What is a large enough random sample?

With the well deserved popularity of A/B testing computer scientists are finally becoming practicing statisticians. One part of experiment design that has always been particularly hard to teach is how to pick the size of your sample. The two points that are hard to communicate are that:

  • The required sample size is essentially independent of the total population size.
  • The required sample size depends strongly on the strength of the effect you are trying to measure.

These things are only hard to explain because the literature is overly technical (too many buzzwords and too many irrelevant concerns) and these misapprehensions can’t be relieved unless you spend some time addressing the legitimate underlying concerns they are standing in for. As usual explanation requires common ground (moving to shared assumptions) not mere technical bullying.

We will try to work through these assumptions and then discuss proper sample size. Continue reading