Independency in cell culture experiment My question is related to the assumption of independence in observations between groups.
In brief: I use human cells from three different donors (n=3, three biological replicates). These are splitted into two groups by technical replication. One is receiving Treatment A and the other is receiving Treatment B. A series of dependent variables are assessed and in the end, I report and analyze the means comprised of Donor1, Donor2 and Donor3 for both treatments.
I know that applying statistics to small sample sizes are problematic and in worst case misleading. However, in this example it is mostly about understanding the two groups I compare.
The problem (as I see it) is that the group receiving Treatment A is not different (independent) from the group receiving Treatment B. This is due to the fact that the groups are just technical replicates from the same donor. When comparing the means of the two groups, I'm essentially comparing two groups containing the same cells (Treatment A(Donor1, Donor2, Donor3) compared to Treatment B(Donor1, Donor2, Donor3).
This raises the question: is it a weakness that I violate the assumption of independency between groups AND/OR a strength since the effect can now only be caused by the treatment because the groups are identical (assuming little to no variation in how I prepare my samples)?
 A: This is a common design method called repeated measures. In organismal studies (or human studies), this is usually done by testing the same individual, but in this case you would treat each cell line source as the 'individual'. In most cases, this is considered a strength, and is quite easily handled by linear mixed-effects models (LMM; or, depending on your stats program/statistical training, repeated-measures ANOVA). You're also correct about your sample size being fairly worrisome - in the case of a LMM, where Individual or Cell Source would be treated as a random variable, it's generally suggested that you need at least 4-5+ levels to treat it as random (rather than fixed, like Treatment - A vs B).
Edit: To state it explicitly, repeated measures is almost always a strength, for reasons beyond statistical power (e.g., maximize sample sizes). Yes, if you would run this with a simple one-way ANOVA you would violate assumptions of indepence, but it's usually a trivial matter to use other 'flavours' of linear model that do not have this limitation.
