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I am performing a retrospective study on patients looking at the size of their nostril (continuous variable measured in millimetres) and the need for treatment which is either conservative or surgical (this is a categorical variable).
Sample size is only 15.

What would be the right test to compare groups to determine if size of nostril was a significant factor in predicting method of treatment?

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Note that the sample size is very small and it is therefore higly likely that you run into power problems if you get a nonsignificant result. Therefore, definitely report the effect size whatever the result of your test will be (i.e., the differences in nostril size between the two treatment groups, in relation to the standard deviations = cohen's d et al.).

As a test, the t-test for independent samples seems to be appropriate.

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    $\begingroup$ (+1) As an alternative, we might consider a permutation test. Good that you indicated to report ESs. $\endgroup$
    – chl
    May 26 '11 at 21:46

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