[R] inquiry about anova and ancova

[Peter Dalgaard]

Anderson, Mary-Jane wrote:
> Dear R users,
> 	 I have a rather knotty analysis problem and I was hoping that
> someone on this list would be able to help. I was advised to try this list
> by a colleague who uses R but it is a statistical inquiry not about how to
> use R.
>  In brief I have a 3x2 anova, 2 tasks under 3 conditions, within subjects. I
> also took a variety of personality measures that might influence the results
> under the different conditions. I had thought that an ancova would be the
> best test, but it might be the case that this would not work with a within
> subjects design. I have not found anything that explicitly states whether or
> not it would, but all the examples I have read are between subjects design.
>  I also thought of investigating a manova, but it is not really the case
> that I have more than one DV, it is the same DV in 6 different combinations
> of task and condition. 
>  There were 4 personality measures and I wanted to look at the degree to
> which they affected the task/ condition interaction. 
>  I have explained this briefly here, but I can of course provied more
> details to anyone who can advise me further with this.
>   
This sounds like a job for a Multivariate Linear Model (assuming that
you have complete data for each subject or are prepared to throw away
subjects with missing values).

This lets you decompose the response into mean, effects of task and
condition, and the interaction effect. Each component can then be
separately tested for effect of predictors, using multivariate tests, or
F tests under sphericity assumptions.

Have a look at example(anova.mlm); this mostly looks at cases where
effects are tested against zero, but the last example involves a (bogus)
between subject factor f.

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