Use the most appropriate test. That is more important than unequal sample sizes (which is irrelevant).

Unequal samples can matter in several ways, notably for the t test where its a big issue is coupled with unequal variances. However, the Welch corrected t test is often a good choice in these situations (or indeed as a default). Whether that's best depends on the outcome.

Your problem is going to be that nothing other than a barn-door difference is going to be significant. If you really want to distinguish between cancer and polyp tissue, this is too important a question to be decided on the basis of small numbers. The only thing that a small sample is useful for in a case like this is where there is a stunning difference between the groups – passes the Mark I Eyeball Test – indicating that the marker has possibly got clinical potential.

The sample size is small, so it is nonparametric. In addition, the groups are independent, therefore I suggest to use Mann-Whitney test.

Actually, David R Bristol , unequal sample sizes is a problem. The highest statisical power exists when the two sample sizes are equal. Holding N constant, a split of 60/40 has little effect on effective sample size (it reduces it by 4%) but when you get to 80/20, effecive sample size is down by 36% and at 90/10 it's down by 64%.

The question was to select the "best statistical method to compare two groups with unequal sample size". The answer to that question is not impacted by the equality of the sample sizes.

David R Bristol – ah, you are right. I misunderstood your reply.

What is the outcome (or dependent) variable?

Hadi Feizi, are you still following this thread? I asked what the dependent variable is because readers need to know that before they can offer any (sensible) advice on what type of analysis might be appropriate and defensible. Thanks for clarifying.

Dear Bruce Weaver, sorry for my late response.

We did 16S rRNA Sequencing in order to identify bacteriome differences and 1HNMR for metabolome identification between these study groups. We found good results using DESeq2. Thank you for your valuable time.

Thank you Hadi Feizi. I am not a medical scientist, so I don't know what those things mean, or how they are measured. But I expect some other readers will.