Confidence Interval Estimate of the Correlation Coefficient for Age and Systolic Blood Pressure of 20, 30 and 50 Individuals

A formula for the confidence interval of correlation coefficient based on the Fishers’ z-transformation, (where z = arctanh(r) and is used to convert the skewed distribution of sample correlation, r to a normal distribution) was applied to the age and systolic blood pressure of 20 individuals. Confidence intervals using percentile and bias-corrected and accelerated (BCa) bootstrap with 2000 replications were also obtained for the same sample sizes respectively. The interval lengths from the derived formula are 0.5997, 0.5073 and 0.3297 for 20, 30 and 50 observations respectively. The interval lengths from the percentile bootstrap are 0.6223, 0.5303 and 0.3077, while interval lengths from BCa bootstrap are 0.6214, 0.4958 and 0.3031 respectively. The interval length decreases as the sample size increases, giving a more accurate confidence interval. The derived formula gives a slightly shorter interval length for n = 20.