  Detecting entanglement in multipartite quantum states is an inherently
probabilistic process, typically with a few measured samples. The level of
confidence in entanglement detection quantifies the scheme's validity via the
probability that the signal comes from a separable state, offering a meaningful
figure of merit for big datasets. Yet, with limited samples, avoiding
experimental data misinterpretations requires considering not only the
probabilities concerning separable states but also the probability that the
signal came from an entangled state, i.e. the detection scheme's efficiency. We
demonstrate this explicitly and apply a general method to optimize both the
validity and the efficiency in small data sets providing examples using at most
20 state copies. The method is based on an analytical model of finite
statistics effects on correlation functions which takes into account both a
Frequentist as well as a Bayesian approach and is applicable to arbitrary
entanglement witnesses.
