An exact multinomial test for equivalence.

Existing equivalence tests for multinomial data are valid asymptotically, but the alpha 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.

Main Author: Frey, Jesse.
Format: Villanova Faculty Authorship
Language: English
Published: 2009
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:176352
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An exact multinomial test for equivalence.
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title An exact multinomial test for equivalence.
title_short An exact multinomial test for equivalence.
title_full An exact multinomial test for equivalence.
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description Existing equivalence tests for multinomial data are valid asymptotically, but the alpha 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.
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dc.title An exact multinomial test for equivalence.
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dc.description Existing equivalence tests for multinomial data are valid asymptotically, but the alpha 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.
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