It is easy to compare paired data, using paired t-test. But suppose this pairing is hierarchical. Below is an example:
The stem cells of two mouse strains S1 and S2 are cultured in two different culture conditions C1 and C2, having 3 replicates for each Strain/Condition (2 x 2 x 3 = 12 samples total). We have examined the expression level of N genes in all of these samples. We want to identify the genes which are significantly (p < 0.02) higher expressed in culture condition C1 in any strain.
The case was easy if we had no replicates: just pairing the identical samples in two conditions C1 and C2 and running a paired t-test. If we had replicates but no strains the problem was easier: just running a normal t-test on two population of cells cultured in C1 and C2.
But how to deal the case while our data is hierarchical?