IWS 2015: Statistics and Simulation pp 315-328

# 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)

## Abstract

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.

## Keywords

Optimal experimental design Minimum sample size Simulation Sequential analysis

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© 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