The Clopper–Pearson interval is an early and very common method for calculating binomial confidence intervals. This is often called an 'exact' method, because it is based on the cumulative probabilities of the binomial distribution (i.e., exactly the correct distribution rather than an approximation). However, in cases where we know the population size, the intervals may not be the smallest possible. For instance, for a population of size 20 with true proportion of 50%, Clopper–Pearson gives 0.728, which has width 0.456 (and where bounds are 0.0280 away from the "next achievable values" of 6/20 and 14/20); whereas Wilson's gives 0.701, which has width 0.401 (and is 0.0007 away from the next achievable values).