I have two populations of codon translation rate data. They are all in terms of translation time. The first population is the codon translation time for each codon of the transcriptome. The second population is the codon translation time for each codon at a given position from the domain boundary. All translation times are divided by the average synthesis time of the transcript. More or less, population two is a smaller subset of population one, relative to a position on the transcript.

My advisor and I were discussing the best way to calculate p values for each of the codons in the second population. Our goal is to see if there is a significant difference between population two and population one. Some methods that we considered were two-sided t tests, paired t tests, Wilcoxon signed rank sum test, and the Mann-Whitney U test. The paired t test and Wilcoxon signed rank sum test will not work because population two is smaller than population one. The two-sided t test probably would not be ideal, because we have a relatively small sample size for the second population, so it's unclear to me whether we could assume normal distribution. The Mann-Whitney U test seems like the best test to apply to these data, but given my limited statistics background, I do not feel qualified to make this judgment. Any input would be greatly appreciated! I can provide more information as it becomes necessary.

Thank you!