# Which statistical test to use (percentages of codon usage)?

I would like to compare each codon usage percentages between analyzed organisms (which will result in 6 separate statistical tests, subject to 6 codons). Which statistical test should I use?

   codon1   codon2   codon3   codon4   codon5   codon6
org1 0.069 0.060 0.282 0.238 0.142 0.210

org2 0.084 0.073 0.276 0.220 0.140 0.206

org3 0.073 0.069 0.274 0.237 0.139 0.208

org4 0.074 0.073 0.268 0.236 0.137 0.213

org5 0.076 0.071 0.274 0.234 0.139 0.205

org6 0.069 0.069 0.279 0.234 0.141 0.207

org7 0.075 0.070 0.275 0.233 0.140 0.207

org8 0.070 0.065 0.288 0.234 0.142 0.201

org9 0.121 0.105 0.261 0.208 0.124 0.182

• Formulating your null hypothesis first will always make the choice of statistical test much easier, and that ultimately relies on domain knowledge which I assume you have. You probably need counts as well as percentages too. My guess is that you'll end up doing some sort of ANOVA test.
– djma
Commented Jul 24, 2017 at 17:24
• Sure, the null hypothesis would be that there are no differences between these precentages. As for the counts - using these for the comparizon would be pointless since the number of available sequences for each organism was considerably different. I'm just concerned about comparing single values (percentages) with ANOVA
– Tom
Commented Jul 24, 2017 at 17:37
• To give you some intuition on why counts is necessary for any statistical test, here's an example: Let's say I tell you in group A, 60% of people are male and group B, 50% of people are male. Is group A systematically male biased? Well, if N=10 for both groups, then it doesn't really seems like it. But if N = 1000000, then the null hypothesis can be rejected with high confidence.
– djma
Commented Jul 24, 2017 at 18:00
• Yes, I am aware of that. But how to incorporate the counts to my test then? For example testing if for codon1 there are differences in usage between orgs?
– Tom
Commented Jul 24, 2017 at 18:06
• Form my non-specialist view of the problem, I think I would be comparing organisms instead of codons. I.e. Orgs 1's codons are significantly different from orgs2. Then the test becomes pretty natural. If the hypothesis is something like "codon1's distribution is different from codon2 in nature", then you'd have to define what is "one sample". I.e. do organisms that have more dna count more, or does each organism contribute equally?
– djma
Commented Jul 24, 2017 at 18:12