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Statistical Papers

, Volume 56, Issue 3, pp 689–699 | Cite as

A sequential triangular test of a correlation coefficient’s null-hypothesis: \(0 < \rho \le \rho _{0}\)

  • Berthold Schneider
  • Dieter RaschEmail author
  • Klaus D. Kubinger
  • Takuya Yanagida
Regular Article

Abstract

A sequential triangular test of the null-hypothesis \(\hbox {H}_{0}{:} 0<\rho \le \rho _{0}\) is derived, given a two-dimensional vector of normal random variables (x, y). The test is based on an approximate normally distributed test statistic by Fisher’s transformation of the sample correlation coefficient. We show via simulation that for certain requirements of precision (type-I-, type-II-risk, and a practical relevant effect \(\delta =\rho _1 -\rho _0\)) the average sample size of the sequential triangular test is smaller than the sample size of the pertinent fixed sample size test.

Keywords

Correlation coefficient Test of hypothesis Simulation  Triangular sequential test 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Berthold Schneider
    • 1
  • Dieter Rasch
    • 2
    Email author
  • Klaus D. Kubinger
    • 3
  • Takuya Yanagida
    • 4
  1. 1.Institute for BiometryHannover Medical SchoolHannoverGermany
  2. 2.Department of Landscape, Spatial and Infrastructure SciencesUniversity of Natural Resources and Life SciencesViennaAustria
  3. 3.Division of Psychological Assessment and Applied Psychometrics, Faculty of PsychologyUniversity of ViennaViennaAustria
  4. 4.School of Applied Health and Social SciencesUniversity of Applied Sciences Upper AustriaViennaAustria

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