Determination of the Optimal Size of Subsamples for Testing a Correlation Coefficient by a Sequential Triangular Test

  • Dieter Rasch
  • Takuya Yanagida
  • Klaus D. Kubinger
  • Berthold Schneider
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)


Schneider, Rasch, Kubinger and Yanagida [8] (Schneider, Rasch, Kubinger and Yanagida [8]. Stat. Pap. 56, 689 600) suggested a sequential triangular test for testing a correlation coefficient (see also Rasch, Yanagida, Kubinger, and Schneider [6]). In contrast to other sequential (triangular) tests, it is not possible to decide after each additional sampled research unit whether
  1. (a)

    the null-hypothesis is to accept or

  2. (b)

    to reject or

  3. (c)

    to sample further units.


For the calculation of the correlation coefficient and to use Fisher’s transformation, step-by-step \(k \ge 4\) units are needed at once. In the present chapter, we improve the test proposed by Rasch, Yanagida, Kubinger and Schneider (2014) by determining which number k of subsampled research units is minimal (optimal), in order to hold the type-I-risk, given a specific type-II-risk and a specific effect size \(\delta =\rho _{1}-\rho _{0}\). Selected results are presented. For parameters not included irrespective tables, the reader may use a R package called seqtest for own simulations.


Optimal experimental design Minimum sample size Simulation Sequential analysis 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Dieter Rasch
    • 1
  • Takuya Yanagida
    • 2
  • Klaus D. Kubinger
    • 3
  • Berthold Schneider
    • 4
  1. 1.University of Natural Resources and Life SciencesViennaAustria
  2. 2.University of ViennaViennaAustria
  3. 3.Division of Psychological Assessment and Applied Psychometrics, Faculty of PsychologyUniversity of ViennaViennaAustria
  4. 4.Institute for BiometryHannover Medical SchoolHannoverGermany

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