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. He 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). He 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 Journaling Physical Activity Community Service Sample Totals Factor A: Years in Military M 57.7 1-2 M 59.0 M 53.9 TA1 1,194 T = 413 T = 404 T 377 SS = 22.00 SS 43,43 SS 2.86 M 56.9 M 57.7 TA21,183 3-4 M 54.4 T 381 T 398 T = 404 SS 43.43 SS 22.86 SS 75.43 EX2 134,877 Sample Totals TB1 794 TB2 802 TB3 781
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.
Source of Variation Sum of Squares Mean Square E-ratio Degrees of Freedom Between treatments 143.83 2.8810 Factor A 2.88 0.50 Factor B 16.0476 8.02 1.40 AXB interaction 124.9048 62.45 10.90 Within 206.29 5.73 Total 350.12 41
Use the significance level alpha = .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.
The critical F value for factor B (program component) is 3.97. Therefore, the main effect due to factor B is.
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.
Given the results of the preceding analysis, what does the researcher conclude?
a. 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).
b. 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.
c. Veterans who took different components of the program had different PTSD symptom scores. By itself, length of service was not associated with differences in severity; however, the various components of the program resulted in different degrees of PTSD symptoms depending on length of service.
d. Veterans who took different components of the program had different PTSD symptom scores. The severity of PTSD symptoms was unrelated to length of service either by itself or In conjunction with the various components of the program.
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.)
eta^2 for factor A (years in military) =
eta^2 for factor B (program component) =
eta^2 for the interaction =