A command for significance and power to test for the existence of a unique most probable category

Bryan M. Fellman, Joe Ensor

Research output: Contribution to journalArticle

Abstract

The analysis of multinomial data often includes the following question of interest: Is a particular category the most populous (that is, does it have the largest probability)? Berry (2001, Journal of Statistical Planning and Inference 99: 175–182) developed a likelihood-ratio test for assessing the evidence for the existence of a unique most probable category. Nettleton (2009, Journal of the American Statistical Association 104: 1052–1059) developed a likelihood-ratio test for testing whether a particular category was most probable, showed that the test was an example of an intersection-union test, and proposed other intersection-union tests for testing whether a particular category was most probable. He extended his likelihood-ratio test to the existence of a unique most probable category and showed that his test was equivalent to the test developed by Berry (2001, Journal of Statistical Planning and Inference 99: 175–182). Nettleton (2009, Journal of the American Statistical Association 104: 1052–1059) showed that the likelihood ratio for identifying a unique most probable cell could be viewed as a union-intersection test. The purpose of this article is to survey different methods and present a command, cellsupremacy, for the analysis of multinomial data as it pertains to identifying the significantly most probable category; the article also presents a command for sample-size calculations and power analyses, power cellsupremacy, that is useful for planning multinomial data studies.

Original languageEnglish (US)
Article numberst0348
Pages (from-to)499-510
Number of pages12
JournalStata Journal
Volume14
Issue number3
DOIs
StatePublished - Sep 2014

Keywords

  • Cell inferiority
  • Cell supremacy
  • Cellsupremacy
  • Cellsupremacyi
  • Most probable category
  • Multinomial data
  • Power cellsupremacy
  • St0348

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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