Remarks Concerning Chase's Results on Testing for Ordered Alternatives.

Abstract

Chase (Biometrika (1974)) found a good approximation for the chi-bar-square and E-bar-square distributions for an important special case. These distributions are fundamental to the theory of order restricted tests. Chase had in mind the problem of comparing ordered dose levels with a control and considered the case where there are more observations on the control. He obtained a recursive relation for the limiting values of the coefficients in those distributions as the sample size on the control becomes infinite and the other sample sizes remain fixed and equal. His approximation is the result of an interpolation between critical values in this limiting case and critical values in the case where all the sample sizes are equal. Starting with Chase's formula we derive a sharper recursion relation and table the limiting coefficients. This allows one to determine approximate P-values; to use critical values not included in Chase's tables and to apply these approximations to testing problems where other versions of the chi-bar-square and e-bar-square distributions occur.

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Document Details

Document Type
Technical Report
Publication Date
Oct 10, 1981
Accession Number
ADA108148

Entities

People

  • F. T. Wright
  • Tim Robertson

Organizations

  • University of Iowa

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Computations
  • Computer Programs
  • Data Science
  • Estimators
  • Information Science
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • New York
  • Precision
  • Probability
  • Statistical Algorithms
  • Statistical Inference
  • Statistics
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Applied Combinatorial Optimization and Logic Circuit Design.
  • Calculus or Mathematical Analysis
  • Regression Analysis.