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# 5. Measuring effect size for the repeated-measures ANOVA Alicia F. Lieberman and Patricia Van Horn have...

5. Measuring effect size for the repeated-measures 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 parent-child relationship, which has been disrupted by the stress and trauma of family violence.

As a clinical psychology intern, you are learning parent-child therapy with Drs. Lieberman and Van Horn. You see six parent-child 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

12-Month Follow-Up

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 parent-child 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 ___________ .