23
Views
9
CrossRef citations to date
0
Altmetric
Theory and Method

Bartlett's, Cochran's, and Hartley's Tests on Variances are Liberal When the Underlying Distribution is Long-Tailed

Pages 124-128 | Received 01 Dec 1983, Published online: 12 Mar 2012

References

  • Andrews , D. F. , Bickel , P. J. , Hampel , F. R. , Huber , P. J. , Rogers , W. H. and Tukey , J. W. 1972 . Robust Estimates of Location: Survey and Advances , Princeton , NJ : Princeton University Press .
  • Andrews , D. F. and Mallows , C. L. 1974 . “Scale Mixtures of Normal Distributions” . Journal of the Royal Statistical Society , 36 : 99 – 102 . Ser. B
  • Barlow , R. E. and Proschan , F. 1975 . Statistical Theory of Reliability and Life Testing: Probability Models , New York : Holt, Rinehart & Winston .
  • Bartlett , M. S. 1937 . “Properties of Sufficiency and Statistical Tests” . Proceedings of the Royal Society , 160 : 268 – 282 . Ser. A
  • Benjamini , Y. 1983 . “Is the T-Test Really Conservative When the Parent Distribution Is Long-Tailed?” . Journal of the American Statistical Association , 78 : 645 – 654 .
  • Bickel , P. J. and Lehmann , E. L. 1975 . “Descriptive Statistics for Nonparametric Models, II: Location” . The Annals of Statistics , 3 : 1045 – 1069 .
  • Box , G. E. P. 1953 . “Non-Normality and Tests on Variances” . Biometrika , 40 : 318 – 335 .
  • Brown , L. D. , Johnstone , L. M. and MacGibbon , K. B. 1981 . “Variation Diminishing Transformations: A Direct Approach to Total Positivity and Its Statistical Applications” . Journal of the American Statistical Association , 76 : 824 – 832 .
  • Brown , M. B. and Forsythe , A. B. 1974 . “Robust Tests for the Equality of Variances” . Journal of the American Statistical Association , 69 : 364 – 367 .
  • Chmielewski , M. A. 1981 . “Invariant Tests for the Equality of K Scale Parameters Under Spherical Symmetry” . Journal of Statistical Planning and Inference , 5 : 341 – 346 .
  • Cochran , W. G. 1941 . “The Distribution of the Largest of a Set of Estimated Variances as a Fraction of Their Total” . Annals of Eugenics , 11 : 47 – 52 .
  • Conover , W. J. , Johnson , M. E. and Johnson , M. M. 1981 . “A Comparative Study of Tests for Homogeneity of Variances, With Applications to the Outer Continental Shelf Bidding Data” . Technometrics , 23 : 351 – 361 .
  • Dyer , D. D. and Keating , J. P. 1980 . “On the Determination of Critical Values for Bartlett's Test” . Journal of the American Statistical Association , 75 : 313 – 319 .
  • Efron , B. and Olshen , R. A. 1978 . “How Broad Is the Class of Normal Scale Mixtures?” . The Annals of Statistics , 6 : 1159 – 1164 .
  • Gartside , P. S. 1972 . “Study of Methods for Comparing Several Variances” . Journal of the American Statistical Association , 67 : 342 – 346 .
  • Hartley , H. O. 1950 . “The Maximum F-Ratio as a Short-Cut Test for Heterogeneity of Variances” . Biometrika , 37 : 308 – 312 .
  • Keating , J. P. and Hensley , O. L. 1983 . “A Note of the Critical Values of the F Max-Test” . Communications in Statistics, Simulation and Computation , 12 : 257 – 264 .
  • Kendall , M. and Stuart , A. 1977 . The Advanced Theory of Statistics, , 4th ed. , Vol. 1 , London : Charles W. Griffin .
  • Marshall , A. W. and Olkin , I. 1979 . “Inequalities: Theory of Majorization and Its Applications” , New York : Academic Press .
  • Pearson , E. S. and Hartley , H. O. 1970 . Biometrika Tables for Statisticians, , 3rd ed. , Vol. 1 , Cambridge , , U.K. : Cambridge University Press .
  • Portnoy , S. L. 1977 . “Robust Estimation in Dependent Situations” . The Annals of Statistics , 5 : 23 – 43 .
  • Rivest , L. P. 1982 . “Products of Random Variables and Star-Shaped Ordering” . The Canadian Journal of Statistics , 10 : 219 – 223 .
  • Rivest , L. P. 1985 . “Tests Based on Equivariant Estimators” . The Canadian Journal of Statistics , 13 : 211 – 216 .
  • Tietjen , G. L. and Beckman , R. J. 1972 . “Tables for Use of the Maximum F-Ratio in Multiple Comparison Procedures” . Journal of the American Statistical Association , 67 : 581 – 583 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.