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Design and Analysis of Simulation Experiments Read chapter Read first chapter

2018 | OriginalPaper | Chapter

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

Authors : Dieter Rasch, Takuya Yanagida

Published in: Statistics and Simulation

Publisher: Springer International Publishing

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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.

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previous chapter Change Point in Panel Data with Small Fixed Panel Size: Ratio and Non-ratio Test Statistics
next chapter Performances of Poisson–Gamma Model for Patients’ Recruitment in Clinical Trials When There Are Pauses in Recruitment or When the Number of Centres is Small
Footnotes
1
Random variables are boldt print.
 
Literature
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Fleishman, A.J.: A method for simulating non-normal distributions. Psychometrika 43, 521–532 (1978)CrossRef
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Rasch, D., Guiard, V.: The robustness of parametric statistical methods. Psychol. Sci. 46, 175–208 (2004)
3.
Rasch, D., Pilz, J., Gebhardt, A., Verdooren, R.L.: Optimal Experimental Design with R. Chapman and Hall, Boca Raton (2011a)
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)MathSciNetCrossRef
5.
Rasch, D., Kubinger, K.D., Yanagida, T.: Statistics in Psychology using R and SPSS. Wiley, New York (2011c)CrossRef
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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)
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Wald, A.: Sequential analysis of statistical data. Theory Statistical Research Group Report 75, Columbia University (1943)
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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)
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Welch, B.L.: The generalization of Students problem when several different population variances are involved. Biometrika 34, 2835 (1947)MathSciNet
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Whitehead, J.: The Design and Analysis of Sequential Clinical Trials, Ellis Horwood, Chichester (1992)
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Metadata
Title
How Robust Is the Two-Sample Triangular Sequential T-Test Against Variance Heterogeneity?
Authors
Dieter Rasch
Takuya Yanagida
Copyright Year
2018
Book
Statistics and Simulation

Print ISBN: 978-3-319-76034-6

Electronic ISBN: 978-3-319-76035-3

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-76035-3_19

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