The use of bootstrap confidence intervals for the correlation coefficient in climatology

Summary The importance of defining confidence intervals for sample statistics that are used to estimate characteristics of the parent population(s) is emphasised. Not all sample statistics are unbiased estimators or have normally distributed sampling distributions and so it is not always easy to reflect the reliability of the estimator. In such cases, Efron's bias corrected percentile method, which uses bootstrap samples to estimate the bias and makes no assumptions about the distribution of the sample statistic can be used to define confidence limits for the population parameter. The method is explained and the procedure for calculating the confidence limits is outlined.As an example, bootstrap confidence limits calculated for the maximum correlation between the Southern Oscillation Index and rainfall at South African stations over the period 1935–1983 suggest that the sample correlation is an unreliable measure of the true association. One possible reason for this is that the association is thought to have broken down during the 1940s. However, the reliability of the estimator does not seem to improve when confidence limits are calculated for the 30-year period 1954–1983. It is possible that the width of the confidence interval is an indication of more than one distinct statistical population.