Journal of Statistical Theory and Practice

, Volume 11, Issue 3, pp 393–401 | Cite as

How robust is the modified sequential triangular test of a correlation coefficient against nonnormality of the basic variables?

  • Dieter RaschEmail author
  • Takuya Yanagida


There is a big lack of knowledge as concerns a test of the null hypothesis H0: 0 < ρρ0. 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 H0: ρ = ρ0. 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.


Triangular sequential test correlation coefficient robustness nonnormality Fleishman system of distributions 

AMS Subject Classification



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Copyright information

© Grace Scientific Publishing 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Natural SciencesViennaAustria
  2. 2.School of Applied Health and Social SciencesUniversity of Applied Sciences Upper AustriaLinzAustria
  3. 3.RostockGermany

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