An Interval Estimation of Pearsonâ€™s Correlation Coefficient by Bootstrap Methods
Keywords:Confidence Interval, Pearsonâ€™s correlation, Bootstrap method, Fisherâ€™s transformation.
In this paper, we compare three confidence intervals for Pearsonâ€™s correlation coefficient which are Fisherâ€™s transformation, standard bootstrap and percentile bootstrap methods. The performance of these confidence intervals is considered by the coverage probability and the average width. Monte Carlo simulation results for generating non-normal distribution show that the percentile bootstrap confidence interval is the best method, when the distribution is a uniform distribution and the sample sizes are larger than or equal to 50. For the logistic and Laplace distributions, the percentile bootstrap method is the most efficiency method when the sample sizes are larger than or equal to 200 and the correlation coefficients are at least 0.5. However, the Fisher method gives the best confidence interval when the correlation coefficients are 0.2.
Efron B., and Tibshirani R.J, An introduction to the bootstrap, Chapman & Hall, USA, 1994
Fisher R.A., Statistical methods for research workers, Oliver and Boyd, London, 1934
Mukaka M.M., â€œA guide to appropriate use of Correlation coefficient in medical researchâ€, Malawi Medical Journal, vol. 24, no. 3, pp.69-71, 2012
Shang Y., â€œGeometric Assortative Growth Model for Small-World Networksâ€, The Scientific World Journal, Article ID759391, vol. 2014, 8 pages, 2014.
Weaver B., and Koopman R., â€œAn SPSS Macro to Compute Confidence Intervals for Pearsonâ€™s Correlationâ€, The Quantitative Methods for Psychology, vol. 10, no. 1, pp.29-39, 2014
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