Re: Normality assumption for ANOVA (was: Effect statistics for non-normality)
It depends on whether your are testing based on means or testing based on sums of squares. The former is of course, the z or t test, with the t test being preferred from theoretical aspects. The latter is of course the F test or variations on the chi-square test. Way back in ancient history, R. C. Geary (Biometrika 34, pages 209-242) explored the effects of skewness and kurtosis on the distribution of means (t distributions) for small samples. The work is somewhat hard to draw generalizations from. For sums of squares involving two independent samples drawn at random from the same universe, the variance of z is proportional to (B2-1)/4, where B2 is the kurtosis of the universe. This is just an expansion of Fisher's approximate formula for normal samples on page 228 of Fisher (Statistical Methods...). z here is Fisher's one-half the log of the ratio of the two variances. Kurtosis is then the primary concern on tests using Chi-square or F tests. Geary shows that the distortions in the normal t distribution due to kurtosis is slight, even for small samples. In reality, large skewness values and large kurtosis values occur at the same time, under normal sampling. Therefore it is not unreasonable to look at kurtosis values rather than skewness values to estimate departures from the standard mean or sum of squares distributions derived from normal distributions. DAHeiser - Original Message - From: Will Hopkins <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, January 19, 2001 1:31 PM Subject: Re: Normality assumption for ANOVA (was: Effect statistics for non-normality) > Yes, I was wrong about the need for normality of the residuals. I somehow > had the idea that estimates of the precision of estimates come directly > from normality of the individual errors, but it just ain't so. Estimating > the confidence limits for the mean of a sample is the way to see how the > central limit theorem smooths out a nasty distribution of > residuals. According to Bill Ware and Paul Swank, the distribution of the > variance of the mean takes a bigger sample to settle down than the > distribution of the mean, but I can't really see how that matters, unless > you can make it the basis of the kind of test for non-normality I am > looking for. > > So when I plot residuals (Y) against predicteds (X), the scatter in the Y > direction can look quite discrete (as in residuals from a Likert scale with > only a few levels) and skewed (as in responses piled up at either end of > the Likert scale, or as in Robert Dawson's example of Poisson distributions > with small means). All that matters is that I have enough observations > for the central limit theorem to smooth out the "graininess". It's really > cool to learn that I may not have to use logistic regression for Likert > scales, but how do I know whether I have enough observations? Someone > suggested some function of the sample size and the third and/or fourth > moments. Anyone know of any simulations done on anything like that? > > While we're on the subject of residuals vs predicteds... We are supposed > to check for substantial curvature in the plot (which would indicate the > model needs refining) and substantial non-uniformity in scatter for > different predicted values (heteroscedasticity, which biases the estimates > towards the observations with more scatter and also stuffs up the > confidence limits). The rule for these two problems seems to be: if you > can see it on the plot, you should do something about it. Anyone got > anything more quantitative than that? I guess you have to make your own > decision about curvature, based on what you know from clinical experience > about what effects are substantial. (You could use Cohen's scale of > magnitudes as a default.) But what about the non-uniformity of > scatter? How big does a difference in variance between groups or between > either ends of the residuals vs predicteds have to be before the associated > bias is a concern? > > Will > > > > = > Instructions for joining and leaving this list and remarks about > the problem of INAPPROPRIATE MESSAGES are available at > http://jse.stat.ncsu.edu/ > = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
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Re: AW: AW: eigenvalue: origin of term
I appreciate your thoughts, and I write with
hesitation, since I don't really want to get
involved in a bootless controversy.
However, much of the information that I have seen
in general purpose "histories" is not what it
should be -- some of those on the internet are
quite flawed especially the "treasure trove" that
you referenced, and of course the Encyclopaedia
Britanica has always been in a class by itself.
Gauss did so much and was such a great man that
the is often credited where he should not be. I
would place long odds on what Herman said about
"eigenvalue" being correct. On this sort of thing
he is seldom wrong. There are a number of reliable
histories of statistics. Hald has written and
extensive one, and of course the most readable
are those by Stigler. You will of course find
justification for my comments therein, and as for
Fisher, one only has to read his papers.
Werner Wittmann wrote:
>
> Hi folks back again:
> Bob, yes I said guess (which is the only strategy if one does not know
> exactly). Here is what I found in:
> Merriam-Webster's WWWebster Dictionary -includes definition (English),
> illustration, phonic pronunciation, origin, thesaurus (indexed Oct 10 1997)
> Main Entry: ei·gen·val·ue
> Pronunciation: 'I-g&n-"val-(")yü, -y&(-w)
> Function: noun
> Etymology: part translation of German Eigenwert, from eigen own, peculiar +
> Wert value
> Date: 1927
> : a scalar associated with a given linear transformation of a vector space
> and having the property that there is some nonzero vector which when
> multiplied by the scalar is equal to the vector obtained by letting the
> transformation operate on the vector; especially : a root of the
> characteristic equation of a matrix
> Here are two links to Gauss:
> http://www.treasure-troves.com/bios/Gauss.html
>
> http://britannica.com/bcom/eb/article/1/0,5716,117281+2+109423,00.html
>
> Herman here is what Britannica says:
> "About 1820 Gauss turned his attention to geodesy--the mathematical
> determination of the shape and size of the Earth's surface--to which he
> devoted much time in theoretical studies and field work. To increase the
> accuracy of surveying he invented the heliotrope, an instrument by which
> sunlight could be utilized to secure more accurate measurements. By
> introducing what is now known as the Gaussian error curve, he showed how
> probability could be represented by a bell-shaped curve, commonly called the
> normal curve of variation, which is basic to descriptions of statistically
> distributed data."
>
> Here is the history of matrices and determinants:
> http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/HistTopics/Matrices_a
> nd_determinants.html
>
> This source says that Gauss coined the term determinant, but not in the
> meaning we use it today.
> The origin and first use of "Eigenwert" eigenvalue unfortunately is not
> discussed.
> I guess(again in the same meaning as above) that Herman's explanation about
> its origins is too complicated to be true,given
> the whole history of matrices, but I may be wrong.
>
> Bob you're right pointing to the problem that Gauss often claimed having
> found something earlier, but not having it published.
> He also was accused of plagiarism, but his diaries showed the contrary,
> unless he had not falsified these (p
> Cohen: Jacob (Jack) Cohen is one of our heroes in psychology (and behavioral
> sciences understood broadly):
> Here is an obituary:
> "Jacob Cohen made at least three major contributions to quantitative
> methods, any one of which would have been enough to secure a world-wide
> reputation as a leader in this field. Cohens kappa is cited in his
> Distinguished Lifetime Contribution Award as "the gold standard for the
> measurement of agreement between categorical judgments." He championed the
> use of multiple regression as a general dataanalytic framework,
> illustrating the relationships between what are often treated as separate
> methods of analysis, and he developed multivariate analogs (e.g., set
> correlation) that allowed researchers to apply the regression framework to
> virtually any data-analytic problem in the social and behavior sciences.
> Finally, his work in statistical power analysis changed the way we think
> about the meaning of significance tests, and his emphasis on effect-size
> measures foreshadowed the development of meta-analysis."
> Here is a full obituary for Jack:
> http://web.missouri.edu/~psycmm/bgnews/1998/msg00036.html
>
> The cite for Jack's seminal paper is:
> Cohen,J.(1968) Multiple regression/correlation as a general data analytic
> system.Psychological Bulletin.(sorry don't have the
> exact ref.not handy because I'm at home)
> This developed into the bestseller with his wife Patricia:
> Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation
> analysis for the behavioral sciences (2nd edition). Hillsdale, NJ: Erlbaum.
> Jack once told me that the 1968 paper was almost not published due to the
> r
Re: A much more basic MCAS fallacy?
In article <[EMAIL PROTECTED]>, "Daniel P. B. Smith" <[EMAIL PROTECTED]> wrote: > (Thanks, Rich Ulrich, for pointing out this thread) > > Thank goodness my kids are long out of school... Forgive me jumping in > as a layperson with a post that may only be marginally on-topic... > > In my local community (Norwood), the same thing happened. The school > with the best score--the Callahan--is the one that got slapped with the > "failing" grade. I have to say that "regression to the mean" was > certainly the first thing that crossed MY mind. > > But what seems far more puzzling to me is that the stated figures are: > > SchoolScoreChange > > Callahan 245.3-1.0 > Oldham242.2 6.5 > Prescott 242.5 5.5 > > These seem to me like minuscule differences. > > Needless to say, all public reporting and discussion of MCAS scores > seems to assume that the scores are perfectly accurate, with no stated > margin of error. I believe individual scores are being reported to > students the same way. > > Can anybody possibly believe that a difference of one point in 245.3 can > possibly be significant? We're talking about schools with a less than a > maybe sixty fourth-graders in them. This just runs against common > sense... > > Worse yet, if such tiny differences are being taken seriously by > officials, there would seem to be strong motives for all kinds of > mischief and "gaming the system" in various ways. > > -- > Daniel P. B. Smith > Preferred email address: [EMAIL PROTECTED] > Alternate email address: [EMAIL PROTECTED] > "Lifetime forwarding" address: [EMAIL PROTECTED] > Visit alt.books.jack-london! > For each grade and school, the MA Dept. of Education had 3 scores: 1998, 1999 & 2000. The Mass Dept. of Ed. decided to make the evaluations based on the mean of 1999 and 2000 vs. 1998. In Norwell, every school failed. The School head pointed out that the 2000 scores were higher than the 1998 scores but that a low 1999 brought down the mean. I think much of the current evaluation needs to be redone, but at a start, there can be little justification for using the 1998 datum as the baseline for assessing change. -- Eugene D. Gallagher ECOS, UMASS/Boston Sent via Deja.com http://www.deja.com/ = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
AW: AW: eigenvalue: origin of term
Hi folks back again:
Bob, yes I said guess (which is the only strategy if one does not know
exactly). Here is what I found in:
Merriam-Webster's WWWebster Dictionary -includes definition (English),
illustration, phonic pronunciation, origin, thesaurus (indexed Oct 10 1997)
Main Entry: ei·gen·val·ue
Pronunciation: 'I-g&n-"val-(")yü, -y&(-w)
Function: noun
Etymology: part translation of German Eigenwert, from eigen own, peculiar +
Wert value
Date: 1927
: a scalar associated with a given linear transformation of a vector space
and having the property that there is some nonzero vector which when
multiplied by the scalar is equal to the vector obtained by letting the
transformation operate on the vector; especially : a root of the
characteristic equation of a matrix
Here are two links to Gauss:
http://www.treasure-troves.com/bios/Gauss.html
http://britannica.com/bcom/eb/article/1/0,5716,117281+2+109423,00.html
Herman here is what Britannica says:
"About 1820 Gauss turned his attention to geodesy--the mathematical
determination of the shape and size of the Earth's surface--to which he
devoted much time in theoretical studies and field work. To increase the
accuracy of surveying he invented the heliotrope, an instrument by which
sunlight could be utilized to secure more accurate measurements. By
introducing what is now known as the Gaussian error curve, he showed how
probability could be represented by a bell-shaped curve, commonly called the
normal curve of variation, which is basic to descriptions of statistically
distributed data."
Here is the history of matrices and determinants:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/HistTopics/Matrices_a
nd_determinants.html
This source says that Gauss coined the term determinant, but not in the
meaning we use it today.
The origin and first use of "Eigenwert" eigenvalue unfortunately is not
discussed.
I guess(again in the same meaning as above) that Herman's explanation about
its origins is too complicated to be true,given
the whole history of matrices, but I may be wrong.
Bob you're right pointing to the problem that Gauss often claimed having
found something earlier, but not having it published.
He also was accused of plagiarism, but his diaries showed the contrary,
unless he had not falsified these (phttp://web.missouri.edu/~psycmm/bgnews/1998/msg00036.html
The cite for Jack's seminal paper is:
Cohen,J.(1968) Multiple regression/correlation as a general data analytic
system.Psychological Bulletin.(sorry don't have the
exact ref.not handy because I'm at home)
This developed into the bestseller with his wife Patricia:
Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation
analysis for the behavioral sciences (2nd edition). Hillsdale, NJ: Erlbaum.
Jack once told me that the 1968 paper was almost not published due to the
resistance of the editors who where all educated
in seeing a real split between ANOVA and regression as maybe Elliot still
sees it.
BTW: Switzerland had had Euler on their 10Franken bill(6th banknote series
1976):
http://www.snb.ch/e/banknoten/alle_serien/alle_serien.html
Euler's bio is here:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html
There is no reason for any national pride.All the giants are standing on the
shoulders of other normal people and other giants and that pyramid is truly
international!
But it would be nevertheless interesting just in case the new "too close to
call" President of the United States proposes
to put a leading figure from science and one from math/statistics on dollar
bills, just to have a cheap intervention to boost
the attitude towards science and math/statistics, whom would you propose?
If I had a vote my choices would be:
Richard Feynman and John Tukey.
Werner
Werner W. Wittmann;University of Mannheim; Germany;
e-mail: [EMAIL PROTECTED]
-Ursprüngliche Nachricht-
Von: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]Im Auftrag von Bob Wheeler
Gesendet: Sonntag, 21. Januar 2001 02:21
An: [EMAIL PROTECTED]
Betreff: Re: AW: eigenvalue: origin of term
Your national pride does you credit. Gauss was one
of the greats, and he may have used "eigenvalue"
or its equivalent, but I don't know for sure -- do
you really, or are you guessing?
It is hard to be certain with Gauss, because of
his brilliance, but I doubt that he used the
general linear model as we now know it, and
although he did solve least squares equations, he
may not have have invented the technique --
Legendre was the first to publish in 1809. No one
has been able to verify Gauss' use of least
squares before Legendre, because he either made
calculational errors in his analysis or used
something other than least squares. Gauss often
said in his later years upon being shown a new
technique, that he had used it himself but had not
published. Who is to say.
However, your 10DM bill to the contrary, Gauss was
not the first to use the normal distribution:
DeMoivre used it as an approximation the the
bino
Re: Job Opening: Manager Database Marketing Analytics: Holiday Inn Worldwide
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Job Opening: Manager Database Marketing Analytics: Holiday Inn Worldwide
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Checking
I'm sending this message simply to see if I've got the correct address for the listserv. If this message does NOT bounce back to me, I'll assume that (1) the listserv is still in operation and (2) I've got the correct address. Thanks. = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
trivariate normality test statistic
Hi, I'm looking for a test statistic for trivariate normality. Does anybody know such a test-statistic, respectively a book/website where I can find one ? Thanks ! Wendy = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
