• Akritas, M. G., & Papadatos, N. (2004). Heteroscedastic one-way ANOVA and lack-of-fit tests. Journal of the American Statistical Association, 99, 368382.
  • Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation and ANOVA under variance heterogeneity. Journal of Educational Statistics, 19, 91101.
  • Bathke, A. (2004). The ANOVA F test can still be used in some balanced designs with unequal variances and nonnormal data. Journal of Statistical Planning and Inference, 126, 413422.
  • Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144152.
    Direct Link:
  • Brown, M. B., & Forsythe, A. B. (1974). The small sample behavior of some statistics which test the equality of several means. Technometrics, 16, 129132.
  • Chang, C. H., Lin, J. J., & Pal, N. (2011). Testing the equality of several gamma means: a parametric bootstrap method with applications. Computational Statistics, 26, 5576.
  • Chang, C. H., Pal, N., Lim, W. K., & Lin, J. J. (2010). Comparing several population means: a parametric bootstrap method, and its comparison with usual ANOVA F test as well as ANOM. Computational Statistics, 25, 7195.
  • Cribbie, R. A., Fiksenbaum, L., Keselman, H. J., & Wilcox, R. R. (2012). Effect of non-normality on test statistics for one-way independent groups designs. British Journal of Mathematical and Statistical Psychology, 65, 5673.
  • De Beuckelaer, A. (1996). A closer examination on some parametric alternatives to the ANOVA F-test. Statistical Papers, 37, 291305.
  • Dijkstra, J. B., & Werter, P. S. (1981). Testing the equality of several means when the population variances are unequal. Communications in Statistics – Simulation and Computation, 10, 557569.
  • Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York, NY: Chapman & Hall.
  • Fagerland, M. W., & Sandvik, L. (2009). The Wilcoxon–Mann–Whitney test under scrutiny. Statistics in Medicine, 28, 14871497.
  • Gastwirth, J. L., Gel, Y. R., & Miao, W. (2009). The impact of Levene's test of equality of variances on statistical theory and practice. Statistical Science, 24, 343360.
  • Glass, G. V., Peckham, P. D., & Sanders, J. R. (1972). Consequences of failure to meet assumptions underlying the fixed effects analyses of variance and covariance. Review of Educational Research, 42, 237288.
  • Harwell, M. R., Rubinstein, E. N., Hayes, W. S., & Olds, C. C. (1992). Summarizing Monte Carlo results in methodological research: The one- and two-factor fixed effects ANOVA cases. Journal of Educational Statistics, 17, 315339.
  • Hoaglin, D. C. (1985). Summarizing shape numerically: The g- and h-distributions. In D. C. Hoaglin, F. Mosteller & J. W. Tukey (Eds.), Exploring data tables, trends, and shapes (pp. 461513). New York, NY: Wiley.
  • James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324329.
  • Kenny, D. A., & Judd, C. M. (1986). Consequences of violating the independence assumption in analysis of variance. Psychological Bulletin, 99, 422431.
  • Keselman, H. J., Cribbie, R. A., & Holland, B. (2002). Controlling the rate of Type I error over a large set of statistical tests. British Journal of Mathematical and Statistical Psychology, 55, 2739.
  • Keselman, H. J., Huberty, C., Lix, L. M., Olejnik, S., Cribbie, R. A., Donahue, B., Kowalchuk, R. K., Lowman, L. L., Petoskey, M. D., & Keselman, J. C. (1998). Statistical practices of educational researchers: An analysis of their ANOVA, MANOVA, and ANCOVA analyses. Review of Educational Research, 68, 350386.
  • Keselman, H. J., Rogan, J. C., & Feir-Walsh, B. J. (1977). An evaluation of some non-parametric and parametric tests for location equality. British Journal of Mathematical and Statistical Psychology, 30, 213221.
    Direct Link:
  • Krishnamoortthy, K., Lu, F., & Mathew, T. (2007). A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models. Computational Statistics & Data Analysis, 51, 57375742.
  • Krutchkoff, R. G. (1988). One-way fixed effects analysis of variance when the error variances may be unequal. Journal of Statistical Computation and Simulation, 30, 259271.
  • Li, X., Wang, J., & Liang, H. (2011). Comparison of several means: A fiducial based approach. Computational Statistics and Data Analysis, 55, 19932002.
  • Lix, L. M., & Keselman, H. J. (1998). To trim or not to trim: Tests of location equality under heteroscedasicity and nonnormality. Educational and Psychological Measurement, 58, 409429.
  • Lix, L. M., Keselman, J. C., & Keselman, H. J. (1996). Consequences of assumption violations revisited: A quantitative review of alternatives to the one-way analysis of variance F test. Review of Educational Research, 66, 579619.
  • Luh, W. M. & Guo, J.H. (1999). A powerful transformation trimmed mean method for one-way fixed effects ANOVA model under non-normality and inequality of variances. British Journal of Mathematical and Statistical Psychology, 52, 303320.
  • Mehrotra, D. V. (1997). Improving the Brown-Forsythe solution to the generalizied Behrens-Fisher problem. Communications in Statistics – Simulation and Computation, 26, 11391145.
  • Oshima, T. C., & Algina, J. (1992). Type I error rates for James's second-order test and Wilcox's Hm test under heteroscedasticity and non-normality. British Journal of Mathematical and Statistical Psychology, 45, 255263.
    Direct Link:
  • Othman, A. R., Keselman, H. J., Padmanabhan, A. R., Wilcox, R. R., Algina, J., & Fradette, K. (2004). Comparing measures of the ‘typical’ score across treatment groups. British Journal of Mathematical and Statistical Psychology, 57, 215234.
  • Pratt, J. W. (1964). Robustness of some procedures for the two-sample location problem. Journal of the American Statistical Association, 59, 665680.
  • Reiczigel, J., Zakariás, I., & Rózsa, L. (2005). A bootstrap test of stochastic equality of two populations. American Statistician, 59, 16.
  • Rogan, J. C., & Keselman, H. J. (1977). Is the ANOVA F-test robust to variance heterogeneity when samples sizes are equal? American Educational Research Journal, 14, 493498.
  • Scheffé, H. (1959). The analysis of variance. New York, NY: Wiley.
  • Skovlund, E., & Fenstad, G. U. (2001). Should we always choose a nonparametric test when comparing two apparently nonnormal distributions? Journal of Clinical Epidemiology, 54, 8692.
  • Syed Yahaya, S. S., Othman, A. R., & Keselman, H. J. (2006). Comparing the ‘typical score’ across independent groups based on different criteria for trimming. Metodološki Zvezki, 3, 4962.
  • Vargha, A., & Delaney, H. D. (1998). The Kruskal-Wallis test and stochastic homogeneity. Journal of Educational and Behavioral Statistics, 23, 170192.
  • Weerahandi, S. (1995). ANOVA under unequal error variances. Biometrics, 51, 589599.
  • Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330336.
  • Wilcox, R. R. (1990). Comparing the means of two independent groups. Biometrics Journal, 32, 771780.
  • Wilcox, R. R., Keselman, H. J., & Kowalchuk, R. K. (1998). Can tests for treatment group equality be improved? The bootstrap and trimmed means conjecture. British Journal of Mathematical and Statistical Psychology, 51, 123134.
    Direct Link: