How Robust Is the Two-Sample Triangular Sequential T-Test Against Variance Heterogeneity?

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)

Abstract

Reference (Rasch, Kubinger and Moder (2011b). Stat. Pap. 52, 219–231.) [4] showed that in case that nothing is known about the two variances it is better to use the approximate Welch test instead of the two-sample t-test for comparing means of two continuous distributions with existing first two moments. An analogue approach for the triangular sequential t test is not possible because it is based on the first two derivatives of the underlying likelihood functions. Extensive simulations have been done and are reported in this chapter. It is shown that the two-sample triangular sequential t test in most interesting cases holds the type I and type II risks when variances are unequal.

Keywords

Comparing expectations t test Welch test Triangular sequential t-test Unequal variances 

References

  1. 1.
    Fleishman, A.J.: A method for simulating non-normal distributions. Psychometrika 43, 521–532 (1978)CrossRefGoogle Scholar
  2. 2.
    Rasch, D., Guiard, V.: The robustness of parametric statistical methods. Psychol. Sci. 46, 175–208 (2004)Google Scholar
  3. 3.
    Rasch, D., Pilz, J., Gebhardt, A., Verdooren, R.L.: Optimal Experimental Design with R. Chapman and Hall, Boca Raton (2011a)Google Scholar
  4. 4.
    Rasch, D., Kubinger, K.D., Moder, K.: The two-sample t test: pre-testing its assumptions does not pay off. Stat. Pap. 52, 219–231 (2011b)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Rasch, D., Kubinger, K.D., Yanagida, T.: Statistics in Psychology using R and SPSS. Wiley, New York (2011c)CrossRefGoogle Scholar
  6. 6.
    Rasch, D., Schott, D.: Mathematical Statistics, Wiley, Oxford (2018)CrossRefGoogle Scholar
  7. 7.
    Schneider, B.: An interactive computer program for design and monitoring of sequential clinical trials. In: Proceedings of the XVIth international biometric conference, pp. 237–250. Hamilton, New Zealand (1992)Google Scholar
  8. 8.
    Wald, A.: Sequential analysis of statistical data. Theory Statistical Research Group Report 75, Columbia University (1943)Google Scholar
  9. 9.
    Wald, A.: On cumulative sums of random variables. Ann. Math. Stat. 15, 283–296 (1944)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wald, A.: Sequential Analysis. Wiley, New York (1947), Whitehead, J.: The Design and Analysis of Sequential Clinical Trial, 2nd edn. Chichester, Ellis Horwood (1997), Whitehead, J.: The Design and Analysis of Sequential Clinical Trials, 2. rev. edn. Wiley, New York (1997)Google Scholar
  11. 11.
    Welch, B.L.: The generalization of Students problem when several different population variances are involved. Biometrika 34, 2835 (1947)MathSciNetGoogle Scholar
  12. 12.
    Whitehead, J.: The Design and Analysis of Sequential Clinical Trials, Ellis Horwood, Chichester (1992)Google Scholar
  13. 13.
    Yanagida, T.: Seqtest: sequential triangular test. R package version 0.1-0 (2016). http://CRAN.R-project.org/package=seqtest

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Natural Resources and Life SciencesViennaAustria
  2. 2.University of Applied Sciences Upper AustriaViennaAustria

Personalised recommendations