From: lambert@spectrum.cs.unsw.oz.au (Tim Lambert)
Subject: Re: Statistical Analysis
Organization: CS&E, Uni of NSW, Australia
	<LAMBERT.92Dec16015617@nankeen.spectrum.cs.unsw.oz.au>
	<1992Dec16.000630.27853@mtu.edu>
Date: Thu, 17 Dec 1992 16:56:13 GMT

>>>>> On Wed, 16 Dec 1992 00:06:30 GMT, cescript@mtu.edu (Charles Scripter) said:
> (Tim Lambert) writes:

>> I have provided cites, data and extensive analysis to support my
>> claims and refuted all objections raised.  I don't see the point of
>> repeating it in every post.

> Your refutatation of my last objection must not have made it to the U.S.

I've appended it below.

>> Since you`re the one who confused "fitted parameter" with "degree of
>> freedom of a chi-square statistic" and persisted in your error even

> In your notation, is "degree of freedom" identical to "degree of
> freedom of a chi-square statistic"?

No, could be degree of freedom in a t statistic.  However. I said
"degree of freedom in a chi-square statistic", so there is no excuse
for confusion.

> Where I come from "degree of freedom" refers to the the number of
> dimensions required to span the space (which translates to the number
> of fitted parameters in a least square fit).  And you *were* claiming
> you used "19 degrees of freedom"...

> None of the Mathematicians or Physicists I know could figure out what
> you were doing, either.

> [maybe it was your non-standard notation. You should avoid using slang ;-]

Try looking up "degree of freedom" in a statistics book, or an
encyclopedia of science or mathematics.

>>>>> On Sun, 18 Oct 1992 22:03:09 GMT, cescript@mtu.edu (Charles Scripter) said:
>> > lambert@spectrum.cs.unsw.oz.au (Tim Lambert) writes:
>> Very amusing, but that's 20 or 30 FITTED PARAMETERS to fit the
>> elephant.  My 19 df are the degrees of freedom in the DATA, which
>                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

> Here's a good way to confuse everyone on the net.  In the real world,
> data are numbers/events; They are fixed, so talking about 'degrees of
> freedom in the DATA" is contradictory.  The minute you refer to 19
> degrees of freedom, every scientist on the network will immediately
> understand that you are fitting with 19 unresolved constants.  To them, you
> have defined the number of degrees of freedom necessary to span the space.

I'm sorry to confuse you but there really is no way to refer to the
degrees of freedom of a Chi square statistic without using the phrase
"degrees of freedom".  I suggest you consult an elementary book on
statistics and look in the index under Chi square.  I hope that will
clear up your misconception that "'degrees of freedom in the data' is
contradictory.

>> >> >> data values less two fitted parameters) in the Chi square statistic.
>>                        ^^^^^^^^^^^^^^^^^^^^^^
>> >> >> Should I have use 18 df?

>> The evidence that there were but two fitted parameters is underlined
>> above.  You've quoted it twice now.

> But as you see, immediately after mentioning 2 fitted parameters, to
> mentioned 18 degrees of freedom (i.e. 18 parameters to scientists).

I should hope that any scientist worthy of the name would know some
very basic statistics and know what degrees of freedom means in a
statistical context.  Even one who didn't should have noted the
unfamiliar phrase "Chi square statistic" and tried to determine what
it meant before making unfounded assertions about pachyderms.  And
even one who didn't do this should have noticed that it said TWO
PARAMETERS and not posted something asserting that there were 18.

>> If you have some substantive basis for your suspicions, please inform us.

> I will pose the opposite question:  Why should I trust your results?
> This is the way *science* is done.  You propose a theory, and *prove*
> the results.  This means that the author must give convincing evidence,
> and eliminate cause for disbelief in your results (i.e. show that your
> opponents questions of the validity of your data/results are without
> basis).

This is Usenet, not a journal article.  In a journal article, one must
answer all possible objections, since the reader has no easy way to
raise objections with the author.  If you have some substantive
objection or alternative model you only have to post or mail me.

>   Merely stating the chi-squared of your fit does not constitute
> "convincing evidence".  A good start would be to show that *NO OTHER*
> model describes the system as well as your model (this is where you
> can apply your chi-squared arguments...).

This is an absurd requirement.  There are an infinite number of
alternative models, including ones with 21 parameters that will fit
the data perfectly and an elephant pretty well.  I *have* compared it
with a "gradual decline starting before gun control" model and shown
that it gives a better fit.

> My suspicions are based on the fact that I have met very few
> staticians whose results I would trust.  And you and I both know that
> if someone wishes to make their data say something particular, that
> the statistics can be "fudged", via the equation and fitting technique,
> in such a way that it will say exactly what one wants.

Such fudging can easily be exposed by anyone who knows something about
statistics.  If I have "fudged" the statistics I think someone would
have pointed it out by now.

> I see in another post you give your model(s):

>>11*a = 25.6
>>10*b = 14.9

> But you do not give the errors on your experimental data.  It's quite
> possible that once I assign error bars to your data that I can draw a
> straight line through all of points.  (and deviations of 2-3 times the
> standard deviation are not unusual in experiments with low statistics).

> Here, let's pretend I'm a Nuclear Physicist... (so I can get error bars)

> 11*a = 25.6 +/- sqrt(25.6)  ;  a=2.33 +/- 0.46  ;  1.87 < a < 2.79
> 10*b = 14.9 +/- sqrt(14.9)  ;  b=1.49 +/- 0.39  ;  1.10 < b < 1.88

> Examining these two systems, we can trivially see that "a" and "b"
> are indistinguishable.  QED  ;-)

As a case in point, we can easily see how Charles has fudged the
statistics here to prove that `a' and `b' are not significantly
different.  He just made up some errors out of thin air.  Since he got
to control how big his made up errors were, it is not suprising that
he got the answer he did.

The more conventional way to test if `a' and `b' are different is
called a t-test.  I'll just present the numbers and leave it as an
exercise to the reader to perform the computation.

1910-1920 rates (before) 2.6 2.7 2.4 2.1 2.4 2.6 2.1 1.9 1.4 2.7 2.7
1921-1930 rates (after)  1.8 1.6 1.0 0.9 1.1 1.6 1.6 1.9 1.7 1.7

Tim

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