Attempts Average: 10 9. Measuring effect size for two-factor ANOVA Aa Aa It is p

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Attempts Average: 10 9. Measuring effect size for two-factor ANOVA Aa Aa 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 Post-traumatic 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 (journaling, community service, physical activity, 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 Physical Journaling Service Activity Meditation M = 48.5 | M = 48.5 | M = 53 | M = 54 1-2 | T = 485 | T = 485 | T = 530 | T = 540 | TROW1 = 2,040 SS = 52.5 | SS = 52.5 SS = 2401 SS = 210 M = 49.5 | M = 49.5 | M = 48.51 M = 48.5 Factor A: Years in Military 3-4 | T-495 | T = 495 | T = 485 | T = 485 | TROW2 = 1,960 EX2-30 1,175 SS = 62.5 SS = 112.50 SS = 52.5 SS = 52.5 M = 50.5 | M = 50.5 | M = 49.51 M = 49 >4 | T = 505 | T = 505 | T = 495 | T = 490 | TROw3 = 1,995 SS = 152.5 | SS = 202.5 SS = 62.5 SS = 60 TCOL3 = 1,510 COL1 COL2 = 1 COL4 = 1,485 1,485 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 df MS Between treatments 362.2917 Factor A 80.4167 40.2083 3.31

Explanation / Answer

h2 = SSeffect / SStotal

factor A = 80.4167 / 1674.7917

B = 25.6250/ 1674.7917

interaction = 256.25/ 1674.7917

in tabular form

SS n^2 df F F-crit A 80.4167 0.048015941 2 3.31 3.080387 B 25.625 0.01530041 3 0.7 2.688691 Interaction 256.25 0.153004102 6 3.51 2.183657 Total 1674.7917 108

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