A Simplified Monte Carlo Significance Test Procedure

Summary The use of Monte Carlo test procedures for significance testing, with smaller reference sets than are now generally used, is advocated. It is shown that, for given α = 1/n, n a positive integer, the power of the Monte Carlo test procedure is a monotone increasing function of the size of the reference set, the limit of which is the power of the corresponding uniformly most powerful test. The power functions and efficiency of the Monte Carlo test to the uniformly most powerful test are discussed in detail for the case where the test criterion is N(γ, 1). The cases when the test criterion is Student's t-statistic and when the test statistic is exponentially distributed are considered also.