Date: Oct 23, 2013 1:32 PM
Author: Bruce Weaver
Subject: Re: one-way repeated measures ANOVA with more levels than subjects

On 23/10/2013 12:48 PM, Tim wrote:
> Hi everyone,
> I have a quick question about a one-way repeated measures ANOVA in cases where the number of levels in a factor is larger than the number of subjects measured. Let me illustrate my question with a quick example: Say we presented 20 different colors in an experiment and recorded reaction times for every condition in 15 subjects (a total of 20*15=300 measurements). To my understanding, as we have 15 within-subject measurements for every cell, this should work perfectly fine.
> Unfortunately, two of the statistics functions we tried using throw an error stating that the number of conditions is too large given the number of subjects (one seems to directly compare the two numbers, the other one computes negative df_error). However, the same kind of setting works just fine in SPSS (df1 = 19; df2 = 266).
> Is there any principled reason why above setting should be problematic in a repeated-measures ANOVA? My search for an explanation has so far not brought up any reason why the number of levels in a factor should not exceed the number of subjects if all observations have been measured (n_obs = n_sub * n_cond).
> Thanks a lot in advance, looking forward to your answers
> Tim

If you ran this with SPSS, you will have seen that it does not produce
any results in the "Multivariate Tests" table, and a footnote gives this

"Cannot produce multivariate test statistics because of insufficient
residual degrees of freedom."

This makes me wonder if the two "statistics functions" you refer to are
attempting to carry out MANOVA rather than repeated measures ANOVA.
Perhaps you could provide more info about those "functions".


Bruce Weaver
"When all else fails, RTFM."