[R] Mixed Design ANOVA - singular error model

Claus O'Rourke claus.orourke at gmail.com
Mon Oct 18 11:23:08 CEST 2010

Dear r-help list,
I would like to run a mixed design anova to compare the results from
one population sample to another. Here my within subject variable
(stiulusID) has 45 levels and my between subject variable (group) has
two levels. In addition to my number of levels in the within subject
variable being very large, one other 'feature' of my data is that it
is not balanced on the between subject variable. I have attached a
copy of my data for reference.

To run the ANOVA, I did this:
summary(aov(Result ~ StimulusID * Group +
Error(ParticipantToken/(StimulusID + Group)), data = data))

My results were roughly as I had expected, but at the end of the
output I have the warning that the model is singular. I have seen this
warning listed in other help requests, but from what I saw there this
meant that one of my variables was redundant as it was a nesting of
the other. I don't think this is the case in my data.

Can I trust the results of a Mixed Design ANOVA with the warning? Or
indeed with the unbalanced between subject variable?

Many thanks for any help for a stats novice.

Error: ParticipantToken
          Df Sum Sq Mean Sq F value Pr(>F)
Group      1   0.69  0.6934  0.0437 0.8356
Residuals 39 619.47 15.8840

Error: ParticipantToken:StimulusID
                   Df Sum Sq Mean Sq F value    Pr(>F)
StimulusID         44 4607.4 104.713 60.3868 < 2.2e-16 ***
StimulusID:Group   44  170.3   3.870  2.2317 8.106e-06 ***
Residuals        1716 2975.6   1.734
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Warning message:
In aov(Result ~ StimulusID * Group + Error(ParticipantToken/(StimulusID +  :
  Error() model is singular

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