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coefficients of variation AND skewness AND kurtosis
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ivanba...@gmail.com
Apr 23, 2013, 9:35:03 AM4/23/13
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Hi members:
Please. I would like to understand this sentence:
...."Lognormality cannot be treated as a simple departure from normality. For coefficients of variation beyond 0.25, skewness and kurtosis are so severe that most observations concentrate in a small region with only a few extreme values spreading out over a wide range. No parametric tool is robust enough to avoid severe distortion when such data is used".
source: Duarte Trigueiros. University of Algarve. "The use of Accounting Data in Statistical Models".
.................
Then, may I to conclude that... "always when CV (%) is less than 25% then it's possible to do a parametric test on data (for example, to compare the groups by ANOVA one-way)?
TIA
Ivan
Please. I would like to understand this sentence:
...."Lognormality cannot be treated as a simple departure from normality. For coefficients of variation beyond 0.25, skewness and kurtosis are so severe that most observations concentrate in a small region with only a few extreme values spreading out over a wide range. No parametric tool is robust enough to avoid severe distortion when such data is used".
source: Duarte Trigueiros. University of Algarve. "The use of Accounting Data in Statistical Models".
.................
Then, may I to conclude that... "always when CV (%) is less than 25% then it's possible to do a parametric test on data (for example, to compare the groups by ANOVA one-way)?
TIA
Ivan
Rich Ulrich
Apr 23, 2013, 12:58:49 PM4/23/13
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On Tue, 23 Apr 2013 06:35:03 -0700 (PDT), ivanba...@gmail.com
wrote:
No. And, of course, the data can have other features besides
seeming to be pretty much log-normal.
The statement says that CVs of over 25% are always a problem.
I'm not sure that, at 25%, I would say that "most observations
concentrate in a small region" -- for exactly 25% -- but that is
what you are headed toward.
Perhaps it should have gone on to add that CVs of over 10%
potentially can be a problem, and CVs of under 10% will not often
be a problem (for parametric testing).
What also matters is the precision of the model and the
completeness of the fit. If you successfully fit 90% of the
variance, the heterogeneity of the residuals will matter
a whole lot more than if your model only fits 50% of the
variance. That guideline of 25% depends on some particular
set of problems that the author has in mind.
When I started to write this statement, I was thinking that,
"Well, with there's never a problem when the CV is under 5%."
That is surely true for the models that I have built. But now
that I consider the prospect of R^2= 0.99, I can imagine
problems even there. - The tests at 0.99 would be "significant"
but the non-fit is apt to induce interactions, etc.
--
Rich Ulrich
wrote:
seeming to be pretty much log-normal.
The statement says that CVs of over 25% are always a problem.
I'm not sure that, at 25%, I would say that "most observations
concentrate in a small region" -- for exactly 25% -- but that is
what you are headed toward.
Perhaps it should have gone on to add that CVs of over 10%
potentially can be a problem, and CVs of under 10% will not often
be a problem (for parametric testing).
What also matters is the precision of the model and the
completeness of the fit. If you successfully fit 90% of the
variance, the heterogeneity of the residuals will matter
a whole lot more than if your model only fits 50% of the
variance. That guideline of 25% depends on some particular
set of problems that the author has in mind.
When I started to write this statement, I was thinking that,
"Well, with there's never a problem when the CV is under 5%."
That is surely true for the models that I have built. But now
that I consider the prospect of R^2= 0.99, I can imagine
problems even there. - The tests at 0.99 would be "significant"
but the non-fit is apt to induce interactions, etc.
--
Rich Ulrich
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