The way you conducted the statistical inference is conceptually right but
methodologically wrong.
let's assume your data are from normal distribution or hopefully you have
sample size that is large enough. Since they are time-dependent, this is
what I would suggest to do -- treat 5 mean differences as a mean vector. In
other words, think of a set of five gene expression differences along the
time axis as a random sample. In this way, each random sample is independent
of one another. The null hypothesis is it's a zero mean vector. This is
what you want to test against.
The test statistic under this null hypothesis follows T-squared distribution
. In case the null is rejected, you could turn to inspect simultaneous
confidence interval to see at which time point expression difference between
A and B would have caused this rejection.
It's not clear from your description should paired sample be used. But
anyhow the test statistic remains the same while the only difference is the
degree of freedom in the distribution.
Hope this helps.
