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A sequential triangular test of a correlation coefficient’s null-hypothesis: $$0 > \rho \le \rho _{0}$$ 0 > ρ ≤ ρ 0

Author

Listed:
  • Berthold Schneider
  • Dieter Rasch
  • Klaus Kubinger
  • Takuya Yanagida

Abstract

A sequential triangular test of the null-hypothesis $$\hbox {H}_{0}{:} 0>\rho \le \rho _{0}$$ H 0 : 0 > ρ ≤ ρ 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 $$\delta =\rho _1 -\rho _0$$ δ = ρ 1 - ρ 0 ) the average sample size of the sequential triangular test is smaller than the sample size of the pertinent fixed sample size test. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Berthold Schneider & Dieter Rasch & Klaus Kubinger & Takuya Yanagida, 2015. "A sequential triangular test of a correlation coefficient’s null-hypothesis: $$0 > \rho \le \rho _{0}$$ 0 > ρ ≤ ρ 0," Statistical Papers, Springer, vol. 56(3), pages 689-699, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:689-699
    DOI: 10.1007/s00362-014-0604-8
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