Can an unpaired t-test be used to compare two experimental groups of data where there are technical replicates within each group? I have done a Western blot experiment and I am trying to figure out the best statistical test to perform on my data. I am comparing the differences in the expression levels of a certain protein in the brains of wild-type mice from two different age groups (postnatal day 12 and postnatal day 30). I have 10 samples in the postnatal day 12 group and 9 samples in the postnatal day 30 group.
I have performed an unpaired parametric t-test to see if there is a statistically significant difference in the protein expression levels between the two age groups. I have performed an unpaired t-test because evidently the mice in the two age groups are different from each other.
However, within each age group, there are some technical replicates (e.g. samples from the same mouse that were used in repeats of the experiment to see if the observed effect is reproducible). I was wondering if it is suitable to use an unpaired t-test if there are technical replicates of a sample within an experimental group?
Any insights are appreciated.
 A: No, you cannot treat two samples from the same mouse as independent and identically distributed - two technical replicates from the same mouse are obviously going to be more similar than two samples from different mice. As a general rule of thumb, you can only assume that samples at the level of your treatment unit (in this case, individual mice) are IID samples. Failure to do so results in a higher false positive rate than you intend.
You have a few options available to you.
A. You can average your technical replicates so that you have a single measurement from each mouse, then perform an unpaired t-test. This errs on the side of being slightly conservative depending on how skewed your data is.
B. Do a randomization test that considers every level of hierarchy in your experimental design, see here. For full disclosure, I wrote this paper.
Basically, when you have a hierarchical (or nested) experiment like this one, it's important to make sure your statistical analysis plan maintains whatever alpha level you choose (typically 5%). Treating technical replicates as independent samples (which many call "pseudoreplication") automatically fails this criterion.
