Heteroscedasticity irrelevance when testing means difference

• Pablo Flores M. ^[2] ; Jordi Ocaña ^[1]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  2. [2] Escuela Superior Politécnica de Chimborazo
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 42, Nº. 1, 2018, págs. 59-72
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Heteroscedasticity produces a lack of type I error control in Student’s t test for difference between means. Pretesting for it (e.g., by means of Levene’s test) should be avoided as this also induces type I error. These pretests are inadequate for their objective: not rejecting the null hypotheses is not a proof of homoscedasticity; and rejecting it may simply suggest an irrelevant heteroscedasticity. We propose a method to establish irrelevance limits for the ratio of variances. In conjunction with a test for dispersion equivalence, this appears to be a more affordable pretesting strategy.

• Referencias bibliográficas
  • Altman, D.G. and J.M. Bland (1995). Statistics notes: Absence of evidence is not evidence of absence. BMJ, 311, 485.
  • Box, G.E. (1979). Robustness in the strategy of scientific model building. Robustness in Statistics, 1, 201–236.
  • Cochran, W.G. (1942). The χ2 correction for continuity. Iowa State College Journal of Science, 16, 421– 436.
  • Hsu, P. (1938). Contribution to the theory of “student’s” t-test as applied to the problem of two samples. Statistical Research Memoirs.
  • Ocaña, J. and E. Vegas (1995). Variance reduction for bernoulli response variables in simulation. Computational Statistics and Data Analysis,...
  • Overall, J.E., R.S. Atlas and J.M. Gibson (1995). Tests that are robust against variance heterogeneity in k×2 designs with unequal cell frequencies....
  • Rasch, D. and V. Guiard (2004). The robustness of parametric statistical methods. Psychology Science, 46, 175–208.
  • Rasch, D., K.D. Kubinger and K. Moder (2011). The two-sample t test: pre-testing its assumptions does not pay off. Statistical Papers, 52,...
  • Scheffé, H. (1970). Practical solutions of the behrens-fisher problem. Journal of the American Statistical Association, 65, 1501–1508.
  • Vegas, E. and J. Ocaña (1992). Variance reduction for bernouilli response variables. In Computational Statistics, pp. 103–107. Springer.
  • Welch, B. (1951). On the comparison of several mean values: an alternative approach. Biometrika, 38, 330–336.
  • Welch, B.L. (1947). The generalization of student’s problem when several different population variances are involved. Biometrika, 34, 28–35.
  • Wellek, S. (2010). Testing Statistical Hypotheses of Equivalence and Noninferiority. USA: CRC Press.
  • Zimmerman, D.W. (2004). A note on preliminary tests of equality of variances. British Journal of Mathematical and Statistical Psychology,...