A Command for Significance and Power to Test for the Existence of a Unique Most Probable Category. (September 2014)

• Record Type: Journal Article
• Authors: Fellman, Bryan M.; Ensor, Joe
• Is Part Of: Stata journal. Volume 14:Number 3(2014)
• Page Start: 499
• Page End: 510
• Publication Date: 2014-09
• Subjects: st0348 -- cellsupremacy -- cellsupremacyi -- power cellsupremacy -- most probable category -- multinomial data -- cell supremacy -- cell inferiority; Statistics -- Periodicals; Statistics -- Computer programs -- Periodicals; 001.422
• DOI: 10.1177/1536867X1401400303
• Languages: English
• ISSNs: 1536-867X

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.