = 152.5 SS = 202.5 SS = 62.5 SS = 60
TCOL1COL1= 1,485 TCOL2COL2= 1,485 TCOL3COL3= 1,510 TCOL4COL4= 1,515

The researcher performs an analysis of variance (ANOVA) to test the hypothesis that the populations defined by the treatment combinations are equal. The results are presented in the following ANOVA table.

ANOVA Table

Source SS df MS F
Between treatments 362.2917 11
Factor A 80.4167 2 40.2083 3.31
Factor B 25.6250 3 8.5417 0.7
AXB interaction 256.2500 6 42.7083 3.51
Within treatments 1,312.5000 108 12.1528
Total 1,674.7917 119

Use the significance level = 0.01 to complete the following conclusions.

The critical F value for factor A (years in military) is 4.81. Therefore, the main effect due to factor A is (significant/not significant)

The critical F value for factor B (program component) is 3.97. Therefore, the main effect due to factor B is

(significant/not significant)

The critical F value for the interaction of factors A and B is 2.97. Therefore, the effect due to the interaction of factors A and B is (significant/not significant)

Given the results of the preceding analysis, what does the researcher conclude?

1) Veterans with different lengths of service had different PTSD symptom scores. By itself, the program that veterans took was not associated with differences in severity; however, length of service resulted in different degrees of PTSD symptoms depending on program.

2) Neither length of service nor program component was related to the severity of PTSD symptoms, whether examined alone or in conjunction with the other factor.

3)Neither length of service nor program component was related to the severity of PTSD symptoms when looked at alone. However, there was an interaction between the two factors such that severity differed by program component differently depending on length of service (and vice versa).

4) Veterans with different lengths of service had different PTSD symptom scores. The severity of PTSD symptoms was unrelated to program component either by itself or in conjunction with length of service.

Measure the effect size for factor A (years in military), factor B (program component), and the interaction by computing (partial) eta squares. (Express the value of each eta square as a percent.)

for factor A (years in military) = options: 22.2%, 6.1%, 5.8%, 4.6%

for factor B (program component) = options: 2.0%, 1.9%, 1.5%, 7.1%

for the interaction = options: 16.3%, 70.7%, 19.5%, 13.3%

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