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Is it possible to run Somers' D (and its accompanying significance tests) on a very small sample? In my case, I have a 2x3 (one variable is ordinal, the other 0/1 coded) table but only 36 cases. If it is (not) okay, does anyone know the exact assumption?

PS: A similar question is asked here: Measure of Association between two Ordinal Variables

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It's OK to do any analysis on a small sample if you completely understand the data quality and possible sample selection biases. But it is very important to include self-contained statistical quantifications that capture the limitations of the information base used in the analysis. In your case this can be done in the frequentist statistics setting using a compatibility interval (aka confidence interval). For example the R Hmisc package rcorr.cens function will give you the standard error of $D_{xy}$ which can be used to get an approximate compatibility interval.

Note: compatibility is related to the fact that the confidence interval includes the set of $D_{xy}$ values that if null hypothesized would not be rejected at the $1 - \alpha$ level.

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