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

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. 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.