Analysis of means type tests for variances using subsampling and jackknifing

American Journal of Mathematical and Management Sciences

Volumn 17, Issue 1-2, 1997, Pages 31-60

  Fujikoshi, Yasunori ^a  

^a HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Analysis of means; Homogeneity of variances; Jackknifing; Multiple comparisons; Subsampling

Indexed keywords

GRAPHIC METHODS; MONTE CARLO METHODS; PROBABILITY;

ANALYSIS OF MEANS (ANOM); ANALYSIS OF VARIANCE (ANOVA); SUBSAMPLING;

STATISTICAL TESTS;

EID: 0030691645     PISSN: 01966324     EISSN: None     Source Type: Journal    
DOI: 10.1080/01966324.1997.10737429     Document Type: Article

References (35)

1. Barnes, M. J. (1981). “The Effects of Kurtosis, Skewness and Sample Size on the Type I Error Rates and Power of Tests of Homogeneity of Variance”. Ph.D. Thesis, Hofstra University, Hempstead, NY.
2. Bartlett, M. S. (1937). Properties of Sufficiency and Statistical Tests. Proceedings of the Royal Society 160, pp. 268-282.
3. 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, pp. 128-138.
4. Box, G. E. P (1953). “Nonnormality and Tests of Variance”. Biometrika.
5. Burr, I. W. and Foster, L. A. (1972). “A Test for Equality of Variances”. Technical Report 282, Purdue University.
6. 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, pp. 422-426.
7. 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, pp. 47-52.
8. Conover, M. E.; Johnson, W. J.; 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, pp. 351-361.
9. David, H. A. (1952). “Upper 5 and 1% Points of the Maximum F-Ratio”. Biometrika 39, pp. 422-424.
10. Dyer, D. and Keating, J. (1980). “On the Determination of Critical Values of Bartlett’s Test”. Journal of the American Statistical Association 75, pp. 313-319, 1980.
11. Efron, B. (1982). The Jackknife, the Bootstrap and Other Resampling Plans. Society for Applied and Industrial Mathematics, Philadelphia, 1982.
12. Fleishman, A. I. (1978). “A Method for Simulating Non-normal Distributions”. Psychometrika 43, pp. 521-532.
13. Foster, L. A. (1964). “Testing for Equality of Variances”. Ph.D. Thesis, Purdue University, Lafayette, Indiana.
14. Games, P. A. and Wolfgang, G. S. (1983). “A Review of Six Multifactor Tests for Homogeneity of Spread”. Computational Statistics and Data Analysis 1, pp. 41-52.
15. Numerical Algorithms Group (1991). The NAG Fortran Library Manual, Mark 15. NAG Ltd, Oxford, United Kingdom.
16. Hartley, H. O. (1940). “Testing the Homogeneity of a Set of Variances”. Biometrika 31, pp. 249-255.
17. Hartley, H. O. (1950). “The Maximum F-Ratio as a Short Cut Test of Heterogeneity of Variances”. Biometrika 37, pp. 308-312.
18. Izenman, A. J. (1976). “On the Extremal Quotient from a Gamma Sample”. Biometrika 63, pp. 185-190.
19. Layard, M. W. J. (1973). “Robust Large-Sample Tests for Homogeneity of Variance”. Journal of the American Statistical Association 68, pp. 195-198.
20. Levene, H. (1960). “Robust Tests for Equality of Variances”. In I. Olkin, editor, Contributions to Probability and Statistics, pp. 278-292. Stanford University Press.
21. Miller, R. G. (1968). “Jackknifing Variances”. Annals of Mathematical Statistics 39, pp. 567-582.
22. Nelson, L. S. (1983). “Exact Critical Values for the Analysis of Means”. Journal of Quality Technology 15, pp. 40-44.
23. Nelson, L. S. (1987). “Upper 10%, 5% and 1% Points of the Maximum F Ratio”. Journal of Quality Technology 19, pp. 165-167.
24. Nelson, P. R. (1981). “Numerical Evaluation of an Equicorrelated Multivariate Non-central t Distribution”. Communications in Statistics - Simulation and Computation BIO, pp. 41-50.
25. Nelson, P. R. (1982). “Exact Critical Values for the Analysis of Means”. Communications in Statistics - Theory and Methods All, pp. 699-709.
26. Nelson, P. R. (1985). “Power Curves for the Analysis of Means”. Technometrics 27, pp. 65-73.
27. Odeh, R. E. and Olds, E. G. (1959). “Notes on the Analysis of Variances of Logarithms of Variances”. Technical report, United States Air Force. WADC Technical Note 59-82, ASTIA Document No. AD211917.
28. Ott, E. R. (1967). “Analysis of Means - a Graphical Procedure”. Industrial Quality Control 24, pp. 101-109. (Reprinted in Journal of Quality Technology 15, pp. 10-18.)
29. Quesenberry, C. P. (1991). “SPC Q Charts for Start-Up Processes and Short or Long Runs”. Journal of Quality Technology 23, pp. 213-224.
30. Ramig, P. F. (1983). “Applications of the Analysis of Means”. Journal of Quality Technology 15, pp. 19-25.
31. Schelfe, H. (1959) The Analysis of Variance. John Wiley & Sons, New York.
32. Solomon, H. and Stephens, M. A. (1990). “Percentage Points for the Cochran Test for the Equality of Variances”. Journal of Quality Technology 22, pp. 46-56.
33. Tang, J. and Gupta, A. K. (1987). “On Testing the Homogeneity of Variances for Gaussian Models”. Journal of Statistical Computation and Simulation 27, pp. 155-173.
34. Tukey, J. W. (1962). “Data Analysis and Behavioral Science”. Unpublished monograph.
35. Wludyka, P. S. and Nelson, P. R. (1996). “An Analysis of Means Type Test for Variances from Normal Populations” Technometrics, to appear.