An Alternative Test for the Equality of Variances for Several Populations When the Underlying Distributions are Normal

Madhusudan Bhandary, Hongying Dai

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Homogeneity of variance test has been studied by Bartlett (1937), Hartley (1950), Levene (1960), and Box (1953), among others. The tests developed by the above statisticians are either approximate tests or tests using numerical tabulation of the critical points, so the validity of the tests relies on sample sizes. We have developed a test, the so-called New-Test, for the equality of variances whose Type I error is well controlled and whose power is competitive to the optimal alternative tests. Extensive empirical experiments are conducted to compare the performance of the New-Test with three classical methods. An experiment with exponential data is also done by simulation. It seems that under exponential distribution situation, Type I error is not as controlled as in the case of normal distribution situation. With relatively higher power and precise control of Type I error, the New-Test can be recommended for future use by the practitioners when the underlying data are from normal distribution.

Original languageEnglish (US)
Pages (from-to)109-117
Number of pages9
JournalCommunications in Statistics: Simulation and Computation
Volume38
Issue number1
DOIs
StatePublished - Nov 21 2008

Fingerprint

Normal distribution
Equality
Alternatives
Type I error
Experiments
Gaussian distribution
Homogeneity of Variances
Exponential distribution
High Power
Experiment
Critical point
Sample Size

Keywords

  • Bartlett's test
  • Hartley's F max-Test
  • Homogeneity of variances
  • Levene's test
  • New-Test

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation

Cite this

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