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A note on levene's tests for equality of variances


  • Carroll, Raymond J.
  • Schneider, Helmut


Consider testing for equality variances in a one-way analysis of variance. Levene's test is the usual F-test for equality of means computed on psuedo-observations, which one defines as the absolute deviations of the data points from an estimate of the group 'center'. We show that, asymptotically, Levene's test has the correct level whenever the estimate of group 'center' is an estimate of group median. This explains why published Monte-Carlo studies have found that Levene's original proposal of centering at the sample mean has the correct level only for symmetric distributions, while centering at the sample median has correct level even for asymmetric distributions. Generalizations are discussed.

Suggested Citation

  • Carroll, Raymond J. & Schneider, Helmut, 1985. "A note on levene's tests for equality of variances," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 191-194, July.
  • Handle: RePEc:eee:stapro:v:3:y:1985:i:4:p:191-194

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    References listed on IDEAS

    1. Panaretos, John & Xekalaki, Evdokia, 1986. "On Generalized Binomial and Multinomial Distributions and Their Relation to Generalized Poisson Distributions," MPRA Paper 6248, University Library of Munich, Germany.
    2. Panaretos, John, 1983. "A Generating Model Involving Pascal and Logarithmic Series Distributions," MPRA Paper 6246, University Library of Munich, Germany.
    3. Xekalaki, Evdokia & Panaretos, John, 1983. "Identifiability of Compound Poisson Distributions," MPRA Paper 6244, University Library of Munich, Germany.
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