A NEW APPROXIMATION FOR FISHER'S Z

摘要: Summary As the sample size increases, coefficient of skewness Fisher's transformation z= tanh-1r, correlation decreases much more rapidly than excess its kurtosis. Hence, distribution standardized z can be approximated accurately in terms t with matching kurtosis by unit normal distribution. This can, turn subjected to Wallace's approximation resulting a new for transform. approximation, which used estimate probabilities, as well percentiles, compares favorably both accuracy and simplicity, two best earlier approximations, namely, those due Ruben (1966) Kraemer (1974). Fisher (1921) suggested approximating variance stabilizing transform z=(1/2) log ((1 +r)/(1r)) r mean = (1/2) + p)/(lp)) =l/(n3). is generally recognized being remarkably accurate when ||Gr| moderate but not so large, even n small (David (1938)). Among various alternatives normalizing (1973), are interesting on grounds novelty, and/or aesthetics. If r= r/√ (1r2) r|Gr |Gr/√(1|Gr2), then showed that (1) gn (r,|Gr) ={(2n5)/2}1/2rr{(2n3)/2}1/2r|GR, {1 (1/2)(rr2+r|Gr2)}1/2 approximately normal. (1973) suggests (2) tn (r, |Gr) (r|GR1) √ (n2), √(11r2) √(1|Gr2) Student's variable (n2) degrees freedom, where after considering valid choices |Gr1 she recommends taking |Gr1= |Gr*, median given |Gr.