There is something wrong with your thinking, but I can't quite put my finger on it. Let me try: Either you assume a prior distribution of salaries or not. If y

There is something wrong with your thinking, but I can't quite put my finger on it. Let me try: Either you assume a prior distribution of salaries or not. If you don't, then you don't know mean salary, and so group of any size will not tell you if you're anomaly. Because they can all be anomalous as well. On the other hand, if you assume a prior distribution (which is pretty much what Bayesian statistics does), then even one sample will modify the prior, and you gain information (i.e. "suggestion that you're anomaly or not"). Of course more samples is always better, but if you can make conclusion from multiple samples, then you can make conclusion from one sample. It seems to me that in the first case, you're saying we cannot assume any prior, but in the second case, you're doing exactly that - assuming that there is a mean - 1st moment of the prior distribution and maybe even other moments - which indicate whether an observation is anomaly or not.