to correct or not correct? I apologize in advance for the level of simplicity of the question but I have been trying to wrap my head around this for a while now and I would like to hear sb's else opinion.
I am checking the expression of four genes in two different tissues (liver and kidney). I am interested in examining the difference in expression (for each gene separately) between the two tissues and report it separately. I am not interested in any comparisons between genes' expression. I am using a single linear mixed model and then using contrasts I am examining the significance of the difference in expression of gene A, of gene B, of gene C and of gene D. 
If I do not correct (e.g. Bonferroni) 2/4 contrasts are significant. If I correct then nothing is significant. My question is: why should I correct since I am examining the difference in gene expression, for each gene separately... and therefore I could have 2 genes or 20.000 genes... 
any advice is very welcome
 A: You need to correct for multiple hypothesis because you did four experiments: when you compare those results, you are selecting only the best ones, affecting the meaning of those p-values.
In fact, imagine this scenario.
You test 20 genes, and you find that only one of them is significant (p-value <0.05). You can go on, and publish a paper reporting the result for that gene only, without telling anyone how many genes you actually tested.
However, the next team trying to repeat your experiment will not find the same level of significance, because they will only test that gene, whereas you have tested multiple of them.
So, even if you are interested in the single genes, the mere fact that you highlight the one with the best p-value is introducing a selection: and this is distorting the meaning of the p-value.
You might have seen this:
https://xkcd.com/882/
It's a really important issue in science!
You should also check the paper:
Why Most Published Research Findings Are False.
A: You are testing four genes thus you have a multiple comparison problem. You don’t have a problem if you test only on a single gene but you have four.
You are not forced to make any adjustment if you don’t want to - you just need to understand your inflated Type I errors.
Bonferroni is known to be conservative so your data might not be strong enough. You could try other methods or simply report your results - you don’t have very significant data to reject your hypothesis.
