[EMAIL PROTECTED] (Bob Roberts) wrote in message news:<[EMAIL PROTECTED]>... > 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 not a very useful test (the significance level will change dramatically, for example). It may be vaguely useful as a diagnostic in some circumstances, but it depends on what you're doing > 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. Say what? There's only one variance (only one sample), right? How can one variance be anything but homogeneous? This test is optimal for a test vs uniformity. It has good power vs light tailed alternatives. Try D'Agostino and Stephens book on goodness of fit as a starting place. There's an extensive literature on this subject. > Does anyone know of a formal test for normality employing the mean and > median, i.e. the central tendency instead of the dispersion? Well, you could construct a test based on the skewness statistic (mean-median)/s . The test statistic would be better adjusted for sample size so that it has a nice asymptotic distribution (which is going to be normal). That would be a suitable test for skew alternatives but useless against symmetric alternatives. Glen . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
