# How do I compare the means of 2 sets when they have different distributions?

I want to compare the means of 2 sets of data. I have already taken the log and removed spurious outliers.

But the 2 sets have different shapes and I don't want to blindly throw them into a linear model.

Any tips?

One set is called liv and the other is called noliv. noliv is probably going to have a larger mean but using an appropriate test is the issue.

Is there any more general statistical test I can use here that doesn't assume normality. Obviously liv is normal but noliv isn't.

Even if the best answer is "take the log again", can someone please recommend a second best option to this?  If you want to compare means, do not take logs first. $$(1,4)$$ has a larger mean than $$(2,2)$$, but $$(\log 1,\log 4)$$ has the same mean as $$(\log 2, \log 2)$$. You can easily find examples where the relation of means is swapped by taking logs.
• An excellent point about the central limit theorem. I wasn't aware. t-test is what I'll go with. I'm right in thinking that by taking the log then I'm comparing geometric mean? $(1,4)$ and $(2,2)$ have the same geometric mean and so their logs have the same arithmetic mean? Dec 12, 2019 at 15:11