5. Measuring effect size for the repeatedmeasures ANOVA
Alicia F. Lieberman and Patricia Van Horn have created a psychotherapy model for young children who have witnessed family violence. The therapy focuses on building the parent’s capacity to nurture and protect the child, thereby promoting the child’s emotional health and repairing the parentchild relationship, which has been disrupted by the stress and trauma of family violence.
As a clinical psychology intern, you are learning parentchild therapy with Drs. Lieberman and Van Horn. You see six parentchild dyads for a year and then evaluate them before therapy, after therapy, and again one year after therapy is finished. You are interested in assessing whether the treatment had an effect on the child’s anxiety.
In the experiment above, the null hypothesis is:
There are no differences among the anxiety means across the three time points
At least one anxiety mean is different from another
There are no individual differences in the anxiety means
The results of the study are presented in the following data table. All scores are from the Achenbach Child Behavior Checklist.
Anxiety Score
Child 
Before Treatment 
After Treatment 
12Month FollowUp 
Participant Totals 


A  2.23  1.91  1.71  P = 5.85  n = 6 
B  1.75  1.52  1.38  P = 4.65  k = 3 
C  0.96  1.09  1.11  P = 3.16  N = 18 
D  1.35  1.26  1.16  P = 3.77  G = 25.68 
E  0.77  0.51  0.52  P = 1.80  ΣX² = 41.9396 
F  2.27  2.15  2.03  P = 6.45  
T = 9.33  T = 8.44  T = 7.91  
SS = 2.0173  SS = 1.7446  SS = 1.3695 
The three treatment evaluations define three populations of interest. Use analysis of variance (ANOVA) to test the hypothesis that the three population means are equal.
Source 
SS 
ANOVA Table 
MS 
F 

df 

Between treatments  0.1716  2  0.0858  
Within treatments  5.1314  15  0.3421  
Between subjects  4.9919  5  0.9984  
Error  0.1395  10  0.0140  
Total  5.3028  17 
Fill in the missing value for the F test statistic in the ANOVA table.
1. Use the F distribution in the Distributions tool to find the critical value of F for α = 0.05. The critical value is F = _______ .
2. At a significance level of α = 0.05, evaluate the null hypothesis that the population means for all treatments are equal. The null hypothesis is _____________ (rejected/not rejected? . You ____________ (can/cant) conclude that parentchild therapy has an effect on anxiety in children who have witnessed family violence.
3. To measure the effect size, calculate η². The η² is __________ . The percentage of variance accounted for by the treatment effect is ___________ .
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