A New Method for Constructing Exact Tests Without Making Any Assumptions

Abstract

We present a new method for constructing exact distribution-free tests (and confidence intervals) for variables that can generate more than two possible outcomes. This method separates the search for an exact test from the goal to create a non- randomized test. Randomization is used to extend any exact test relating to means of variables with finitely many outcomes to variables with outcomes belonging to a given bounded set. Tests in terms of variance and covariance are reduced to tests relating to means. Randomness is then eliminated in a separate step. This method is used to create confidence intervals for the difference between two means (or variances) and tests of stochastic inequality and correlation.

Keywords: Distribution-free, nonparametric, exact hypothesis testing, unavoidable inaccuracy, nonparametric Behrens-Fisher problem, UMPU test, Kendall's tau, Qn

JEL Classification: C12, C14