From: cescript@mtu.edu (Charles Scripter)
Subject: Re: A Coffee-House Conversation with an Imaginary Nadja
Organization: Michigan Technological University
Date: Sat, 19 Dec 1992 23:11:32 GMT

In article <LAMBERT.92Dec18020905@nankeen.spectrum.cs.unsw.oz.au>,
lambert@spectrum.cs.unsw.oz.au (Tim Lambert) writes:

> >>>>> On Tue, 15 Dec 1992 22:51:49 GMT, cescript@mtu.edu
> (Charles Scripter) said:
> > (Tim Lambert) writes:
> >> I understand perfectly well how you can manufacture a trend by
> >> creative data selection.
> 
> > I'm sure you do know this, *you* manufacture trends all the time.
> 
> Oh, really?  Provide ONE example where I have done this.

Using the data from a recent posting of yours:

>From: lambert@spectrum.cs.unsw.oz.au (Tim Lambert)
>Subject: Re: Statistical Analysis
>In-Reply-To: cescript@mtu.edu's message of Wed, 16 Dec 1992 00:06:30 GMT
>Message-ID: <LAMBERT.92Dec18025613@nankeen.spectrum.cs.unsw.oz.au>
>
> 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

You have manufactured a trend where a law "caused a decrease in the
crime rate"...  (the original article was a couple months back, so
I can't post the full text of Tim's claim).

See my response to the referenced article for more details.

> >> If you take four successive random numbers
> >> there is one chance in eight that they will form an ancreasing or
> >> decreasing sequence.
> 
> > This depends on the limits of your random numbers.  If you allow any
> > number between -Inf and +Inf, then the probability that your new number
> > will be greater than the previous is 0.5 (it's not obvious that this will
> > be true if you limit yourself to the natural numbers or positive reals).
> 
> Far too generous, Charles.

Perhaps you misunderstand.  The probability of choosing the 1st number
between -Inf and +Inf is 1.0, the probability of choosing the 2nd number
higher than the 1st is 0.5, and so on.  The total probability is the
product of the individual probabilities.

The reason this is true, is that the ordinality of each set,
"greater than" and "less than" the chosen 1st number "X", is equal.
Since every number is equally likely, and there are as many numbers
"> X", as "< X", the probability of the new number being higher is 1/2
(NOTE:  Only true, in general, for an infinite set!)

> (Choosing a random number between -Inf and +Inf, is an any event
> impossible.)

Wrong again, Tim.  Provide a counter-example where your random number
does *NOT* lie between -Inf and +Inf.  ;->  (Ho Ho Ho!...)

I assume you meant to say the the set of numbers accessible to us is
restricted to a finite number (which is exactly what I said in my
previous posting!).
 
> > If you reduce the available numbers to something finite, this is no longer
> > true, as the sets differ greatly in size.  You no longer have your nice
> > equal probabilities, and need to be more clever.  You can demonstrate this
> > easily by rolling a 100 sided dice (or write a program to give 4 random
> > numbers).  In fact, if you do this using random numbers between
> > 0.0 =< N < 1.0, you will find that it's more like a ~4% chance.
> 
> To be precise: 1/24 regardless of distribution, if ties are not possible.

Do you intend this solution only for 0.0 =< N < 1.0?  I disagree that
it is "precise", as you *MUST* worry about the granularity of your
numbers.  The example I provided is granular at the level of a REAL*4,
fine enough for real world applications, but too grainy for claiming
precise solutions.  You must work up a more general solution; Try
working one up for the integers 0,1,2,3,4,5 and then generalize it. 

> > Don't take my word for it, try it for yourself (obviously Fortran):
> > [FORTRAN with evil assault goto deleted]

Hehehehehe!!  Couldn't resist putting a GOTO in there!....  ;-)

-- 
Charles Scripter   *   cescript@phy.mtu.edu
Dept of Physics, Michigan Technological University, Houghton, MI 49931
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