My only comment would be that performing anomaly detection on the same data that you use to "train" your detector in the first place, is a classic example of a

My only comment would be that performing anomaly detection on the same data that you use to "train" your detector in the first place, is a classic example of a "data-leak" in data science, and very likely to lead to errors in itself. But thats the whole point of the very well established concept of standard deviation - to look at a dataset in isolation and analyse it.