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

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.

Keywords:

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

Mathematics Subject Classification:

• 62F03
• 62F99