On the finite sample behavior of testing whether new is better than used of a specified age

Ibrahim A. Ahmad, Wei Liu, Ying Zhang

Research output: Contribution to journalArticle

Abstract

Hollander, Park and Proschan (1986) proposed a test of new is better than used of a specified age. It is based on large sample normality of the test statistic. There is, however, no study in the literature on its actual size for small and moderate sample sizes. To shed some lights on this, the results of a Monte Carlo simulation study as well as two real data examples are reported and these indicate that the test can have a quite liberal size, especially for small to moderate sample sizes. In order to improve on this weakness, a modified test is proposed and studied. It is noticed that this modified test seems to over-correct the original test to an extent that it becomes unduly conservative sometimes. Hence we propose another modification that combines the original test and the modified test turns out to have its size quite close to the nominal level and is therefore preferable to both the original and modified tests.

Original languageEnglish (US)
Pages (from-to)287-294
Number of pages8
JournalMetrika
Volume60
Issue number3
DOIs
StatePublished - Nov 1 2004

Fingerprint

Testing
Sample Size
Finite sample
Normality
Test Statistic
Categorical or nominal
Monte Carlo Simulation
Simulation Study
Sample size

Keywords

  • Asymptotic normality
  • Bias correction
  • Hypotheses test
  • New better than used of age t
  • U-statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

On the finite sample behavior of testing whether new is better than used of a specified age. / Ahmad, Ibrahim A.; Liu, Wei; Zhang, Ying.

In: Metrika, Vol. 60, No. 3, 01.11.2004, p. 287-294.

Research output: Contribution to journalArticle

Ahmad, Ibrahim A. ; Liu, Wei ; Zhang, Ying. / On the finite sample behavior of testing whether new is better than used of a specified age. In: Metrika. 2004 ; Vol. 60, No. 3. pp. 287-294.
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