Testing for positive evidence of equally likely outcomes

Goodness-of-fit tests allow one to conclude that kk possible outcomes are not equally likely. In this paper, we develop an exact equivalence test that allows one to conclude that kk possible outcomes are approximately   equally likely. We show that the power properties of the test compare favorably to those of possible alternative tests, and we develop an associated simultaneous confidence interval procedure. We apply the test to data sets on the digits of ππ, winning roulette numbers, and winning numbers from the Pennsylvania Lottery.

► We develop an exact multinomial equivalence test. ► The alternative hypothesis is that the outcomes are approximately equally likely. ► We also develop an associated confidence interval procedure. ► We apply the new procedures to several interesting data sets.