Re: Goodness of fit measures for a distribution


Aleks Jakulin wrote:
> Reef Fish wrote:
> > Chi-square is based on histograms -- it's worthless.
> >
> > Kolmogorov uses on ONE POINT in the difference between the
empirical
> > and theoretical cdfs, the point of maximum departure.
> >
> > Your EYEBALLS can do an infinitely better job than that, looking at
> > the plot of the entire cdfs.
>
> In principle yes.

In principle AND in practice.

Here is a very simple PRINCIPLE. If something is INAPPROPRITE for
1 (ONE) <such as a histogram>, it's inappropriate for the other 999
of a thousand also.


> But what do you do when you have a few dozen or
> hundred variables in a complex data mining task?

You should mine more carefully and delicately than running a steam-
roller over all of them when more delicate tools are required.

When you have a few thousand variables, the first task is to
selectively consider ONLY a few dozen, if that many, that seem
most appropriate, for substantive reasons.


> Then you do want a one-number summary: you have no time to manually
> inspect a few hundred thousand QQ plots.

It's easy to do a one number summary. Just generate one RANDOM NUMBER,
and say "that's what the 'puter gave me!" And that number is probably
as meaningful <or meaningless> as your single number from GIGO
(Garbage In, Garbage Out).

What you have argued is in fact the WORST that has happened to the
application of statistics -- when computer programs and packages
are readily availble for any Tom, ***, and Harry to throw data
into the bin to get some meanless and useless number(s) out.

Progress takes 10 steps backwards.

-- Bob.


> mag. Aleks Jakulin
> http://kt.ijs.si/aleks/
> Department of Knowledge Technologies,
> Jozef Stefan Institute, Ljubljana, Slovenia.

.