## Abstract

There is a big lack of knowledge as concerns a test of the null hypothesis H_{0}: 0 < ρ ≤ ρ_{0}. Usually a test applies by some z-statistic according to Fisher (1921), which is approximately normally distributed. However, there is no evidence of whether the approximation is actually good enough—that is, it is of interest how the factual distribution of the respective test statistic holds the type-I risk—and which type-II risk results. Because this question cannot be answered theoretically at present, we try a simulation study in order to gain respective knowledge. For this, we even investigate the case of variables that are not (at all) normally distributed. Moreover, we consider variables not normally distributed but test the simple case of the exact t-test of H_{0}: ρ = ρ_{0}. The results show, in particular, that the test tracing back to R. A. Fisher does not hold the type-I risk if severe nonnormality of the variables’ distributions is given.

Original language | English |
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Pages (from-to) | 393-401 |

Number of pages | 9 |

Journal | Journal of Statistical Theory and Practice |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 3 Jul 2017 |

## Keywords

- Fleishman system of distributions
- Triangular sequential test
- correlation coefficient
- nonnormality
- robustness