Abstract
A standardized mean difference in a paired samples design using a pooled standard deviation, dp, requires knowledge of the population correlation, rho, in order to generate an accurate estimate of a noncentral t confidence interval (CI). Using the observed empirical correlation introduces a source of random error which causes bias in the variance of Hedges’ gp and in the coverage of the CI which is most notable at sample sizes below 50 pairs. By contrast, a bootstrap BCa (bias-corrected and accelerated) CI for dp does not require an estimate of rho, and with unpaired samples the BCa method produces a CI for dp with nominal coverage when the underlying distribution is normal. New simulations demonstrate that the coverages of BCa CIs for dp with paired samples and a pooled error term are also nominal across a wide range of values of rho and the population effect sizes except at very small sample sizes (n = 10 pairs) where the coverage is slightly depressed. Thus, the BCa CI is more accurate than a noncentral t CI when using dp with a normal distribution. Because the estimation of rho affects the variance of gp rather than the central tendency, the value of gp can be reported along with the BCa CI for dp. However, simulations to generate a BCa CI for the unbiased gp instead of dp produced biased coverage results with 50 or fewer pairs, presumably because of the bias in the variance of gp when estimating rho. Software for generating the intervals is provided.