In article <[EMAIL PROTECTED]>, Bob Roberts <[EMAIL PROTECTED]> wrote: >Lothar Sachs (1984, Applied Statistics (a book, not the journal), >Section 4.3.3, p. 322-329) says that a rule of thumb for testing >normality is to divide the median by the mean, and if the ratio is >between 0.9 and 1.1, the distribution is approximately normally >distributed. This is actually a measure of the skewness.
This is difficult to understand. Mean and median are both location parameters, but dividing one by the other almost needs positive observations. But even this will not do that much if there is a large "origin" effect. >He continues to present a test for normality based on the range >divided by the standard deviation developed by Pearson and Stephens >(Biometrika, v. 51, 1964, p. 484-487). As he notes, this is actually >a test of the homogeneity of the variances. >Does anyone know of a formal test for normality employing the mean and >median, i.e. the central tendency instead of the dispersion? The difference of the mean and median in a typical distribution, especially a symmetric unimodal distribution, is asymptotically normal with a variance O(1/n) if the variance exists. In such situations, the power of the test will not improve with sample size. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Deptartment of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
