My dataset consists of $n$ genes, each of them described by a vector of expression values, $5$ for "healthy" individuals, and $5$ for "unhealthy" individuals.
I am going to run $n$ t-tests (one for each gene) to identify which genes show a different behaviour between healthy population and unhealthy population.
Should I consider a correction (such as Bonferroni, Holm, Benjamini & Hochberg...) for the $n$ p-values ?
I am wondering whether my case is a multiple comparisons problem or not.
Actually I do not compare the genes, but only the values of two different populations (healthy vs. unhealthy) for each gene. Therefore, I do not see the multiple comparisons.
In other words, I am interested in finding those genes that behave differently between healthy samples and unhealthy samples. I am not interested in finding whether or not two genes behave the same.
Obviously, running $n$ t-tests I get much more p-values lower that $0.05$ than after computing the correction.