Midterm Take Home Exam — PSY 444 — Fall, 2008 — Due 11/4/08
Address each of the following questions by creating a WORD document, cutting and pasting only relevant
or requested syntax and output from SPSS. The exam is a “take home” examination, and thus you may
utilize any internet resources, the textbook, lecture notes, and so forth. You may not, however, discuss the
questions or your responses with anyone except the course instructor. (See syllabus for academic honesty
policies). Any questions you have about interpreting questions should be addressed to the instructor.
1. Consider the two design matrices defined below and address the following questions.
D1=
1 12
1 13
1 9
1 10
1 6
1 14
1 8
1 7
and D2=
12 1
13 1
9 1
10 1
6 1
14 1
8 1
7 1
.
(a) Write a sentence or two to describe the type of research design that these designs matrices repre-
sent.
(b) In what way will the parameter vector estimated by the general linear model differ for these two
design matrices?
Hint: If you need to think more concretely about it, create an arbitrary DV vector, Y, and estimate
the design parameters.
2. Consider the following two design matrices and address the questions below.
D3=
1 1
1 1
1 1
1 1
1 0
1 0
1 0
1 0
and D4=
1 1
1 1
1 1
1 1
1−1
1−1
1−1
1−1
.
(a) Write a sentence or two to describe the research design that would employ either design matrix.
(b) In what way will the parameter vector estimated by the general linear model differ for these two
design matrices?
Hint: If you need to think more concretely about it, create an arbitrary DV vector, Y, and estimate
the design parameters.
(c) Which of these two design matrices will generate parameter estimates that are orthogonal?
(d) Create three additional design matrices that could be used for the same design, at least one of
which generates orthogonal parameter estimates.
3. Consider a 4x5 two-way ANOVA (e.g., an ANOVA in which there are four levels of factor A and five
levels of factor B. Answer the following questions.
(a) How many parameters total will be estimated for this design?
(b) How many columns will there be in the design matrix?
(c) How many parameters must be estimated to fully characterize the effects of factor A?
(d) How many columns do we need in the design matrix to represent the effects of factor A?
(e) How many parameters must be estimated to fully characterize the effects of factor B?
(f) How many columns do we need in the design matrix to represent the effects of factor B?
(g) How many parameters must be estimated to fully characterize the effects of the AB interaction?
