Taylor-Russell tables for dichotomous criterion variables

[ericmelse]

Dear Stata-listers,

I am searching for syntax to be able to compute 'Taylor-Russell tables for dichotomous criterion variables' which lists the proportion of successful selectees for each combination of a point-biserial validity (rpb, or r tetrachoric correlation, also called the validity coefficient), a base rate, and a selection ratio.
Such tables were published by HC Taylor JT Russell, The relationship of validity coefficients to the practical effectiveness of tests in selection, Journal of Applied Psychology,1939 (23) 5, 565-578, and by NM Abrahams EF Alf JJ Wolfe, Taylor-Russell tables for dichotomous criterion variables, Journal of Applied Psychology, 1971 (55) 5, 449-457.

To get an idea what I am looking for, consider the following:

clear all
set obs 1000
gen snr=_n
gen x=0
gen y=0
local A 82    // x-below y-above
local B 418    // x-above y-above
local C 182    // x-above y-below
local D 318    // x-below y-below
local admission = `B'+`C'
local xsuccess = _N-(`B'+`C')
local ysuccess = `A'+`B'
replace x=1 if _n>`xsuccess'
replace y=1 if _n<=`A'
gsort -snr
replace y=1 if _n<=`B'
sort snr
* This table lists the four categories of cases that meet the criterion (B+C), or not (A+D)),
* and who are (later) successful by some measure of outcome (A+B) or not (C+D):
table y x , row column
tetrachoric x y

Note that the result of the command tetrachoric includes: Tetrachoric rho = 0.6976, which actually is the proportion of successful selectees (which can be found in the table published by Abrahams & Wolfe, 1971).
This follows from the example data used above for illustration purposes.

However, how can this proportion of successful selectees be derived if only the tetrachoric correlation (.55), the base rate (.5) and the selection ratio (.6) are known?
Any suggestion is appreciated.