4. Determining main effects and interactions in a two-way ANOVA It is projected

Question

4. Determining main effects and interactions in a two-way 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. 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 Second Factor: Program Component Journaling Community Service Physical Activity Meditation X 14-45 X24 = 49.1 XP4 = 47.05 Totals Xu = 40.63 XY2 = 46.38 Xgm = 43.50 First Factor: -13 = 42 1-2 3-4 Totals X21 = 44 XP1 = 40.25 23 = 47.6 XP3 = 44.80 Years in Military X22 = 44.8 Xp2 = 41.90 The researcher performs an analysis of variance (ANOVA) to test the hypothesis that the populations defined by the treatment combinations are equal Some of the results are presented in the following ANOVA table

Explanation / Answer

a = 2 , b = 4

df_Y = a-1 =1

df_P=b-1=3

df_YP=1*3=3

Y- since F =11.1987>3.97 ,hence significant

P- since F =3.095>2.73 ,hence significant

YP - since F = 0.1639 < 2.73 , hence insignificant

ss df MS F Y 661.252 1 661.252 11.1987 P 548.3 3 182.7667 3.095263 YP 29.048 3 9.682667 0.163982 error 4251.4 72 59.04722 79

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