Dear all,
I'm having a "discussion" with a medic over use of the
coefficient of variation (CV) as a measure of variability.
My instinctive feeling is that CV is really only of use when
the range of the variable is limited to the positive real
line. It's often used, for example, for concentrations of
hormones in the blood; this seems entirely appropriate,
especially as the SD of concentrations tends to increase
with the mean.
But the medic wants to use CV as a measure of spread of
the log of concentrations. There are obvious objections
to this; for example, negative or even exact zero means.
But I haven't yet found any authoritative statement saying
that the CV is only appropriate when the range of the
variable is restricted to the positive real line. Worse,
there are some descriptions of CV which specifically mention
its use with negative values. For example, the Wikipedia
entry (yes, I know it's only Wikipedia!) actually *defines*
CV as SD divided by *modulus* of mean.
My question is, therefore:
Am I overlooking a statistically valid use of CV for
data which may contain negative as well as positive values?
If so, I'd be grateful to be told about it. If not, can
anybody point me to an authoritative statement limiting the
use of CV?
Please remember that allstat policy is that replies to a query
should go to the sender rather than to the list. So please
respond to me, and I'll try to summarise to the list in due
course.
Thanks
Eryl Bassett
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