General instructions. Please write your full name at the top of every page you hand in. Please collate and staple your pages together. Please write clearly and thoroughly explain all your computations; an unannotated series of formulas that mysteriously ends up with the correct number will not be given full credit. When doing the homework, you are encouraged to use all resources at your disposal to the extent that they help you learn the material; nevertheless, you must write your own answers in your own words.

1. Consider only the data from p. 678, #10 (10 pts.)
   For these data, do the following:
   * In SPSS, do an omnibus test, using a multivariate analysis. Include only the multivariate ANOVA table in what you turn in. Under the table, state the conclusion of the test.
   * Suppose we have two planned comparisons. One is the "Circle" versus the "White" patterns. A second is the average of the "Face", "Circle" and "Newspaper" versus the "White" pattern. Conduct the two comparisons in SPSS. Include the relevant output tables. Be sure to explain exactly what you did to get those results. Also, state the conclusion of the tests, making sure to use the Bonferroni correction.
   * If the tests had been post-hoc instead of planned, what would the critical value have been? (HINT: See Eqn. 27, p. 652.)

2. (10 pts.)
   * Suppose we are planning a four-group within-subjects study. For example, suppose we are planning the research described in Exercise 10, p. 678. We plan to use the multivariate approach to analyze our data and we will use an alpha level of .05. We want to achieve a power of .80.
   * We believe that the maximum group mean will be about 25, the minimum group mean will be about 22, and the standard deviation within groups will be about 4. Suppose we also believe that the minimum correlation among the four groups will be about .2. What is the minimum number of subjects we need?
   * If we ran the study between-subjects, what is the minimum total number of subjects we would need?
   * Repeat the previous two parts, but this time get the max and min group means, the SD within groups, and the min correlation among the four groups, from the data in Exercise 10, p. 678. That is, use the data as if they were pilot data, from which we were going to determine the number of subjects for the full experiment. (If these "toy" data generate values outside the range in the power tables, explain the process by which the values would be used if they were in range.)