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I am comparing rate of capture (animal captures per hour) between two years. I'm interested in determining whether there is a difference between rate of capture between the two years. A survey night represent a sample and measures are independent. Sample sizes are small for each group (n1=18, n2=12), variances are unequal, and QQ plots, histograms, and box plots strongly suggest a non-normal distribution.

Because of the non-normality nature of the data, I have explored using a Mann-Whitney U-test test. I realize others have asked similar questions regarding if Mann-Whitney can be used if variance is unequal and I understand that it can be used, but that interpretation becomes more narrow. Specifically, my understanding is that if variances are unequal (i.e., distributions between the two groups differ) then hypothesis testing addresses differences in distribution, not differences in mean (or median).

My two questions are as follows:

1) Can I interpret the results from a Mann-Whitney U-Test - given the unequal variance of my 2 groups - in the context of difference in means?

2) If not, is there a more appropriate test for my situation?

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  • $\begingroup$ Are these groups randomised or do you need top account for other factors (harder to do in rank tests)? Could your capture rates plausibly follow e.g. a negative binomial distribution (=negative binomial regression could be an option)? $\endgroup$ – Björn May 18 '16 at 5:10
  • $\begingroup$ I believe I'm unsure what you mean by randomized in this context. My two groups are years (i.e., capture/hr for each survey night in 2005 (group 1) and capture/hr for each survey night in 2016 (group 2)). I really just want to perform a non-parametric equivalent of a t-test that allows for unequal variance between the 2 groups. Hope this helps and thank you for your thoughts! $\endgroup$ – Beth S. May 18 '16 at 13:41
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After some further research, I found that the Central Limit Theorem is validated if combined sample size (not sample size of each group) is 30. Since n1=18 and n2=12, combined sample size is 30. Therefore, I believe a parametric test is appropriate and have decided to use Welch's t-test due to unequal variance.

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