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# Assignment 7

**
Multivariate Data Analysis **

Psychology 6140

- Tabachnick & Fiddell, Chapter 9 (ignore ANCOVA stuff)
- Johnson & Wichern, Chapters 5- 6
- * Stevens, Chapter 4
- * Morrison, Chapter 4, 5.1-5.3, 5.6-5.8 [*In Resource Center]

## Supplements

- A simplified approach to determining the power for an ANOVA factor,
or the sample size required to achieve a given power is carried out
using the FPOWER macro on the server.
You can run this program from the WWW using the WebPower forms-based interface.
- SAS Design Code Generator
A Web-Based SAS Code Developer for Experimental Designs in JavaScript.
Select your design from a form, the copy/paste the code into a SAS
session or program editor window.

A study by Robert Hart examined the ability of standard laboratory
memory tasks to distinguish between patients with mild Alzheimer's
disease, from those with depression and control subjects. The
memory tasks included free recall and selective reminding with both
high and low imagery words, a measure of short term memory storage,
and a recognition memory task. The data are stored in the file **
alzheim sas** on the server
(there's also an SPSS version in psy6140/lib/spss/),
and you can use them by starting
your SAS program with the line
%include data(alzheim);

The data file gives the following names to the
variables:
label subj = 'Subject ID'
trecall = 'Total recall'
hirecall= 'HI Imagery Recall'
lirecall= 'LO Imagery Recall'
tunrem = 'Unreminded Memory'
hiunrem = 'HI Imagery Unreminded Memory'
liunrem = 'LO Imagery Unreminded Memory'
store = 'Storage'
recog = 'Recognition Memory';

(Note that TRECALL and TUNREM are each calculated as the sum or average of
the two RECALL and UNREM measures.)
- Using Proc GLM, test the hypothesis of equal mean vectors for
the three groups at alpha = 0.05 by an appropriate
multivariate test.
- If the multivariate test is significant, determine which
variables are individually showing significant overall group
differences by univariate tests.
- Obtain a printout of the H and E matrices for the overall
one-way MANOVA. Show how the univariate F statistics relate
to the elements of the H and E matrices. Interpret the
elements in the matrix labelled "Partial correlation
coefficients from the Error SS&CP Matrix".
- Carry out multivariate tests of the following contrasts: (a)
of the Alzheimer's group vs. (Depressed and Normals), (b) of
the Depressed vs. the Normal subjects.
- For the overall one-way MANOVA, use the CANONICAL option to
determine whether the memory tests distinguish among the
group mean vectors along one or more than one dimension.
- Write a short (half-page or less) abstract summarizing the
results of these analyses. One's normal expectations are
that Alzheimer's patients should differ from non-Alzheimer
subjects on at least some of the tasks. Include in your
abstract information that comes from the multivariate tests,
as well as information about the effects on each variable
and the contrasts tested.

** Author:**
*Michael Friendly* © 1995
**Email:**friendly@yorku.ca
to PSY6140 home page.