On a rank-order test for the equality of probability of an event

Abstract

Abstract The following situation is considered. A fixed number (= n) or sequence of independent trials T 1 T 2,…, T n is given, and in each of these an event E mayor may not occur, It is further observed that the event E occurs a total of k times amongst the n trials T i , (i = l,…, n). It is then required to test the hypothesis H 0 that the probability of the occurrence of E is constant from trial to trial, i.e. H 0 is the hypothesis: p 1 = p 2 = ⋯ = p n = p, if p n (i = 1, …, n) represents the probability that E occurs on the ith trial.