An exact multinomial test for equivalence

Existing equivalence tests for multinomial data are valid asymptotically, but the α level is not properly controlled for small and moderate sample sizes. We resolve this difficulty by developing an exact multinomial test for equivalence and an associated confidence interval procedure. We also derive a conservative version of the test that is easy to implement even for very large sample sizes. Both tests use a notion of equivalence that is based on the cumulative distribution function, with two probability vectors being considered equivalent if their partial sums never differ by more than some specified constant. We illustrate the methods by applying them to Weldon's dice data, to data on the digits of π , and to data collected by Mendel. The Canadian Journal of Statistics 37: 47–59; © 2009 Statistical Society of Canada