Question

It is projected that approximately 580,000 veterans will take advantage of the Gt 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 (physical activity, journaling, community service, 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 Physical Community Activity Journaling Service Meditation 1-2 M = 44 M43.5 M. 43 T440 T = 435 T-430 SS = 740 SS 802.5 SS 660 M = 42.5 T-425 SS-612.5 TROW - 1,730 EX2 - 161,175 Factor A: Years in Military M-37 M = 41 T= 370 T410 Ss = 802.5 SS 490 M47 M53.5 T-470 T=535 SS = 910 SS-652.5 TROW = 1,785 Teou Tcou 810 Teous - 900 Тcouse 960 845 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. df MS F 7 1 0.53 ANOVA Table SS 1,607.1875 37.8120 645.9380 923.4400 5,127.4975 6,734.6875 Source Between treatments Factor A Factor B AXB interaction Within treatments Total 3 37.8120 215.3127 307.8133 71.2152 3.02 4.32 3 72 79 Use the significance level a - .01 to complete the following conclusions. The critical F value for factor (years in military) is 7.00. Therefore, the main effect due to factor Als The critical F value for factor (program component) is 4.07. Therefore, the main effect due to factor Bis The critical value for the interaction of factors A and B is 4.07. Therefore, the effect due to the interaction of factors A and Bis Given the results of the preceding analysis, what does the researcher conclude?

Answer 1

The level of significance is provided as 0.01.

For factor A;

Using the F-distribution table, for df = 1, 72, the F-critical value is 7 which is more than the calculated F value = 0.53, the main effect due to factor A is not significant.

For factor B;

Using the F-distribution table, for df = 3, 72, the F-critical value is 4.07 which is more than the calculated F value = 3.02, the main effect due to factor B is not significant.

For AXB;

Using the F-distribution table, for df = 3, 72, the F-critical value is 4.07 which is more than the calculated F value = 4.32, the effect due to interaction is not significant.

Conclusion: 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.

Using the mentioned ANOVA table, the effect sizes are;

SS = 37.8120 SS, = 645.9380 SS = 923.4400 SS Toral = 6734.6875 SS SS -SS-SS 37.8120 - = 0.0073 = 0.73% 6734.6875 - 645.9380-923.4400 B SS . Total AXA SS3 Toral -SS-SS - AXB 645,9380 = 0.1119 = 11.19% 6734.6875-37.8120-923.4400 SS AXB SS, 923.4400 = 0.1526 = 15.26% 6734.6875-37.8120-645.9380 Stotal -SS-SS