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. (8 pts.) #11, p. 188, modified as follows:
   (a) Do this in SPSS by including another column of group codes, labeling the first 18 scores as group 1 and the last 6 scores as group 2. Run a Oneway ANOVA using the new grouping variable.
   * Include the ANOVA output table with your homework.
   * What is the conclusion of the test?
   * Important: State the full and restricted models involved in this analysis.
   (b) Do this in SPSS.
   * Include the ANOVA output table (with contrast) with your homework.
   * What is the conclusion of the test?
   * Important: State the full and restricted models involved in the contrast.
   Do not do parts c-g in the book, but do answer the following:
   * Why are the degrees of freedom different in the tests of part (a) and (b)? Answer this by explaining how many parameters are being estimated in the full and restricted models in the two tests.
   * Can the test done in part (a) be expressed as a contrast among the four groups of part (b)? Why or why not? [Hint: The answer is no.]
   * What is the difference between the two analyses in terms of what they are asking about the treatment and control groups?

2. (6 pts.) #13, p. 189, modified as follows:
   When it asks you to "test a comparison using MS_W" you should do the corresponding contrast in Oneway ANOVA. When it asks you to "test a comparison using a separate error term" you should do a Oneway ANOVA on only the data in the relevant groups, completely excluding the irrelevant groups. You can accomplish this latter task by copying just the relevant data and group codes to new columns.
   (a) Do this in SPSS, as explained above. Include the output tables of the analyses. Be sure to answer the question, How do the results compare?
   (b) Do this in SPSS, as explained above. Include the output tables of the analyses. Be sure to answer the questions asked in exercise.
   (c) Do not do this part.

3. (6 pts.) #16, p. 190.
   Do this one as stated in the book. Hint: To show that the set is orthogonal, you must show that all the contrast vectors are pairwise orthogonal according to Equation 58. Thus, you apply Eqn. 58 to Ψ₁ and Ψ₂, to Ψ₁ and Ψ₃, to Ψ₁ and Ψ₄, to Ψ₂ and Ψ₃, etc. To show that the set is not orthogonal, show that at least one pair is not orthogonal.