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This is a question that landed on my desk, and I don't have the requisite experience to reply.

A researcher has been asked to perform (by a journal reviewer) a two-way factorial ANCOVA on some microrarray data (a single array will be a single measurement of ~30,000 entities from a single sample in this case).

The suggestion was to use ethnicity and age as co-variables. I understand that ANCOVA requires at least one categorical and one continuous predictor variables.

The researcher has 3 ethnic groupings in his samples - 6 of group A, 2 of group B and 1 of group C. These samples are spread across three treatments (X, Y and Z), with 3 samples per treatment. This means the treatments cannot be split evenly by ethnicity, group C will only appear in one of the treatments.

Is this sample size/grouping issue a barrier to running a two-way factorial ANCOVA? Is there another test that might be more appropriate under the circumstances?

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A total sample size of nine is simply too small to do a two-way factorial ANCOVA or a two way-factorial ANOVA. I would have thought it's stretching things to even do a one-way ANOVA on nine observations, especially with 30,000 different outcomes. I think you need a bigger sample if you wish to make any statistical inferences.

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I don't understand how small sample size, by itself, necessarily limits statistical inferences. Sometimes the effect size is so huge that you only need enough samples to estimate variability and to check any model assumptions. –  whuber Jan 23 '11 at 17:55
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