I am working my way through ([T.J. Diccio & B. Efron, "Bootstrap Confidence Intervals", *Statistical Science*, 1996, *11*(3), 189–228][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.  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