Re: Repeated measures ANOVA with one measurement

Aniko wrote:
A few follow up questions and
clarifications:

First, the real setup.
- I have 10 subjects (7 good performers, 3 bad performers - hence the
suggestion that I do a repeated-measures ANOVA to remove some of the
variance between subjects)
- I have three factors: 4 M's, 4 N's, and 4 S's. Thus 64 conditions.
- I measure percent correct (Pc - transformed to a linear scale) once
for each condition.
So, from your response, it appears that all the 'yes'es apply.
- Lastly, I'd like to use Tukey post-hoc tests and I heard that in an
ANCOVA the power of post-hoc tests are dramatically reduced.

Now the questions:
1) Are the power of post-hoc tests reduced in RM ANOVA like an ANCOVA?

The standard array of multiple comparison procedures (i.e., Tukey HSD, Newman-Keuls, Dunnett's test, etc) are not available for repeated measures factors in SPSS, because those procedures were designed for between-Ss ANOVA.


I am not sure what have you heard about ANCOVA. The power is reduced
compared to what? Are there any other "legal" alternatives? In
general, having unaccounted for variation reduces power, so repeated
measures ANOVA should do better than regular ANOVA, not to mention not
violating the independence assumption.

2) Since a 1-way RM ANOVA is equivalent to a 2-way ANOVA without
interaction, does this mean that a 2-way RM ANOVA is equivalent to a 3-
way ANOVA without interactions? I'd like to be able to check the
significance of the interaction between N and M, N and S, and M and S.

Don't worry, you can have interactions between your factors of
interest (N,M,S), but they cannot interact with the nuisance repeated
measure factor - subject. So a 3-way repeated measures ANOVA is the
same as a 4-way ANOVA with no interaction with the repeated measure
factor.

3) Technical SPSS v 15 question: How do I do this RM ANOVA with one
measurement?
- I go to Analyze > General Linear Model > Repeated Measures ...
- A text box opens asking for a "within-subject factor name" and
number of levels, and a "measure name". The first is necessary, the
second seems to be an optional label. It seems to me that I'd want
"Pc" to be my within-subject factor name and my number of levels to be
1. However, it won't let me have just 1 level, at least 2 are
necessary for this program. (This I think is my major problem. It
makes me think SPSS doesn't do 1 measurement RM ANOVA.) Then as we go
to the next screen it allows me to select my within-subject variables
(numbers only allowed, so Pc) and the between-subject factors (M, N,
S).

All of this should have been clear in the tutorial on the website I pointed you to. And if you didn't like that one, there are dozens of others on the web.


Again, I have not used SPSS, so I might be wrong, but I think you have
not set up a repeated measure factor - Subject. This should have a
unique value for each subject. Then you would have 10 levels for your
repeated measures factor. "Pc" is not a factor, but the outcome. The
data might look like this:

Subject M N S Pc
1 M1 N1 S1 0.7
1 M2 N1 S1 0.8
1 M1 N2 S1 0.4
...
10 M2 N2 S2 0.6

Anyway, that's how other software tends to like it.

The standard way of doing repeated measures ANOVA in SPSS wants one row of data per subject with the repeated measures in multiple columns. With this set-up, there is no need to include SUBJECT explicitly as a variable in the model--the software knows that each row is a different subject.

Having said that, you can cajole the "between-Ss" ANOVA routine (UNIANOVA) into performing a repeated measures (or mixed design) ANOVA. In order to do *that* though, you do have to include SUBJECT explicitly. You also have to include all of the interaction terms involving Subject explicitly except for the final one, which must be omitted. If you include it, there is no residual variation, and things don't work properly.


4) I thought of a way around my problem by duplicating the Pc scores,
thus having Pc1 and Pc2. So I could have 2 levels for SPSS. Then the
RM ANOVA in SPSS would probably work. But I'm guessing this would
artificially inflate my error terms. Is this a good idea or not?


No, it certainly does not sound like a good idea.

Right. It's a terrible idea. Go look at some of the dozens of tutorials that are available online.


Just as a side-note: if your outcome is often close to 100% or 0%, you
might have all kind of issues with the basic ANOVA assumptions of
additivity and equal variance.

Aniko



--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
"When all else fails, RTFM."
.

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