Question

4. Measuring effect size for two-factor ANOVA Аа Аа 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, and physical activity: factor B). She then assigns them one of the three 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 Service Journaling Activity 1-2 M 51.6 M 52.4 M 53.2 T 516 T 524 T 532 TROW1 1,572 SS 38.4 SS = 25.6 SS 38.4 EX2 167,976 Factor A Years in Military 3-4 M 52.0 M 54.4 M 53.6 T 544 T 520 T 536 TROW2 1,600 SS 46.4 SS 38.4 SS 38.4 TcOL1 ТooLz 3 TooLз 3 1,060 1,036 1,076

Answer 1

The critical F value for factor A (years in military) is 4.02. Therefore, the main effect due to factor A is insignificant because calculated value of F = 3.11 < Fc = 4.02.

The critical F value for factor B (program component) is 3.17. Therefore, the main effect due to factor B is significant because calculated value of F = 4.82 > Fc = 3.17.

The critical F value for interaction of factor A and B is 3.17. Therefore, the main effect due to interaction of factor A and B is insignificant because calculated value of F = 0.25 < Fc = 3.17.

Hence the result of this analysis can be concluded as;

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.

η² for factor A:

η²A = SSA /(SST - SSB - SSAxB) = 13.0667/(282.9333 - 40.5333 - 2.1333) = 0.0544 = 5.44%

η²B= SSB /(SST - SSA - SSAxB) = 40.5333/(282.9333 - 13.0667 - 2.1333) = 0.1514 = 15.14%

η²AxB = SSAxB /(SST - SSA - SSB) = 2.1333/(282.9333 - 13.0667 - 40.5333) = 0.0093 = 0.93%