Small sample comparisons for the blended weight chi-square goodness-of-fit test statistics

Dong Wan Shin, Ayanendranath Basu, Sahadeb Sarkar

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The small sample properties of the family of blended weight chi-square (BWCS) goodness-of-fit tests are investigated. Like the power divergence family, this family is a very rich subclass of a more general class of goodness-of-fit tests called the disparity tests (Basu and Sarkar 1994a). Use of the standard asymptotic chi-square distribution in small samples can give quite inaccurate critical regions for most members of the BWCS family. We derive three other asymptotic approximations of the exact distributions in order to obtain more accurate significance levels for the BWCS tests. Two of these approximations are computationally simple to use in practice. Numerical comparisons are made for the equiprobable null hypothesis, for various multinomial sample sizes and numbers of cells. Exact power comparisons show that under specific alternatives to the equiprobable null hypothesis there may be other members in the BWCS family that have more power than the commonly used Pearson's chi-square.

Original languageEnglish
Pages (from-to)211-226
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Issue number1
StatePublished - 1996

Bibliographical note

Funding Information:
The TPS~;L~Z:'I ~f the ?kt author was supported by a grant from Korea Science a.nd Engineeiiiig fonndltinr?, the research ui thc scconri au:hr?r w-5 supported in part by the URI summer research grant, University of Texas at Austin and the research of the third author was supported by a grant from the College of Arts and Sciences Fund at Oklahoma State University.


  • Blended weight chi-square
  • Chi-squared statistic
  • Goodness-of-fit
  • Large sparse multinomial
  • Likelihood ratio test
  • Power


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