Convicted drug dealers held in Grimsville Prison are placed in cell block A, B, or C according to their city of origin. Danny (who has little knowledge of statistics) was once an inmate in the prison. Now released, he still bears a grudge against the prison authorities. Danny wishes to make up a series of statistics to show that the convicts in the various blocks are treated differently. According to his fictitious sample, the mean number of hours of exercise per week given to the inmates is 10 hours for block A offenders, 20 hours for block B offenders, and 30 hours for block C offenders. Shown below are two fictitious sets of results.

Fictitious study 1:

Fictitious study 2:

a. From simply looking at the numbers, without running any statistical tests, which of the two fictitious studies would you expect to provide stronger backing for Dannys claim? Explain your answer.

b. Calculate the between sum of squares and the within sum of squares for study 1.

c. Calculate the between sum of squares and the within sum of squares for study 2.

d. Calculate the value of eta for each study. How do you account for the difference?