An Interval Estimation of Pearson’s Correlation Coefficient by Bootstrap Methods

Bumrungsak Phuenaree, Sirikun Sanorsap


In this paper, we compare three confidence intervals for Pearson’s correlation coefficient which are Fisher’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.


Confidence Interval, Pearson’s correlation, Bootstrap method, Fisher’s transformation.

Full Text:



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., “A guide to appropriate use of Correlation coefficient in medical research”, Malawi Medical Journal, vol. 24, no. 3, pp.69-71, 2012

Shang Y., “Geometric Assortative Growth Model for Small-World Networks”, The Scientific World Journal, Article ID759391, vol. 2014, 8 pages, 2014.

Weaver B., and Koopman R., “An SPSS Macro to Compute Confidence Intervals for Pearson’s Correlation”, The Quantitative Methods for Psychology, vol. 10, no. 1, pp.29-39, 2014



  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.