A Comparison of the Accuracy of the Formula for the Standard Error of Pearson “r” with the accuracy of Fisher’s z-Transformation

Abstract

ESTIMATES BASED on the approximate I standard error formula Or = (1 r2)/VN 1 are used in education and psychology (3), for the purpose of rendering a judgment on the samp ling significance of an obtainedproduct-moment correlation. Fisher's normalizing transforma tion zT = logeV (1 + r)(l r) (in connection with the formula oz? = 1/V~N 3 ) is also used for the same purpose (2). Neither of these processes is completely accurate (4) and since a conven ient basis for study is afforded by the extensive and exact tabulation of F. N. David (1), it is the purpose of this paper to present in tabular form a numerical comparison of the error in t h e s e two methods. The Fisher process is more elaborate, but on mathematical grounds is known to be, in gen eral, of greater accuracy. Aside from theoret ical interest, therefore, themain purpose of our tabulation is to yield more precise informa tion as to when it is safe to use the standard er ror formula and when it is better to u s e t h e more complex procedure of the z-transforma tion.