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Original Articles

An Analysis-of-Means-Type Test for Variances From Normal Populations

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Pages 274-285 | Published online: 12 Mar 2012

REFERENCES

  • Arnold , S. F. 1990 . Mathematical Statistics , Englewood Cliffs , NJ : Prentice-Hall .
  • Bartlett , M. S. 1937 . “Properties of Sufficiency and Statistical Tests,” . Proceedings of the Royal Society , 160 : 268 – 282 .
  • Bartlett , M. S. and Kendall , D. G. 1946 . “The Statistical Analysis of Variance Heterogeneity and the Logarithmic Transformation,” . Journal of the Royal Statistical Society , 8 : 128 – 138 .
  • Box , G. E. P. 1953 . “Nonnormality and Tests of Variance,” . Biometrika , 40 : 318 – 335 .
  • Burr , I. W. and Foster , L. A. 1972 . “A Test for Equality of Variances,” , Purdue University, Dept, of Statistics . Technical Report 282
  • Chao , M. and Glaser , R. E. 1978 . “The Exact Distribution of Bartlett's Test Statistic for Homogeneity of Variances With Unequal Sample Sizes,” . Journal of the American Statistical Association , 73 : 422 – 426 .
  • 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 .
  • Cohen , A. and Marden , J. I. 1989 . “On the Admissibility and Consistency of Tests for Homogeneity of Variances,” . The Annals of Statistics , 17 : 226 – 251 .
  • Cohen , A. and Strawderman , W. E. 1971 . “Unbiasedness of Tests for Homogeneity of Variance,” . The Annals of Mathematical Statistics , 42 : 355 – 360 .
  • 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 .
  • David , H. A. 1952 . “Upper 5 and 1% Points of the Maximum F-Ratio,” . Biometrika , 39 : 422 – 424 .
  • Doornbos , R. 1956 . “Significance of the Smallest of a Set of Estimated Normal Variances,” . Statistica Neerlandica , 10 : 117 – 126 .
  • Dyer , D. and Keating , J. 1980 . “On the Determination of Critical Values of Bartlett's Test,” . Journal of the American Statistical Association , 75 : 313 – 319 .
  • Foster , L. A. 1964 . “Testing for Equality of Variances,” , Purdue University, Dept. of Statistics . unpublished Ph.D. thesis
  • Games , P. A. and Wolfgang , G. S. 1983 . “A Review of Six Multifactor Tests for Homogeneity of Spread,” . Computational Statistics and Data Analysis , 1 : 41 – 52 .
  • Hartley , H. O. 1940 . “Testing the Homogeneity of a Set of Variances,” . Biometrika , 31 : 249 – 255 .
  • Hartley , H. O. 1950 . “The Maximum F-Ratio as a Short Cut Test of Heterogeneity of Variances,” . Biometrika , 37 : 308 – 312 .
  • Hochberg , Y. and Tamhane , A. C. 1987 . Multiple Comparison Procedures , New York : Wiley .
  • IMSL, Inc . 1987 . Math Library , Houston , TX : Author .
  • Izenman , A. J. 1976 . “On the Extremal Quotient From a Gamma Sample,” . Biometrika , 63 : 185 – 190 .
  • Kounias , E. G. 1968 . “Bounds for Probability of a Union, With Applications,” . The Annals of Mathematical Statistics , 39 : 2154 – 2158 .
  • Nelson , L. S. 1981 . “Analysis of Heterogeneity of Variation,” . Journal of Quality Technology , 13 : 143 – 144 .
  • Nelson , L. S. 1983 . “Exact Critical Values for the Analysis of Means,” . Journal of Quality Technology , 15 : 40 – 44 .
  • Nelson , L. S. 1987 . “Upper 10%, 5% and 1% Points of the Maximum F Ratio,” . Journal of Quality Technology , 19 : 165 – 167 .
  • Nelson , L. S. 1993 . “Testing the Smallest of a Set of Variances,” . Journal of Quality Technology , 25 : 144 – 148 .
  • Nelson , P. R. 1988 . “Testing for Interactions Using the Analysis of Means,” . Technometrics , 30 : 65 – 73 .
  • Neyman , J. and Pearson , E. S. 1931 . “On the Problem of k Samples,” . Bulletin Academie Polonaise Sciences et Lettres, Ser. A , 3 : 460 – 481 .
  • Numerical Algorithms Group . 1991 . The NAG Fortran Library Manual, Mark 15 , Oxford , , U.K. : NAG Ltd .
  • Overall , J. E. and Woodward , J. A. 1974 . “A Simple Test for Heterogeneity of Variance of Complex Factorial Designs,” . Psychometrika , 39 : 311 – 318 .
  • Pitman , E. J. G. 1939 . “Tests of Hypotheses Concerning Location and Scale Parameters,” . Biometrika , 31 : 200 – 215 .
  • Scheffé , H. 1959 . The Analysis of Variance , New York : Wiley .
  • Sobel , M. , Uppuluri , V. R. R. and Frankowski , K. 1977 . Selected Tables in Mathematical Statistics: Volume 4: Dirichlet Distribution—Type , Providence , RI : American Mathematical Society .
  • Solomon , H. and Stephens , M. A. 1990 . “Percentage Points for the Cochran Test for the Equality of Variances,” . Journal of Quality Technology , 22 : 46 – 56 .
  • Tang , J. and Gupta , K. 1987 . “On Testing the Homogeneity of Variances for Gaussian Models,” . Journal of Statistical Computation and Simulation , 27 : 155 – 173 .
  • Wilks , S. S. 1962 . Mathematical Statistics , New York : Wiley .
  • Wludyka , P. S. and Nelson , P. R. “Analysis of Means Type Tests for Variances Using Subsampling and Jackknifing,” . American Journal of Mathematical and Management Sciences , 17 (in press)

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