Re: Comparing two variation coefficients


Bruce Weaver wrote:
Reef Fish wrote:
Alfred wrote:
Thanks,

Here is a practical situation where it can be useful
to test for difference between two CV :

CV (also named "Relative Standard Deviation") is a recognized measure of
measurement repetability in Analytics. For instance, in can be used to
monitor drug tablet homogeneity (the so called "uniformity content test"
is a pre-requisite of the FDA for approval).

see : http://www.fda.gov/ora/compliance_ref/cpg/cpgdrg/cpg460-600.html

While it is true that the FDA used the term "relative standard
deviation",
but there is no indication that it meant CV!

Surely the statisticians in the FDA are not THAT statistically
challenged.
Or are they?

Is the FDA ignorant of the term Coefficient of Variation? If so, why
does it
use the ill-defined and undefined term "relative standard deviation"
repeatedly in the document? In particular it never even suggested
WHAT
the standards were.

So, how can you test if something meets the FDA standard if you don't
even know what the FDA is talking about?

-- Bob.


I'd never heard of the "relative standard deviation" either. But
according to this glossary...

http://stats.oecd.org/glossary/detail.asp?ID=5061

it is another name for coefficient of variation. Here is the entry for
"coefficient of variation".

Thanks for the reference.

Just when I thought I've heard of all of the standard terms of
statistics
and the terms for the same used by other disciplines, there pops up
ANOTHER one, for no good reason whatsoever! :-)

I think it was only after I had my Ph.D. in statistics before I heard
of
the "exogenous" and "endogenous" variables in regression problems
used by economists, and abused by the economists. :)

----
Definition: The standard deviation of a random variable divided by the
mean.

Context: Its dimensionless form makes it convenient for summarization.

The United States Bureau of Census alternatively refers to the
coefficient of variation as the ratio of the standard error to the value
being estimated, usually expressed in terms of a percentage.

This makes even LESS sense, the way I read what I thought it was
saying.

The variable to be estimated is a paramter, an unknown constant.

I think that statement is trying to define the SAMPLE CV as the ratio
of the standard error (estimated standard deviation) and the estimated
mean of some population or statistic.


Also known
as the relative standard deviation. (United States Bureau of Census,
Glossary of Selected Abbreviations and Acronyms - refer
http://eire.census.gov/cgi-bin/ssd/Glossary).

Source Publication: The International Statistical Institute, "The
Oxford Dictionary of Statistical Terms", edited by Yadolah Dodge, Oxford
University Press, 2003.
----

The bit that perplexes me is how the Census Bureau can refer to the COV
as the SE over the estimated value. Surely that should be SD, not SE.

We were perplexed at the same thing. But I think we came to the same
resolution of what was meant in the sloppy language.

SE is synonymous to "standard deviation", the ESTIMATED standard
deviation, as opposed to SD, the known or unknown population standard
deviation. Also there's the sample standard deviation of the
dependent
variable Y and the sample standard deviation of the errors in a
regression. So, the latter is often called the SE.

I believe that was the reason the term SE was introduced in the first
place,
to lessen the ambiguity when one says "standard deviation" because
there
are so darn many different ones of the same quantity. :-)

-- Bob.

.

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