4. Measuring effect size for two-factor ANOVA It is projected that approximately

Question

4. Measuring effect size for two-factor ANOVA It is projected that approximately 580,000 veterans will take advantage of the GI Bal 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 isto assist deployed, postdeployed, and veteran students in making a positive transton from military to civilian are or from deployment to postdeployment Ire, 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. He recruts a group of combat veterans and couects 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). He then assigns them one of the four components. The study wia evaluate which components ofthe program are the most effective for reducing PTso symptoms. The results of the hypothetical study are summarized in the following data matrix. Each cell reports the average (M), the total m, and the sum of squares (SS) of the symptom score p) 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 Activity Journaling Service M 43.5 M 42.5 T 435 T 430 TROwu 1.730 SS m 740 SS 802.5 SS 660 SS 612.5 161,175 Factor A: Years in Military M 41 3-4 T 370 T m 410 T 470 T S3s Taowa 1.785 ss 802.5 SS 490 SS 910 SS m 652.5 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. ANOVA Table 1,607.1875 37.8120 Factor A 215.3127 645.9380 307.8133 71.2152 5,127A975 6,734.6875 Sign Acant A) Use the significance level a .05 to complete the following condusions. Not Sgnificant The critical F value for factor A (years in military) s 397. Therefore, the main etect due to factor Ais The critical F value for factor B (program component) is 2.73. Therefore, the main enect due to factor B is The interaction of factors A and B is 2.73. Therefore, the enect due to the interaction of factors A and Bis critical F value for the

Explanation / Answer

Answer to part a)

For factor A , critical value 3.97 > F statistic 0.53 , hence it is "not significant"

For factor B, critcal vlaue 2.73 < F statistic 3.02 , hence it is "significant"

For interaction, critical value 2.73 < F statistic 4.32 , hence it is "significant"

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Answer to part b)

From the above working we get to know , that length has individually no effect , but the program cmponent and the interaction of program component and length of service totgether have an impact. Thus the correct answer choice is the first one.

"Veterans who took different components of 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 based on the length of service"

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Answer to part c)

Formula of effect size = SSeffect / SStotal

For Factor A = 37.8120 / (37.8120+5127.4975)

Factor A effect size = 37.8120 / 5165.3095

Factor A effect Size = 0.00732 = 0.7%

.

For Factor B , effect size = 645.9380 / (645.9380+5127.4975)

For Factor B , effect size = 645.9380 / 5773.4355

For Factor B , effect size = 0.1119 = 11.2%

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For the interaction, effect size = 923.44 / (923.44 +5127.4975)

For the interaction, effect size = 923.44 / 6050.9375

For the interaction, effect size = 0.1526 = 15.3%

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