FROM: William B. Ware, Professor and Chair 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]
>Both SPSS and SAS report the Fisher coefficients. If I understand you,
>you are saying that each of these measures contains some "measure" of
>variation in its denominator... Agreed... But there are formulas for SEs
>for both g1 and g2... which vary as a function of sample size... I think
>that's what they are referring to...
Lets look at the g1 and g2 first.
Fisher defined these in terms of the semi-invariants, which were unbiased
estimates of the population second, third and fourth moments. The Pearson
measures were straight sample second, third and fourth moment calculations,
and represented biased estimates of population moment values. g1 is equal to
the ratio of the third semi-invariant divided by the second semi-invariant
to the 3/2's power. It is a dimensionless number, independent of the
measuring units of the original data. It is esentially the third central
sample moment divided by the standard deviation cubed.
g1 is approximately normally distributed for large sample sizes. On this
basis the g1 value should be looked at as a Z value, from which a
probability value from the standard normal distribution can be obtained.
Dividing g1 by the sample standard deviation results in a ratio that is no
longer is dimensionless, and has a value highly dependent on the units the
original data was in. This is what threw me. It didn't make sense. Treating
g1 as a Z value makes sense.
The unbiased g1 value is a population estimate and is independent of N. The
confusion over biased and unbiased values, and Fisher's and Pearson's values
is considerable. Especially since there are significant numerical
differences in computed g2 values.
g2 is the kurtosis, again based on the semi-invariants. However g2 is not
normally distributed and is skewed like a chi distribution. See the American
Statistician, August of this year, vol 53, No. 3, p 267 for Dodge and
Rousson's article related to this.
>Why not...? Although the measures of skewness and kurtosis are not
>normally distributed, the result of such a division does tell you how many
>standard errors you deviate from expectation. I tell students that as
>long as they are both within +/- 2 standard errors, they are probably OK.
>If the measures convert to SEs outside of +/- 3, they might want to be
>careful... Of course, they also need to look at graphics such as
>histograms, box-plots, and/or normal probability plots...
What you want is how many dimensionless Z values, and to "pass directly to
Go", where a p value can be estimated.
A standard deviation has the dimensions of the units of measures. If I
calculate a g1 value of 2.86 and a standard deviation of 23.18 mm, and get
your ratio of 0.2528, what does it mean? If my measure was in feet, my
standard deviation is 0.07604, and your ratio is 37.16. One tells me I have
non-normality and the other tells me I have normality?
DAH
WBW
----- Original Message -----
From: William B. Ware <[EMAIL PROTECTED]>
To: David A. Heiser <[EMAIL PROTECTED]>
Sent: Thursday, December 23, 1999 5:01 AM
Subject: Re: Standards for "Skewness"
> On Wed, 22 Dec 1999, David A. Heiser wrote:
>
> > Your reply throws me. What kind of skewness are you talking about?
> >
> > The historic computation of the term called "skewness" was either
Pearson's
> > (square root b1) or Fisher's (g1) which has already been divided by the
> > standard deviation. Go on the internet and do a search on "skewness" and
> > look at all the definations and sources.
>
> And yours throws me... :)
>
> David,
>
> Both SPSS and SAS report the Fisher coefficients. If I understand you,
> you are saying that each of these measures contains some "measure" of
> variation in its denominator... Agreed... But there are formulas for SEs
> for both g1 and g2... which vary as a function of sample size... I think
> that's what they are referring to...
>
> Bill
>
> __________________________________________________________________________
> William B. Ware, Professor and Chair 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]
> __________________________________________________________________________
>
>
>
