I have Type I CD protein data which consists of 27 Enzymes and 217 non-enzymes. I want to determine if there is a significant difference in the length of enzymes versus non-enzyme. What type of non-parametric test should I use if there is a huge difference between the sample size of enzymes versus non-enzyme?
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Use whichever nonparametric test is suited for your particular null and alternative.
None of the usual tests suitable for two independent samples will care that one sample is larger than the other.
Note that "difference in the length" is sort of vague -- if that's as specific as you can be, I'd lean toward a general one like a Wilcoxon Mann-Whitney (I presume you have ties though), but if you have a particular measure of location you're interested in that can be done fairly easily (e.g. via permutation tests).
So you if you want to see if there's a difference in mean length, you could do that with a nonparametric test (or by adding some assumptions to an existing test).
[What's perhaps less immediately clear, though, is how to construe this as a suitable situation for a hypothesis test in terms of random selection from populations (since clearly there's no random assignment to treatment); it seems to be fairly standard to just charge ahead regardless. I hope someone has constructed appropriate justifications somewhere.]
