Anavex Life Sciences Corp (AVXL)

[Steady_T]

What you said is mostly true.

However the closer you get to an n=30 the more signal strength is required to achieve p<.05.

That is a result of the uncertainty of the sample being representative of the whole population as n becomes smaller.

If the n is less than 30 then different statistical tests are used because of higher possibility of having a non-representative sample due to the variability in sampling.

As you point out the population in question is a distribution of values. The smaller the sample size the more difficult it is to get a sample that is representative of the true distribution. It is that increase in uncertainty that requires a stronger signal to compensate for the increased uncertainty.