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> From: Dr Sarah White [mailto:[log in to unmask]] > Sent: 08 June 2004 07:31 > > There is some ambiguity about the definition of the coefficient of > variation! Both Chatfield (in Statistics for Technology) and Kirkwood > and Sterne (in Essential Medical Statistics, 2003) use the definition of the > ratio of the standard deviation to the mean, expressed as a percentage. > > The first reference given below by Paul Johnson replaces 'standard > deviation' by 'standard error', which clearly has quite a > different meaning. Kish (Survey Sampling, 1965, p 47) describes the "coefficients of variation", namely the "element coefficient of variation" which he denotes as C subscript x and defines as the standard deviation divided by the mean. The "coefficient of variation of the mean" he denotes as CV(ybar) and defines as the standard error divided by the mean. The term then appears (p206ff) in a section on ratio means E(y/x), which includes the comment, "We need to assume that the absolute value of X is so large that (1) the occurence of x near zero is a negligible rarity; and (2) the relative error in x is small enough to permit dropping all but the leading terms of the needed Taylor expansions. ... Hence a reasonable control of the coefficient of variation C_x must be maintained." This appears to be the basis for the calculations in the CTS website quoted. However, as CTS states (quale.pdf p17), "Although coefficients of variation are widely used, a more intuitively meaningful measure of sampling error is the confidence interval of an estimate." I agree, and am therefore puzzled by the dogmatic methodology CTS suggests to justify issuing point estimates. Allan Reese