I am working my way through (T.J.Diccio and B.Efron, "Bootstrap Confidence Intervals", Statistical Science 1996 v11 no3 pp189-228) ([link to paper][1]), and I'm stuck even before I get to the good stuff. In the introduction, there is a table of before/after treatment values called cd4, and the correlation \hat{\theta} is given as 0.723. The paper then states, "We can find an exact interval for \theta if we are willing to assume bivariate normality ... The exact central 90% interval is (0.47, 0.86)." Here I stipulate that I am a stats moron. But when I key in the data and compute a confidence interval by hand in R, either using the Fisher transform or the T distribution, I don't get that interval. How does one compute the interval they are talking about? > cd4 subj base oneyr 1 1 2.12 2.47 2 2 4.35 4.61 3 3 3.39 5.26 4 4 2.51 3.02 5 5 4.04 6.36 6 6 5.10 5.93 7 7 3.77 3.93 8 8 3.35 4.09 9 9 4.10 4.88 10 10 3.35 3.81 11 11 4.15 4.74 12 12 3.56 3.29 13 13 3.39 5.55 14 14 1.88 2.82 15 15 2.56 4.23 16 16 2.96 3.23 17 17 2.49 2.56 18 18 3.03 4.31 19 19 2.66 4.37 20 20 3.00 2.40 > r = cor(cd4$base, cd4$oneyr) > r [1] 0.7231654 Fisher transform: > se = 1/sqrt(17) > se [1] 0.2425356 > tanh(c(r-1.6448*se, r+1.6448*se)) [1] 0.3133382 0.8082940 T distribution: > sr = sqrt((1-r^2)/(20-2)) > sr [1] 0.1627936 > tc = abs(qt(0.05/2, 18)) > c(r-tc*sr, r+tc*sr) [1] 0.3811486 1.0651821 [1]: https://projecteuclid.org/euclid.ss/1032280214