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
-
(a)
the null-hypothesis is to accept or
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(b)
to reject or
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(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.
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Rasch, D., Yanagida, T., Kubinger, K.D., Schneider, B. (2018). Determination of the Optimal Size of Subsamples for Testing a Correlation Coefficient by a Sequential Triangular Test. In: Pilz, J., Rasch, D., Melas, V., Moder, K. (eds) Statistics and Simulation. IWS 2015. Springer Proceedings in Mathematics & Statistics, vol 231. Springer, Cham. https://doi.org/10.1007/978-3-319-76035-3_22
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