Journal of Statistical Theory and Practice

, Volume 11, Issue 3, pp 493–502 | Cite as

Robustness of the test of a product moment correlation coefficient under nonnormality

  • Takuya YanagidaEmail author
  • Dieter Rasch
  • Klaus D. Kubinger
  • Berthold Schneider


There is a considerable lack of knowledge concerning a test of the null hypothesis H0: 0 < ρρ0. Usually a test applies by some z-statistic, according to Fisher, 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 also 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 not normally distributed variables 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.


Correlation coefficient Fleishman system of distributions nonnormality robustness 

AMS Subject Classification

62 Statistics 


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Copyright information

© Grace Scientific Publishing 2017

Authors and Affiliations

  • Takuya Yanagida
    • 1
    Email author
  • Dieter Rasch
    • 2
  • Klaus D. Kubinger
    • 3
  • Berthold Schneider
    • 4
  1. 1.School of Medical Engineering and Applied Social SciencesUniversity of Applied Sciences Upper AustriaLinzAustria
  2. 2.Institute of Applied Statistics and ComputingUniversity of Natural Resources and Life SciencesViennaAustria
  3. 3.Division of Psychological Assessment and Applied Psychometrics, Faculty of PsychologyUniversity of ViennaViennaAustria
  4. 4.Institute of BiometryHannover Medical SchoolHannoverGermany

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