Felt this was a theoretical discussion point.

My thesis includes cell culture experiments with 100,000 cells per condition repeated three times. My scientific supervisor has advised parametric testing, with a presumption of normality. My clinical supervisor has advised non-parametric. Most of the journals I've read follow my scientific supervisors approach.

I can see the argument form both sides. I suspect (perhaps wrongly) that a statisticians opinion will be that normality cannot be assumed. However, I'd be interested in a discussion about this. From my reading it seems the central limit theorem is thought to apply - this works if you take my sample size as 100,000; but is less convincing if you take my sample size as three.

One bit I'm unclear on is whether for parametric testing it is the population, or the sample population, that has to be normally distributed.

I hope this is theoretical enough :0)