It is projected that approximately 580,000 veterans will take advantage of the G

Question

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 (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. 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. Enter the values for degrees of freedom that are missing from the df column in the ANOVA table. Compute the mean square values, and select their correct values in the ANOVA table. Compute the F statistics, and select their correct values in the ANOVA table. Use the significance level alpha = 05 to complete the following conclusions. The critical value of F for the first factor (years in military) is 3.97, Therefore, the main effect due to the first factor is ____. The critical value of F for the second factor (program component) is 2.73. Therefore, the main effect due to the second factor is ____. The critical value of F for the interaction of the first and second factor is 2.73. Therefore, the effect due to the interaction of the first and second factor is Given the results of the preceding analysis, what does the researcher conclude? 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. 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. 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). Length of service and program component were each related to the severity of PTSD symptoms. However, the effect of each factor was independent of the other.

Explanation / Answer

Data shows it is the Analysis of Two way classified data with m-observations per Cell

For Degrees of Freedom Calculations:

There are 2 groups for Factor First: p = 2

There are 4 components for Factor Two: q = 4

Degrees of Freedom for Total is = 79 = pqm -1, where m is no of boservations per cell

therefore pqm = 79+1 = 80

2*4*m = 80 and 8m = 80

m = 10 observations per cell

Calculations in Anova

Conclusion is Option 2.

Veterans who took diffrent components of the program had different PSTD 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 PSTD symptoms depending on length of service.

Source SS df MS F F at 5% level Comparision Result Y 37.8120 p-1 = 2-1 =1 37.8120 1.8834 F(1,72) =3.97 Not Significant P 645.9380 q-1 = 4-1= 3 215.3127 3.0234 F(3,72) =2.73 Significant YP 923.4400 (p-1)(q-1) = 1*3 = 3 307.8133 4.3223 F(3,72) = 2.73 Significant Error 5127.4975 pq(m-1)= 2*4(10-1)= 8*9 =72 71.2152 Total 6734.6875 pqm-1= 79

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