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Thanks to Robert Newcombe (of the Centre for Health Sciences Research, Cardiff University) and to Eddie Channon (of Chirostat Statistical Consulting, Nottingham) for replying to my query (see below my signature). The special name for inverse_g(mean(g(X))is "back-transformed mean". My colleague Sue Chinn commented that she cannot think of a scenario in which anybody would want to meta-analyse correlation coefficients (as distinct from regression coefficients). I cannot easily think of one, either, but I was thinking more of differences between proportions, which are a kind of regression coefficient. Best wishes Roger Roger Newson Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: [log in to unmask] www.imperial.ac.uk/nhli/r.newson/ Opinions expressed are those of the author, not of the institution. **** ORIGINAL MESSAGE Fellow Allstatters: A query about terminology, rather than concepts. Given a random variable X, is there a special name for the hyperbolic tangent of the mean of the hyperbolic arctangent of X? I ask because it would seem to be the natural quantity for which to estimate confidence intervals, if I am meta-analysing correlation coefficients or differences between proportions. (My reasoning is based on an analogy with meta-analysing risk ratios or odds ratios, in which case we estimate confidence intervals for a geometric mean risk ratio or odds ratio, which is the antilog of the mean log risk ratio or odds ratio. In the case of correlation coefficients and differences between proportions, the hyperbolic arctangent is better known as Fisher's z transform.) More generally, given a random variable X and a monotonic transformation g(), is there a special name for inverse_g(mean(g(X))), where inverse_g() is the inverse of g() and mean() denotes expectation? I already know that we call it the arithmetic mean when g(X)=X, the geometric mean if g(X)=log(X), the harmonic mean when g(X)=1/X, and the pth power algebraic mean when g(X)=x^p for a power p. But is there a general term for inverse_g(mean(g(X))) for an arbitrary monotonic transformation g()? Best wishes (and thanks in advance) Roger