A Useful Approximate Formula for the Determination of the Regions of the Sequential Test for the Correlation Coefficient.

A simple approximate formula is shown to be remarkably accurate for the determination of the regions of the sequential test for the correlation coefficient, rho, when the variates follow a bivariate normal distribution. The approximate results are compared with the exact values and with an approximation of Ghosh 1970. The exact results depend on the solution of an equation involving the ratio of two hypergeometric functions. These results, combined with the Monte Carlo evaluations of the OC, operating characteristic function, the ASN, the average sample number, and the exact values of some selected regions provide all the materials needed for this sequential test. The real advantage of a sequential test over a fixed size test is the early termination of the test when rho exceeds or rho sub 1 or rho is less than rho sub 0 by a substantial amount. Additionally the savings in sample size vary from 25 to 80 as compared to a fixed size test.