Interval Estimation of Correlation Coefficients Corrected for Restriction of Range

Abstract

Two objectives guided the present study: (1) to provide a suitable test for the hypothesis rho = 0, and (2) to establish nomograms by which general users of R can set confidence intervals on rho. The first objective was approached by testing several possible solutions similar to the procedure followed by Forsyth. The second objective was pursued via a combination of a general analytical procedure (Mood and Graybill, 1963) together with computer simulation techniques and a curve fitting technique (Usow, 1970). Procedures for achieving both objectives required the use of R distributions. The method used to obtain the necessary r distributions and the two procedures and their results are described.