Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied, and their psychological profiles were graded according to a child behavior checklist. Children were stratified into two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the accompanying table. Complete parts (a) through (f) below. n Sample mean Sample variance Control group 70 11.7 21.5 RAP 70 9.1 13.0 Headache 70 12.4 8.5 (a) Compute the sample standard deviations for each group. The sample standard deviation for the control group is sc = __? (Round to one decimal place as needed.)
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Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the Child Behavior Checklist $4-18$ (CBCL). Children were stratified in two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the following table: $$\begin{array}{lccc} & n & \text { Sample Mean } & \text { Sample Variance } \\\hline \text { Control group } & 70 & 11.7 & 21.6 \\\hline \text { RAP } & 70 & 9.0 & 13.0 \\\hline \text { Headache } & 70 & 12.4 & 8.4\end{array}$$ (a) Compute the sample standard deviations for each group. (b) What sampling method was used for each treatment group? Why? (c) Use a two sample $t$ -test for independent samples to determine if there is a significant difference in mean $\mathrm{CBCL}$ scores between the control group and the RAP group (assume that both samples are simple random samples). (d) Is it necessary to check the normality assumption to answer part (c)? Explain. (e) Use the one-way ANOVA procedure with $\alpha=0.05$ to determine if the mean CBCL scores are different for the three treatment groups. (f) Based on your results from parts (c) and (e), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain.
Comparing Three or More Means
Comparing Three or More Means (One-Way Analysis of Variance)
Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the Child Behaviour Checklist $4-18$ (CBCL). Children were stratified in two age groups: 4 to 11 years and 12 to 18 years. The results of the study are summarized in the following table: $$\begin{array}{lccc} & n & \text { Sample Mean } & \text { Sample Variance } \\ \hline \text { Control group } & 70 & 11.7 & 21.6 \\ \hline \text { RAP } & 70 & 9.0 & 13.0 \\ \hline \text { Headache } & 70 & 12.4 & 8.4 \\ \hline \end{array}$$ (a) Compute the sample standard deviations for each group. (b) What sampling method was used for each treatment group? Why? (c) Use a two sample $t$ -test for independent samples to determine if there is a significant difference in mean CBCL scores between the control group and the RAP group (assume that both samples are simple random samples). (d) Is it necessary to check the normality assumption to answer part (c)? Explain. (e) Use the one-way ANOVA procedure with $\alpha=0.05$ to determine if the mean CBCL scores are different for the three treatment groups. (f) Based on your results from parts (c) and (e), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain.
Researchers wanted to determine if the psychological profile of healthy children was different than that for children suffering from recurrent abdominal pain (RAP) or recurring headaches. Results of the study are summarized in the following table. Determine which pairwise means of the three treatment groups, if any, are different using a familywise error rate of alpha = 0.05. n Sample Mean Sample Variance Control Group 70 11.7 21.6 RAP 70 9.0 13.0 Headache 70 12.4 8.4 a. There is not enough evidence to suggest that the means are different. b. The mean score of the Control Group is different from the mean score of the RAP group. c. The mean score of the Control Group is different from the mean score of the headache group. d. The mean scores of each pairwise group are different.
David N.
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