On the distribution of the correlation coefficient when sampling from a mixture of two bivariate normal densities: Robustness and the effect of outliers |
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Authors: | M. S. Srivastava G. C. Lee |
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Affiliation: | 1. Department of Statistics University of Toronto Toronto, Ontario M5S 1A1;2. 325 Telok Blangah Heights Block 84, # 15 Singapore 0410 |
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Abstract: | The distribution of the sample correlation coefficient is derived when the population is a mixture of two bivariate normal distributions with zero mean but different covariances and mixing proportions 1 - λ and λ respectively; λ will be called the proportion of contamination. The test of ρ = 0 based on Student's t, Fisher's z, arcsine, or Ruben's transformation is shown numerically to be nonrobust when λ, the proportion of contamination, lies between 0.05 and 0.50 and the contaminated population has 9 times the variance of the standard (bivariate normal) population. These tests are also sensitive to the presence of outliers. |
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Keywords: | Correlation coefficient Student's t Fisher's z arcsine transformation Ruben's transformation contaminated normal outlier distribution significance robustness |
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