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A Two-Dimensional T-Distribution and a New Test with Flexible Type I Error Control

  • G. Landenna
  • D. Marasini
Part of the NATO Advanced study Institutes Series book series (ASIC, volume 79)

Summary

The usual t-test for a null hypothesis \(H_o = H_{o1} \wedge H_{o2} ,\),where \(H_{oj} :\mu j = \mu _j^ * ,j = 1,2,\) concerning the means of two normal populations with equal but unknown variance, does not account for the possibility that one of the component hypotheses may be principal, i.e., scientifically more relevant or important than the other. In this we use some properties of a bivariate t-distribution to construct a test which permits asymmetric treatment of the two component hypotheses. The proposed test is shown to be unbiased and consistent.

Key Words

hypothesis testing consistent tests unbiased tests t-tests t-distribution. 

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References

  1. Johnson, N.L., Kotz, S. (1972). Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.MATHGoogle Scholar
  2. Mudholkar, G.S., Subbaiah, P. (1980). A review of step-down procedures for multivariate analysis of variance. In Multivariate Statistical Analysis, R.P. Gupta, ed. North Holland, New York.Google Scholar
  3. Mudholkar, G.S., Subbaiah, P. (1981). Complete independence in the multivariate normal distribution. In Statistical Distributions in Scientific Work, C. Taillie, G.P. Patil, B. Baldessari, eds. Reidel, Dordrecht-Holland. Vol. 5, pp. 157–168.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • G. Landenna
    • 1
  • D. Marasini
    • 1
  1. 1.Instituto di Scienze Statistiche e Matematiche “Marcello Boldrini”Universita degli Studi di MilanoItaly

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