Karl, The text that you forwarded is grossly oversimplified... Pearson derived his measures of skewness and kurtosis. The value of kurtosis is 3 in a normal population... however, one subtracts something close to 3 (based on formula) for samples. Fisher derived a similar, but different, set of formulas for skewness and kurtosis, with correspondingly different standard errors...
The Pearson moments are used by SYSTAT and STATA, last time I checked. The Fisher formulas are used by SAS, SPSS, and Excel. However, when you take sample values and divide by the appropriate standard errors, you get identical results... Bill __________________________________________________________________________ William B. Ware, Professor Educational Psychology, CB# 3500 Measurement, and Evaluation University of North Carolina PHONE (919)-962-7848 Chapel Hill, NC 27599-3500 FAX: (919)-962-1533 http://www.unc.edu/~wbware/ EMAIL: [EMAIL PROTECTED] __________________________________________________________________________ On Wed, 10 Dec 2003, Karl L. Wuensch wrote: > B2, the expected value of the distribution of Z scores which have been raised to > the 4th power, which has a value of 3 for a normal distribution, is often referred > to as "Pearson kurtosis." Subtract 3 from this quantity and you get a parameter > which is often referred to as "Fisher kurtosis." For example, at > http://www2.chass.ncsu.edu/garson/pa765/assumpt.htm, you can find the following: > > Kurtosis is the peakedness of a distribution. A common rule-of-thumb test for > normality is to run descriptive statistics to get skewness and kurtosis, then divide > these by the standard errors. Kurtosis also should be within the +2 to -2 range when > the data are normally distributed (a few authors use +3 to -3). Negative kurtosis > indicates too many cases in the tails of the distribution. Positive kurtosis > indicates too few cases in the tails. Note that the origin in computing kurtosis is > 3 and a few statistical packages center on 3, but the foregoing discussion assumes > that 3 has been subtracted to center on 0, as is done in SPSS and LISREL. The > version with the normal distribution centered at 0 is Fisher kurtosis, while the > version centered at 3 is Pearson kurtosis. SPSS uses Fisher kurtosis. Various > transformations are used to correct kurtosis: cube roots and sine transforms may > correct negative kurtosis. > > Now I happen to think that this statement is dead wrong in associating negative > kurtosis with "too many cases in the tails" and positive kurtosis with "too few > cases in the tails," but I am not looking to start an extended discussion of what > the "tails" of a distribution really are. > > My query to this group is: Why is B2 called Person kurtosis and (B2 - 3) called > Fisher kurtosis? Recently I read Pearson, K. (1905). Das Fehlergesetz und seine > Verallgemeinerungen durch Fechner und Pearson. A Rejoinder. Biometrika, 4, 169-212, > and in that interesting article Pearson defined kurtosis as (B2 - 3). > > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > Karl L. Wuensch, Department of Psychology, > East Carolina University, Greenville NC 27858-4353 > Voice: 252-328-4102 Fax: 252-328-6283 > [EMAIL PROTECTED] > http://core.ecu.edu/psyc/wuenschk/klw.htm > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
