# One way ANOVA Eta and Tukey HSD

Suppose that you are interested in determining the effectiveness of an intensive supervision probation (ISP) program. To examine its effectiveness, you keep track of 12 offenders sentenced to ISP for one year and tabulate the number of new offenses they committed. You also gather two control groups. The first consists of 12 offenders sentenced to routine probation. The second consists of 12 offenders whose cases were dismissed. The following results describe the number of new offenses each offender in each group committed during your one-year follow-up:

Using these data, answer the following questions:

1. Identify the independent and dependent variables.

2. With an alpha of 0.01, test the null hypothesis that the three population means are equal by doing the following: What are the null and alternative hypotheses? Show the calculation and explain how to construct the ANOVA table. Determine the appropriate test statistic and determine whether it is significant.

3. If appropriate, conduct a mean comparison for all pairs of means using Tukey?s HSD test.

4. Calculate the value of Eta-squared, and make a conclusion about the strength of the relationship.

See attached file for full problem description.

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#### Solution Summary

The solution gives the details of calculations of one-way ANOVA, eta, and Tukey HSD.