Generates a normal probability plot and performs a hypothesis test to examine whether or not the observations follow a normal distribution. For the normality test, the hypotheses are,
H0: data follow a normal distribution vs. H1: data do not follow a normal distribution
Tests for Normality There are 3 types of goodness-of-fit test: an ECDF based test, a correlation based test, and a chi-square based test. See [3] and [8] for discussions of these tests for normality.
Anderson-Darling: Choose to perform an Anderson-Darling test for normality. The Anderson-Darling test is an ECDF (empirical cumulative distribution function) based test.
Ryan-Joiner: Choose to perform a Ryan-Joiner test, similar to the Shapiro-Wilk test. The Ryan-Joiner test is a correlation based test.
Kolmogorov-Smirnov: Choose to perform a Kolmogorov-Smirnov test for normality. The Kolmogorov-Smirnov test is an ECDF based test.
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At 12:14 PM 3/17/2003, kjetil brinchmann halvorsen wrote:
On 17 Mar 2003 at 8:34, Mike Wogan wrote:
For normal tests, the chisquare test must have low power. I prefer to teach people to use normal probability plots, better named qq plots, to empasize that they can be used for other distributions also.
If you insist on a formal test, giving you a p-value, there is shapiro-wilk test, in some implementations restricted to very low sample size, but in R and elsewhere it is implemented for up to 5000 observations.
Minitab once had a test based on the pearson correlation coefficient between the data and its normal scores (what you use for the normal probability plot, the minitab handbook gave a tabel of critaical values, based on simulation. But I don't know if that exists anymore, as I havnt used minitab for more than 10 years.
But the idea of basing the test on the correlation in the normal probability plot is nice, especially when taught as thr same time as the normal probability plot.
Kjetil Halvorsen
>
> 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
> >
> >
> > .
> > .
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_________________________________________________________
dennis roberts, educational psychology, penn state university
208 cedar, AC 8148632401, mailto:[EMAIL PROTECTED]
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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