Re: Optimal seperability of distribution

newsgroupie2003@xxxxxxxx wrote:
> Hi,
> I have the following problem that I am not sure how to best go about.
> I have 2 populations (healthy and ill) and I then have a choice of
> different measurement methods to try and seperate them. The measurement
> is univariate.
> What is the best way of characterizing the separability between the
> healthy and sick populations?
>
> I was thinking of ROC curves summarized by the integral of the ROC
> curve, but i guess the problem is quite general in the sense that what
> is needed is measure of how well the 2 distributions are seperated.
> Any input appreciated!
>
> Best regards
> Soren

Unfortunately, there is no measure of separation that is best for all
situations. ROC plots preserve all the ordinal information but discard
all the interval information. The area under an ROC answers the
question "What is the probability that a randomly chosen score from
one population will exceed a randomly chosen score from the other
population?", but that addresses only one aspect of separation.
Before you choose a measure, you need to decide what you mean by
"separation".

.

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