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A note on levene's tests for equality of variances

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  • Carroll, Raymond J.
  • Schneider, Helmut

Abstract

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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    Cited by:

    1. Ryan C. Erps & Kimihiro Noguchi, 2020. "A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 403-425, August.
    2. W. G. S. Hines & R. J. O'Hara Hines, 2000. "Increased Power with Modified Forms of the Levene (Med) Test for Heterogeneity of Variance," Biometrics, The International Biometric Society, vol. 56(2), pages 451-454, June.
    3. David Soave & Lei Sun, 2017. "A generalized Levene's scale test for variance heterogeneity in the presence of sample correlation and group uncertainty," Biometrics, The International Biometric Society, vol. 73(3), pages 960-971, September.
    4. Rizzi, Francesco & Gigliotti, Marina & Runfola, Andrea & Ferrucci, Luca, 2022. "Don't miss the boat when consumers are in-store! Exploring the use of point-of-purchase displays to promote green and non-green products," Journal of Retailing and Consumer Services, Elsevier, vol. 68(C).
    5. Gianluca Gionfriddo & Francesco Rizzi & Tiberio Daddi & Fabio Iraldo, 2023. "The impact of green marketing on collective behaviour: Experimental evidence from the sports industry," Business Strategy and the Environment, Wiley Blackwell, vol. 32(8), pages 5349-5367, December.
    6. Chao Gu & Tingting Huang & Wei Wei & Chun Yang & Jiangjie Chen & Wei Miao & Shuyuan Lin & Hanchu Sun & Jie Sun, 2023. "The Effect of Using Augmented Reality Technology in Takeaway Food Packaging to Improve Young Consumers’ Negative Evaluations," Agriculture, MDPI, vol. 13(2), pages 1-35, January.

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