How robust is the modified sequential triangular test of a correlation coefficient against nonnormality of the basic variables?
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There is a big lack of knowledge as concerns a test of the null hypothesis H0: 0 < ρ ≤ ρ0. 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.
KeywordsTriangular sequential test correlation coefficient robustness nonnormality Fleishman system of distributions
AMS Subject Classification62
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- Demirtas, H., Y. Shi, and R. Allozi. 2016. PoisNonNor: Simultaneous generation of count and continuous data. R package version 1.1. https://doi.org/cran.r-project.org/web/packages/PoisNonNor/.
- Fisher, R. A. 1915. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10:507–21.Google Scholar
- Fisher, R. A. 1921. On the “probable error” of a coefficient of correlation deduced from a small sample. Metron 1:3–32.Google Scholar
- Kubinger, K. D., D. Rasch, and M. Šimečkova. 2007. Testing a correlation coefficient’s significance: Using H0: 0 < ρ ≤ λ is preferable to H0: ρ = 0. Psychology Science 49:74–87.Google Scholar
- Yanagida, T. 2016. Miscor: Miscellaneous functions for the correlation coefficient. R package version 0.1-0. https://doi.org/cran.r-project.org/web/packages/miscor/.