MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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:
At least one anxiety mean is different from another
 
There are no differences among the anxiety means across the three time points
 
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 2.19 1.45 1.94 P = 5.58 n = 6
B 1.35 1.34 1.26 P = 3.95 k = 3
C 1.91 0.69 1.17 P = 3.77 N = 18
D 1.18 0.84 0.76 P = 2.78 G = 27.04
E 2.56 1.17 1.18 P = 4.91 ΣX² = 45.6864
F 2.31 1.82 1.92 P = 6.05  
  T = 11.50 T = 7.31 T = 8.23    
  SS = 1.5072 SS = 0.8551 SS = 1.0877    
 
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 1.6164 2 0.8082     
Within treatments 3.4500 15 0.2300  
  Between subjects 2.5102 5 0.5020  
  Error 0.9398 10 0.0940  
Total 5.0663 17    
 
Fill in the missing value for the F test statistic in the ANOVA table.
 
0123
F Distributiont Distribution
Select a Distribution
 
 
 
Use the F distribution in the Distributions tool to find the critical value of F for α = 0.05. The critical value is F =    .
 
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    . You    conclude that parent-child therapy has an effect on anxiety in children who have witnessed family violence.
 
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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