Psychological Profiles 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:Control group: N: 70 Sample mean: 11.7 Sample variance:21.6 RAP : N:70 Sample mean:9.0 Sample variance:13.0Headache: N:70 Sample mean:12.4 Sample variance :8.4Source: Galli, et al. “Headache and Recurrent Abdominal Pain: A Controlled Study by Means of the Child Behaviour Checklist (CBCL).”Cephalalgia 27, 211–219, 2007(a) Compute the sample standard deviation for each group (rounded to the tenth’s place).(b) 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). Use alpha:0.05 level of significance.(c) Use the one-way ANOVA procedure with alpha:0.05 to determine if the mean CBCL scores are different for the three treatment groups [Note: you will need to use the Chi-Square Table to determine your critical value.] the F-test statistic is F = 15.74 and the p-value = 0.0012.(d) Based on your results from parts (b) and (c), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain why you believe your response is true.

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Psychological Profiles 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:

Control group: N: 70 Sample mean: 11.7 Sample variance:21.6

RAP : N:70 Sample mean:9.0 Sample variance:13.0

Headache: N:70 Sample mean:12.4 Sample variance :8.4

Source: Galli, et al. “Headache and Recurrent Abdominal Pain: A Controlled Study by Means of the Child Behaviour Checklist (CBCL).”
Cephalalgia 27, 211–219, 2007

(a) Compute the sample standard deviation for each group (rounded to the tenth’s place).
(b) 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). Use alpha:0.05 level of significance.
(c) Use the one-way ANOVA procedure with alpha:0.05 to determine if the mean CBCL scores are different for the three treatment groups [Note: you will need to use the Chi-Square Table to determine your critical value.] the F-test statistic is F = 15.74 and the p-value = 0.0012.
(d) Based on your results from parts (b) and (c), can you determine if there is a significant difference between the mean scores of the RAP group and the headache group? Explain why you believe your response is true.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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