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I am having a few issues processing some data in that the number of samples is far less than originally anticipated. In a control and impacted design, there are 11 samples each. I thought this seemed like an ideal format for a the non-parametric sm.ancova function in R (see Nonparametric equivalent of ANCOVA for continuous dependent variables).

However, I have various explanatory variables and I would like to explore their interactive effects. Could anybody suggest anything on this front to help account for this? So rather than having a factor (f), a response (x) and one explanatory variable (y), consider how x would respond to the multiplicative effect of different variables (y and z) across f? Thank you in advance.

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James White
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If I understand this question, you are trying to compare two groups (control and experimental) and each group has 11 members. For some reason you want to use nonparametric tests (but it isn't clear to me why you do).

Given this small sample size, comparing on more than 1 or 2 variables at a time is going to have a high risk of overfitting. If you really need to do this, then some form of permutation test might be appropriate, but a "regular" linear model approach will likely be problematic.

Peter Flom
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  • Thank you for the comment. The nonparametric nature I suggested is because I expect there to be nonlinear responses and the number of samples being so low that assumptions of other analyses will not be met. There is one response variable and several explanatory variables (<100) for each site. I have reduced this set via a PCA and then removed those causing colinearity. Is there a viable way from this point of testing the best combination of explanatory variables against the response variable at both the control and impacted sites? I thought of ranking models by AICc and then use this ANCOVA. – James White Jul 08 '15 at 11:44
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    Nonparametric methods don't get around the sample size issues. Doing what you are proposing, though, will be sure to get an overfitted model. – Peter Flom Jul 08 '15 at 12:06
  • Can you think of an obvious method that may be able to deal with this? i.e. a relationship between multiple explanatory variables and a response variable across a small dataset, specifically with a non-linear basis? Thank you for your help. – James White Jul 08 '15 at 12:19
  • There are lots of methods, but they need more data. A lot more data. – Peter Flom Jul 08 '15 at 17:48