In a study on the effect of caffeine on nervousness, researchers are administering two different levels of caffeine (i.e., 100 mg and 200mg) through pills to two different groups of subjects while a third group receives a pill that contains merely sugar. The subjects were randomly placed in these three groups and that the number of students in each group was chosen to be 10, which is known as a balanced design. The primary measurement that was taken on each of the students was the number of finger tips per minute using an electronic sensor 15 minutes after they had taken their pills. The following table shows the data for this study:

1. Write down the GLM for these data. Write down all assumptions for this model.
2. Compute the ANOVA table for these data by hand, which involves computing the individual sums-of-squares by hand. Show all computations and present the final table including the F -test statistic value and associated p -value.
3. Write down the hypotheses, α-level, and test statistic value for the omnibus F -test reported in the ANOVA table. Sketch the distribution for the test and shade in, if visually possible, the p -value and the α-level for the test. State the test result and interpret it in the context of the problem.
4. Obtain the three measures of effect size (i.e., η 2 , ω 2 , and f ). Interpret the resulting values in the context of the problem.
5. Using the appropriate diagnostic plots, assess whether each of the assumptions of the ANOVA model seems to hold for these data. Attach all relevant plots.
6. Using SPSS or by hand, obtain the treatment-means plot for these data. Describe the pattern that you see in the plot. Then obtain the Tukey, Scheffé, and Bonferroni comparisons for all pairs of means. Using α = .10, what do the three procedures tell you about which means differ? If there are differences in the conclusions that you draw across the three procedures, explain where the differences come from.
7. By hand, construct a 95% confidence interval for the contrast that compares the means for the two non-placebo treatment groups, taken together, with the mean for the placebo group. Interpret the interval. Next, perform the associated hypothesis test and interpret the outcome. Write down all key information for the test. Finally, obtain the contrast information from SPSS and compare your results. Attach all relevant tables from SPSS.
8. Repeat what you did in problem (7) for a linear contrast.

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