Don, I agree with what you say. When I was teaching introductory statistics, the only test for *normality* that I found was a chi square test. Are there others that you know of?
Mike On Mon, 17 Mar 2003, Donald Burrill wrote: > Not to be flippant, but why do you care? I cannot recall an instance in > which knowing the value of a formal measure of skewness (let alone > kurtosis) was useful. Observing that a distribution is skewed is > useful; the formal skewness coefficient is not, so far as I have had > occasion to observe. > > On Sun, 16 Mar 2003, VOLTOLINI wrote: > > > I am preparing a class on Kurtosis and Skewness and I can found different > > formulas to calculate each one. > > > > Another problem is that for some formulas the result zero represents > > a normal distribution but..... using another formula the result > > value 3 represents a normal distribution! > > This is not strictly true. It is true that for a normal distribution > the formal coefficient of skewness has the value zero. It does not > follow that "the result zero represents a normal distribution" if by > "represents" you mean "indicates", or "implies that the distribution is > normal". Similarly, for kurtosis defined as the fourth central moment > of a distribution, for a normal distribution the value is 3, but it does > not follow that "kurtosis = 3" implies "distribution is normal". > > > I think we need to be very careful because different softwares are > > using different formulas. > > Which only reflects, and perhaps emphasizes, the relative lack of > importance of these measures. > > > Does anyone can help me to choose the best formulas or give me some > > explanation? > > For students in an introductory course (which I take to be what you're > engaged in, but I might be wrong about that -- you haven't actually > said), I would not bother much with skewness and kurtosis, except to > point out that the concepts exist, and measures of both are sometimes > used but not very frequently, and supply a citation or two for those who > really want to calculate values as a recreational activity. > > One of the logical problems with skewness and kurtosis is that they were > defined analogously to the variance, as the k-th central moment (k=2 for > the variance, k=3 for skewness, k=4 for kurtosis); what reason can one > offer for stopping at k=4? One could readily define a 5th, 6th, ..., > nth central moment, but hardly anyone ever does; presumably because > their utility is negligibly different from zero. > > I believe that at one time it may have been believed (or perhaps more > correctly, hoped) that knowledge of the first four central moments would > provide a useful empirical way of describing the shape of an empirical > distribution, much as a polynomial of degree 4 can sometimes provide not > too bad a description of many empirical functions (over a limited range > of values, of course). But in practice this seems never to have > happened: perhaps because in practice one is concerned largely with the > shape of the tails of distributions, not with the shape of their central > 75% (say). > Just a thought or three... -- Don. > ----------------------------------------------------------------------- > Donald F. Burrill [EMAIL PROTECTED] > 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 > > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > ================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
