The following are the reference sources from the posts on the homogeneity of variances being presented in the coming weeks.

1. Alexander, R. A. and Govern, D. M. (1994) A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19, 91–101.

2. Andrews, D. F. (1971) A note on the selection of data transformation. Biometrika, 58, 249–254.

3. Andrews, D. F., Gnanadesikan, R. and Warner, J. L. (1971) Transformations of multivariate data. Biometrics, 27, 825–840.

4. Anscombe, F. J. (1948) The transformation of poisson, binomial and negative binomial data. Biometrika, 35, 246–254.

5. Atkinson, A. C. (1985) Plots, Transformations and regression. Oxford University Press, Oxford.

6. Bartlett, M. S. (1937) Properties of suﬃciency and statistical tests. Proceedings of the Royal Society of London, A, 160, 268–282.

7. Bartlett, M. S. and Kendall, D. G. (1946) The statistical analysis of variance-heterogeneity and the logarithmic transformation. J. Roy. Statist. Soc., Suppl. 8, 128–138.

8. Beauchamp, J. J. and Robson, D. S. (1986) Transformation considerations in discriminant analysis. Communication in Statistics–Simulation and Computation, 15(1), 147–179.

9. Bickel, P. J. (1965) On some robust estimates of location. Ann. Math. Statist., 36,847–858.

10. Bickel, P. J., and Doksum, K. A. (1981) An analysis of transformations revisited. J. American Statistical. Assoc., 76, 296–311.

11. Bishop, T. A. and Dudewicz, E. J. (1978) Exact analysis of variance with unequal variances: Test procedures and tables. Technometrics, 20, 419–430.

12. Boneau, C. A. (1960) The eﬀects of violations of assumptions underlying the t-test. Psychological Bulletin, 57, 49–64.

13. Boos, D. D. and Brownie, C. (1989) Bootstrap methods for testing homogeneity of variances. Technometrics, 31(1), 69–82.

14. Box, G. E. P. (1953) Non-normality and tests on variances. Biometrika, 40, 318–335.

15. Box, G. E. P. (1954) Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Eﬀect of inequality of variance in one-way model. Ann. Math. Statist., 25, 290–302.

16. Box, G. P. E. and Andersen, S. L. (1955) Permutation theory in the derivation of robust criteria and the study of departures from assumptions. J. Roy. Statist. Soc., Ser. B, 17, 1–34.

17. Box, G. E. P., and Cox, D. R. (1964) An analysis of transformations (with discussion) J. Roy. Statist. Soc., 26, 211–246.

18. Brown, M. B. and Forsythe, A. B. (1974) Robust tests for the equality of variances. J. American Statistical. Assoc., 69, 364–367.

19. Brown, M. B. and Forsythe, A. B. (1974a) The small sample behaviour of some statistics which test the equality of several means. Technometrics, 16, 129–132.

20. Bryk, A. S. and Raudenbush, S. J.(1987) Heterogeneity of variance in experimental studies: A challenge to conventional interpretations. Psychological Bulletin, 104, 396–404.

21. Camdeviren, H. and Mendes, M. (2005) A simulation study for type III error rates of some variance homogeneity tests. Pak. J. Statist., 21(2), 223–234.

22. Carroll, R. J. (1980) A robust method for testing transformation to achieve approximate normality. J. Roy. Statist. Soc., Series B, 42, 71–78.

23. Carroll, R. J. (1982a) Tests for regression parameters in power transformation models Scand. J. Statist., 9, 217–222.

24. Carroll, R. J., and Ruppert, D. (1984) Power transformations when ﬁtting theoretical models to data. J. American Statistical. Assoc., 79, 321–328.

25. Carroll, R. J. and Ruppert, D. (1987) Diagnostics and robust estimation when transforming the regression model and the response. Technometrics, 28, 287–299.

26. Cassella, G & Berger, R (2002), Statistical Interference, 2^{nd} Ed. Duxbury Press

27. Chang, H. S. (1977a) A computer program for Box-Cox transformation and estimation technique. Econometrica, 45, 1741.

28. Chen, H. (1995) Tests following transformations. Ann. Statist., 23, 1587–1593.

29. Chen, H. and Loh, W. Y. (1992) Bounds on ARE’s of tests following Box-Cox transformations. Ann. Statist., 20, 1485–1500.

30. Chen, S.-Y. and Chen, H. J. (1998) Single-stage analysis of variance under heteroscedasticity. Communication in Statistics–Simulation and Computation, 27, 641–666.

31. Chohen, A., and Sackrowitz, H. B. (1987) An approach to inference following model selection with applications to transformation-based and adaptive inference. J. Amer. Statist. Assoc., 82, 1123–1130.

32. Cochran, W. G. (1941) The distribution of the largest of a set of estimated variance as a fraction of their total. Ann. Eug., 11, 47–52.

33. Cochran, W. G. and Cox, G. M. (1957) Experimental design. New York: John Willey and Sons Inc.

34. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

35. Conover, W. J., Johnson, M. E. and Johnsons, 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.

36. Crowder, M. J. (2000) Tests for a family of survival models based on extremes. In Recent Advances in Reliability Theory, N. Limnios and M. Nikulin, Eds., pp. 307–321. Birkhauser, Boston.

37. Dunn, J. E. and Tubbs, J. D. (1980) VARSTAB: A procedure for determining homoscedastic transformations of multivariate normal populations. Communications in Statistics–Simulation and Computation B, 9(6), 589–598.

38. Draper, N. R. and Cox, D. R. (1969) On distributions and their transformations to normality. J. Roy. Statist. Soc., Series B, 31, 472–476.

39. Draper, N. R. and Hunter, W. G. (1969) Transformations: Some examples revisited. Technometrics, 11, 23–40.

40. Efron, B. (1982) Transformation theory: how normal is a family of distributions? Ann. Statist., 10, 323-339.

41. Ehri, L. C., Nunes, S. R., Stahl, S. A. & Willows, D. M. (2001). Systematic phonics instruction helps students learn to read: Evidence from the National Reading Panel’s meta-analysis. Review of Educational Research, 71(3), 393-447.

42. Fellers, R. R. (1972) The eﬀects of non-normality and sample size on the robustness of tests of homogeneity of variance. Paper presented at the meeting of the Northeast Educational Research Association.

43. Fisher, R. A. and Mather, K. (1943) The inheritance of style length “Lythrum Salicano”. Ann. Eug., 12, 1–23.

44. Fleming, T. R., O’Fallon, J. R., O’Brien, P. C. and Harrington, D. P. (1980) Modiﬁed Kolmogorov-Smirnov test procedures with application to arbitrary right censored data. Biometrics, 36, 607–626.

45. Freiman, J. A., Chalmers, T. C., Smith, H.. & Kuebler, R. R. (1978). The importance of beta, the type II error and sample size in the design and interpretation of the randomized control trial. The New England Journal of Medicine, 299(13), 690-694.

46. Games, P., Winkler, H. and Probert, D. (1972) Robust tests for homogeneity of variance. Educational and Psychological Measurement. 32, 887–909.

47. Gartside, P. S. (1972) A study of methods for comparing several variances. J. American Statistical. Assoc., 67, 342–346.

48. Glass, G. V., Peckham, P. D. and Sanders, J. R. (1972) Consequences of failure to meet assumptions underlying analysis of variance and covariance. Review of Educational Research, 42, 237–288.

49. Goodman, S. N. & Berlin, J. (1994). The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Annals of Internal Medicine, 121, 201-6.

50. Graybill, F. A. (1976) The Theory and Applications of the Linear Model. Duxbury Press, London.

51. Gupta, A. K. and Rathie, A. K. (1983) Distribution of the likelihood ratio criterion for the problem of k samples. Metron, 40, 147–156.

52. Gupta, A. K., Harrar, S. and Pardo, L. (2004) On testing homogeneity of variances for non-normal models using entropy. Department of Mathematics and Statistics, Bowling Green State University, Technical Report, No. 04-11.

53. Hair, Joseph F., Jr; Anderson, Rolph E.; Tatham, Ronald L.; and Black, William C. 1998.* Multivariate Data Analysis*, Fifth Edition. Englewood Cliffs, New Jersey: Prentice Hall.

54. Han, A. K. (1987) A non-parametric analysis of transformation. Journal of Econometrics, 35, 191–209.

55. Hartley, H. O. (1940) Testing the homogeneity of a set of variances. Biometrika, 31, 249–255.

56. Hartung, J. & Argac, D. (2001), Testing for homogeneity in combining two-armed trials with normally distributed responses. Sankhya; the Indian Journal of Statistics Vol. B. Pp 298-310

57. Hartley H. O. (1950) The maximum F -ratio as a short cut test for heterogeneity of variances. Biometrika, 37, 308–312.

58. Hayes, J. P. & Steidl, R. J. (1997). Statistical power analysis and amphibian population trends. Conservation Biology, 11, 273-275.

59. Hedges, L. V. & Pigott, T. D. (2001). The power of statistical tests in meta-analysis. Psychological Methods, 6(3), 203-217.

60. Hedges, L. V. & Pigott, T. D. (2004). The power of statistical tests for moderators in meta-analysis. Psychological Methods, 9(4), 424-445.

61. Hernandez, F., and Johnson, R. A. (1980) The large-sample behaviour of transformations to normality. J. American Statistical. Assoc., 75, 855–861.

62. Hinkley, D. V. (1975) On Power transformations to symmetry. Biometrika, 62, 101–111.

63. Hinkley, D. V. (1985) Transformation diagnostics for linear models. Biometrika, 72, 487–496.

64. Hotelling, H. (1953) New Light on the correlation coeﬃcient and its transform. J. Royal Statistical Soc., Series B, 15, 193–232.

65. Hoyle, M. H. (1973) Transformations: An introduction and a bibliography. The International Statistical Review, 41, 203–223.

66. Hsiung, T. C. and Olejnik, S. (1996) Type I error rates and statistical power for James second-order test and the univariate F test in two-way ANOVA models under heteroscedasticity and/or non-normality. Journal of Experimental Education, 65, 57–71.

67. Huang, C L., Moon, L. C. and Chang, H. S. (1978) A computer program using the Box-Cox transformation technique for the speciﬁcation of functional form. The American Statistician, 32, 144.

68. Huber, P. J. (1972) Robust statistics: A review. Ann. Math. Statist., 43, 1041–1067.

69. JMP Software (2007) JMP Statistics and Graphics Guide, SAS Institute

70. John, J. A., and Draper, N. R. (1980) An alternative family of power transformations. Applied Statistics, 29, 190–197.

71. Kendall, M. G. and Stuart, A. (1966) Advanced Theory of Statistics, 2, Griﬃn, London.

72. Keselman, H. J., Carrier, K. C. and Lix, L. M. (1995) Robust and powerful orthogonal analysis. Psychometrika, 60, 395–418.

73. Keselman, H. J., Wilcox, R. R., Othman, A. R. and Fradette, K. (2002) Trimming, transforming statistics and bootstrapping: Circumventing the biasing eﬀects of heteroscedasticity and non-normality. Journal of Modern Applied Statistical Methods, 1(2), 288–309.

74. Lawless, J. F. (2000) Introduction to two classics in reliability theory. Technometrics, 42, 5–6.

75. Lawless, J. F. (2003) Statistical Models and Methods for Lifetime Data. Second Edition, Wiley Series in Probability and Statistics.

76. Layard, M. W. J. (1973) Robust large sample tests for homogeneity of variances. J. American Statistical. Assoc., 68, 195–198.

77. Levene, H. (1960) Robust tests for equality of variances. Contributions to probability and statistics. edited by I. Olkin. Stanford University Press. Palo Alto. CA., 278–292.

78. Levy, K. J. (1975a) An empirical comparison of several multiple range tests for variances. J. American Statistical. Assoc., 70, 180–183.

79. Levy K. J. (1975b) An empirical comparison of Z-variance and Box-Scheﬀ´e tests for homogeneity of variance. Psychometrika, 40, 519–524.

80. Lim, T. S. and Loh, W. Y. (1996) A comparison of tests of equality of variances. Computational Statistics and Data Analysis, 22, 287–301.

81. Loh, W. Y. (1987) Some modiﬁcations of Levene’s test of variance homogeneity. Journal of Computational Statistics and Simulation, 28, 213–226.

82. Luh, W. M. and Guo, J. H. (2000) Approximate transformation trimmed mean methods to the test of simple linear regression slope equality. Journal of Applied Statistics, 27, 843–858.

83. Manly, B. F. (1976) Exponential data transformation. The Statistician, 25, 37–42.

84. Mendes, M. (2003) The comparison of Levene, Bartlett, Neymann-Pearson and Bartlett 2 tests in terms of actual type I error rates. Journal of Agriculture Sciences, 9(2), 143–146.

85. Mehrota, D. V. (1997), Improving the Brown-Forsythe solution to generalised Behrens-Fisher Problem, Communications in statistics, Series B 26: 1139-1145

86. Miller, R. G. Jr. (1968) Jackkniﬁng variances. Ann. Math. Statist., 39, 567–582.

87. Miller, R. G. Jr. (1986) Beyond ANOVA, Basics of Applied Statistics. Wiley, New York.

88. Murphy, K. R. & Myors, B. (2004). Statistical power analysis (2nd ed.). Mahwah, NJ: Lawrence Erlbaum.

89. Nelson, L. S. (2000) Comparing two variances from normal populations. J. Qual. Technol., 32, 79–80.

90. O’Brien, R. G. (1978) Robust techniques for testing heterogeneity of variance eﬀects in factorial designs. Psychometrika, 43, 327–342.

91. Oshima, T. C. and Algina, J. (1992a) Type I error rates James’s second-order test and Wilcox’s Hmtest under heteroscedasticity and non-normality. British Journal of Mathematical and Statistical Psychology, 45, 255–263.

92. Oshima, T. C and Algina, J. (1992b) A SAS program for testing the hypothesis of equal means under heteroscedasticity: James’s second-order test. Educational and Psychological Measurement, 52, 117–118.

93. Oshima, T. C., Algina, R. A. and Lin, W. Y. (1994) Type I error rates for Welch’s test and James’s second-order test under non-normality and inequality of variance when there are two groups. Journal of Educational and Behavioural Statistics, 19, 275–291.

94. Peechawanich, V. (1992), Probability theory and applications. Prakypueg, Bangkok

95. Phil, E. (1999), Checking Assumptions, Education 230 B/C Linear Statistical Models

96. Proschan, F. (1963) Theoretical explanation of observed decreasing failure rate. Technometrics, 5, 375–383.

97. Rayner, J.C.W. (1997) The Asymptotically Optimal Tests, The Statistician, Vol. 46, No. 3, (1997), pp. 337-346

98. Rayner, J.C.W. and Best, D.J. (1989) Smooth Tests of Goodness of Fit, New York, Oxford University Press.

99. Reed, J. M. & Blaustein, A. R. (1995). Assessment of “nondeclining” amphibian populations using power analysis. Conservation Biology, 9, 1299-1300.

100. Rogan, J. C., and Keselman, H. J. (1977) Is the ANOVA F -test robust to variance heterogeneity when sample sizes are equal? An investigation via a co-eﬃcient of variation. American Educational Research Journal, 14, 493–498.

101. Sattertwaite, F. (1941), Synthesis of Variance, Psychometrica, Vol 6, Pp 309-316.

102. Scheﬀ´e, H. (1959) The Analysis of Variance. Wiley, New York.

103. Schneider, P. J. and Penﬁeld, D. A. (1997) Alexnader and Govern’s approximation: Providing an alternative to ANOVA under variance heterogeneity. Journal of Experimental Education, 65, 271–286.

104. Serﬂing, R. J. (2002) Approximate Theorem of Mathematical Statistics. John Wiley & Sons, Inc.

105. Sharma, S. C. (1991) A new jacknife test for homogeneity of variances. Communications in Statistics-Simulation and Computation, 20(2-3), 479–495.

106. Snee, R. D. (1986) An alternative approach to ﬁtting models when re-expression of the response is useful. J. Qual. Technol. 18, 211–225.

107. Sokal, R. R. and Rholf, F. J. (1995) Biometry, New York: W.H. Freeman and Company.

108. Solomon, P. J. (1985) Transformation for components of variance and covariance. Biometrika, 72, 233–239.

109. Speed, T. P. (1987) Rejoinder: What is an Analysis of Variance? The Annals of Statistics, Vol. 15, No. 3 (Sep., 1987), pp. 937-941

110. Stigler, S. M. (1973) The asymptotic distribution of the trimmed mean. Ann. Statist., 1, 472–477.

111. Tang, J. and Gupta, A. K. (1987) On testing homogeneity of variances for Gaussian models. J. Statist. Comput. Simul., 27, 155–173.

112. Taylor, M. J. G. (1985a) Power transformation to symmetry. Biometrika, 72, 145-152.

113. Taylor, M. J. G. (1985b) Measure of location of skew distributions obtained through Box-Cox transformations. J. American Statistical. Assoc., 80, 427–432.

114. Taylor, D. J. & Muller, K. E. (1995). Computing confidence bounds for power and sample size of the general linear model. The American Statistician, 49(1), 43-47.

115. Thoeni, H. (1967) Transformation of variables used in the analysis of experimental and observational data: a review. Technical Report No. 7, Iowa State University, Ames.

116. Thomas, L. (1997). Retrospective power analysis. Conservation Biology, 11(1), 276-280.

117. Tippett, L. H. C. (1934) Statistical methods in textile research. Part 2. Uses of the binomial and poisson distributions. Shirley Inst. Mem., 13, 35–72.

118. Tukey, J. W. (1957) The comparative anatomy of transformations. Ann. Math. Statist., 28, 602–632.

119. Weerahandi, S. (1995) ANOVA under unequal error variances. Biometrics, 51, 589–599.

120. Welch, B. L. (1951) On the comparison of several mean values: An alternative approach. Biometrika, 38, 330–336.

121. Wei-ming, L. (1999) Developing trimmed mean test statistics for two-way ﬁxed effects ANOVA models under variance heterogeneity and non-normality. The Journal of Experimental Education, 67(3), 243–264.

122. Wilcox, R. R., Charlin, V. L. and Thomson, K. L. (1986) New Monte Carlo results on the robustness of the ANOVA F , W and F ∗ statistics. J. Statist. Comput. Simul., 15, 33–43.

123. 114. Wilcox, R. R. (1988) A new alternative to the ANOVA F and new results on James’s second-order method. British Journal of Mathematical and Statistical Psychology, 41, 109–117.

124. Wilcox, R. R. (1989) Adjusting for unequal variances when comparing means in one-way and two-way eﬀects ANOVA models. Journal of Educational Statistics, 14, 269–278.

125. Wilcox, R. R. (1995) ANOVA: A paradigm for low power and misleading measures of eﬀect size. Review of Educational Research, 65, 51–77.

126. Wilcox, R. R. (1997) A bootstrap modiﬁcation of the Alexander-Govern ANOVA method, plus comments on comparing trimmed means. Educational and Psychological Measurement, 57(4), 655-665.

127. Wilcox, R. R. (2002) Comparing variances of two independent groups. British Journal of Mathematical and Statistical Psychology, 55, 169–175.

128. Wilk, M. B., Gnanadesikan, R. and Huyett, M. J. (1962) Estimation of parameters of the gamma distribution using order statistics. Biometrika, 49, 525–545.

129. Winer, B. J., Brown, D. R. and Michael, K. M. (1991) Statistical Principles in Experimental Design. New York: McGraw-Hill Book Company.

130. Zar, J. H. (1999) Biostatistical Analysis. New Jersey: Prentice–Hall Inc. Simon and Schuster/ A Viacom Company.

131. Zumbo, B. D. & Hubley, A. M. (1998). A note on misconceptions concerning prospective and retrospective power. The Statistician, 47(2), 385-388.

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