A new method for constructing exact tests without making any assumptions

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 meansof variables with finitely many outcomes to variables with outcomes belonging to agiven bounded set. Tests in terms of variance and covariance are reduced to testsrelating to means. Randomness is then eliminated in a separate step.This method is used to create confidence intervals for the difference between twomeans (or variances) and tests of stochastic inequality and correlation.