Testing homogeneity of variances with unequal sample sizes
Tóm tắt
Từ khóa
Tài liệu tham khảo
Akritas MG, Papadatos N (2004) Heteroscedastic one-way ANOVA and lack-of-fit tests. J Am Stat Assoc 99:368–382
Alexander RA, Govern DM (1994) A new and simpler approximation and ANOVA under variance heterogeneity. J Educ Stat 19:91–101
Bartlett MS (1937) Properties of sufficiency and statistical tests. Proc R Soc Lond A Mat A 160:268–282
Bathke A (2004) The ANOVA F test can still be used in some balanced designs with unequal variances and nonnormal data. J Stat Plan Inference 126:413–422
Boos DD, Brownie C (1989) Bootstrap methods for testing homogeneity of variances. Technometrics 31:69–82
Box GEP (1954) Some theorems on quadratic forms applied in the study of analysis of variance problems. I. Effect of inequality of variance in the one-way classification. Ann Math Stat 25:290–302
Brown MB, Forsythe AB (1974b) The small sample behavior of some statistics which test the equality of several means. Technometrics 16:129–132
Carroll RJ, Schneider H (1985) A note on Levene’s test for equality of variances. Stat Probab Lett 3:191–194
Charway H, Bailer AJ (2007) Testing multiple-group variance equality with randomization procedures. J Stat Comput Simul 77:797–803
Clinch JJ, Keselman HJ (1982) Parametric alternatives to the analysis of variance. J Educ Stat 7:207–214
Cochran WG (1954) Some methods for strengthening the common $$\chi ^{2}$$ -tests. Biometrics 10:417–451
Conover WJ, Johnson ME, Johnson MM (1981) A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics 23:351–361
De Beuckelaer A (1996) A closer examination on some parametric alternatives to the ANOVA F-test. Stat Pap 37:291–305
Dijkstra JB, Werter PS (1981) Testing the equality of several means when the population variances are unequal. Commun Stat B-Simul 10:557–569
Glass GV, Peckham PD, Sanders JR (1972) Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance. Rev Educ Res 42:237–288
Harwell MR, Rubinstein EN, Hayes WS, Olds CC (1992) Summarizing Monte Carlo results in methodological research: the one- and two-factor fixed effects ANOVA cases. J Educ Stat 17:315–339
Hui W, Gel YR, Gastwirth JL (2008) lawstat: an R package for law, public policy and biostatistics. J Stat Softw 28. http://www.jstatsoft.org/v28/i03/paper
Hines WGS, O’Hara Hines RJ (2000) Increased power with modified forms of the Levene (Med) test for heterogeneity of variance. Biometrics 56:451–454
Hsiung T, Olejnik S, Huberty CJ (1994) Comment on a Wilcox test statistic for comparing means when variances are unequal. J Educ Stat 19:111–118
Iachine I, Petersen HC, Kyvikc KO (2010) Robust tests for the equality of variances for clustered data. J Stat Comput Simul 80:365–377
James GS (1951) The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika 38:324–329
Johansen S (1980) The Welch-James approximation of the distribution of the residual sum of squares in weighted linear regression. Biometrika 67:85–92
Kenny DA, Judd CM (1986) Consequences of violating the independence assumption in analysis of variance. Psychol Bull 99:422–431
Keselman HJ, Rogan JC, Feir-Walsh BJ (1977) An evaluation of some nonparametric and parametric tests for location equality. Br J Math Stat Psychol 30:213–221
Keselman HJ, Wilcox RR, Algina J, Othman AR, Fradette K (2008) A comparative study of robust tests for spread: Asymmetric trimming strategies. Br J Math Stat Psychol 61:235–253
Keyes TK, Levy MS (1997) Analysis of Levene’s test under design imbalance. J Educ Behav Stat 22: 227–236
Layard MWJ (1973) Robust large-sample tests for homogeneity of variances. J Am Stat Assoc 68:195–198
Levene H, Levene H (1960) Robust tests for equality of variances. Essays in Honor of Harold Hotelling. In: Olkin I, Ghurye SG, Hoeffding W, Madow WG, Mann HB (eds) Contributions to probability and statistics. Stanford University Press, Palo Alto, p 292
Lim TS, Loh WY (1996) A comparison of tests of equality of variances. Comput Stat Data Anal 22:287–301
Lix LM, Keselman JC, Keselman HJ (1996) Consequences of assumption violations revisited, a quantitative review of alternatives to the one-way analysis of variance F test. Rev Educ Res 66:579–619
Loh WY (1987) Some modifications of Levene’s test of variance homogeneity. J Stat Comput Simul 28:213–226
Markowski CA, Markowski EP (1990) Conditions for the effectiveness of a preliminary test of variance. Am Stat 44:322–326
Mehrotra DV (1997) Improving the Brown-Forsythe solution to the generalizied Behrens-Fisher problem. Commun Stat-Simul 26:1139–1145
Neuhäuser M (2007) A comparative study of nonparametric two-sample tests after Levene’s transformation. J Stat Comput Simul 77:517–526
Neuhäuser M, Hothorn LA (2000) Location-scale and scale trend tests based on Levene’s transformation. Comput Stat Data Anal 33:189–200
Noguchi K, Gel YR (2010) Combination of Levene-type tests and a finite-intersection method for testing equality of variances against ordered alternatives. J Nonparametr Stat 22:897–913
O’Neill ME, Mathews K (2000) A weighted least squares approach to Levene’s test of homogeneity of variance. Aust Nz J Stat 42:81–100
Oshima TC, Algina J (1992) Type I error rates for James’s second-order test and Wilcox’s Hm test under heteroscedasticity and non-normality. Br J Math Stat Psychol 45:255–263
Parra-Frutos I (2009) The behaviour of the modified Levene’s test when data are not normally distributed. Comput Stat 24:671–693
Rogan JC, Keselman HJ (1977) Is the ANOVA F-test robust to variance heterogeneity when samples sizes are equal? Am Educ Res J 14:493–498
Rubin AS (1983) The use of weighted contrasts in analysis of models with heterogeneity of variance. P Bus Eco Stat Am Stat Assoc 347–352
Scheffé H (1959) The analysis of variance. Wiley, New York
Schneider PJ, Penfield DA (1997) Alexander and Govern’s approximation, providing an alternative to ANOVA under variance heterogeneity. J Exp Educ 65:271–286
Siegel S, Tukey JW (1960) A nonparametric sum of ranks procedure for relative spread in unpaired samples. J Am Stat Assoc 55:429–444 (corrections appear in vol. 56:1005)
Welch BL (1951) On the comparison of several mean values, an alternative approach. Biometrika 38: 330–336
Wilcox RR (1988) A new alternative to the ANOVA F and new results on James’ second-order method. Br J Math Stat Psychl 41:109–117
Wilcox RR (1989) Adjusting for unequal variances when comparing means in one-way and two-way fixed effects ANOVA models. J Educ Stat 14:269–278
Wilcox RR (1995) ANOVA: a paradigm for low power and misleading measures of effect size? Rev Educ Res 65:51–77
Wilcox RR (1997) A bootstrap modification of the Alexander-Govern ANOVA method, plus comments on comparing trimmed means. Educ Psychol Meas 57:655–665
Wilcox RR, Charlin VI, Thompson KL (1986) New Monte Carlo results on the robustness of the ANOVA F, W and F-statistics. Commun Stat Simul C 15:933–943