Statistics: Analysis of Variance – #29418


Question: A researcher is interested in the effects of family size on delinquency for a group of offenders and examines families with one to four children. She obtains a sample of 16 families, four of each size, and identifies the number of arrests per child for delinquency. The data is as follows:

Group 1
4 children
n=4
Group 2
3 children
n=4
Group 3
2 children
n=4
Group 4
1 child
n=4
Family 1 10 8 5 4
Family 2 8 8 6 5
Family 3 9 6 7 2
Family 4 10 9 9 2

a) Calculate the total sum of squares.

b) Calculate the mean square (between groups).

c) Calculate the F-ratio

d) Use the Turkey HSD (alpha=0.05) to test for significance between groups. Which groups differed?

e) Based on your results, write a 1-2 paragraph essay that describes your observations obtained from this sample in regard to the effects of family size on delinquency for a group of offenders.

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