 As usual in this entry, an inductive method conjectures a hypothesis after observing a finite sequence of observations. A method that conjectures a statistical hypothesis is called a statistical test (see the link in the Other Internet Resource section below). The statistical literature provides an extensive collection of computationally efficient statistical tests for different types of statistical hypothesis. In the following discussion we consider the general learning performance of such methods, with respect to reliable convergence to a true hypothesis and avoiding mind changes. Consider a fixed observation length \(n,\) called the sample size. For sample size \(n\), there is a set of samples of length \(n\) such that the method conjectures hypothesis \(H\)given the sample. For example, for \(n = 3\), the method might conjecture \(H_2 =\) “the coin is not fair” after observing 3 heads. The aggregate probability that the method outputs hypothesis \(H\) given some sample of length \(n\), is the sum of the sample probabilities of the samples such that the method conjectures \(H\) given the sample. In the supplement we give example computations of the aggregate probability. Because this aggregate probability is the key quantity for the methodology of statistical hypotheses, we introduce the following notation for it.