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# ANOVA and Tukey sample problem for statistics students

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We wish to determine whether the homicide rate is different in different parts of the country and, if it is different, what is the pattern. We have data on 36 states - 9 each in the four regions Northeast, Midwest, South and West.

Region Homicide rate
Northeast 3.23
Midwest 5.01
South 7.23
West 5.03

An analysis of variance produced the following partial ANOVA table:

Source SS
Between groups 72.40
Within groups 152.11
TOTAL 224.51

Complete the ANOVA table. Show that at 5% we reject the null. Use the Tukey HSD procedure [at 5% level] to determine which means are statistically different from which other of the means. What are your final conclusions?

https://brainmass.com/statistics/analysis-of-variance/anova-tukey-sample-problem-statistics-students-393325

#### Solution Preview

Below I have completed the ANOVA table as well as the Tukey HSD procedure. Please be sure to verify all calulations.

Source SS df MS F

Between groups 72.40 3 24.13 5.08

Within groups 152.11 32 4.75 ---

Total 224.51 35 --- ---

To fill in the above table, the first step is to determine the within groups df value. It is equal to the total df - between groups df. ...

#### Solution Summary

A step by step solution for an example ANOVA problem, including a Tukey HSD procedure. All steps are completely worked through and contain explanations.

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