From: lambert@spectrum.cs.unsw.oz.au (Tim Lambert)
Subject: Re: A Coffee-House Conversation with an Imaginary Nadja
Organization: CS&E, Uni of NSW, Australia
	<LAMBERT.92Dec14105324@nankeen.spectrum.cs.unsw.oz.au>
	<1992Dec15.225149.26113@mtu.edu>
Date: Thu, 17 Dec 1992 16:09:05 GMT

>>>>> On Tue, 15 Dec 1992 22:51:49 GMT, cescript@mtu.edu (Charles Scripter) said:
> (Tim Lambert) writes:

>>(Peter K. Boucher) 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.

>> 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.  My statement is completely wrong.  I
should have said one chance in twelve.  If the numbers are
independant, all 4!=24 orderings are equally likely. One ordering is
increasing and one is decreasing.  (Choosing a random number between
-Inf and +Inf, is an any event impossible.)

> 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.

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

>> Your "trend" is nothing more than random fluctuations.

> Perhaps, but it only has a 4% probability of occuring.

Yes, but given any sequence of four numbers, the pattern of ups and
downs that occurs has only a 4% chance of occuring.  We really need to
decide in advance which patterns are "intersesting".  In this case,
four increasing numbers, or four decreasing numbers, or six numbers
increasing except for one dip, or decreasing excpet for one hump....
are all "interesting" and we need to consider the possibility of
chance producing any one of them.

>> You can read the article I cited for a proper statistical analysis.

> I have yet to see you perform proper statistical analysis on your postings.

<Sigh>.  Very well, let us apply a statistical test to see if Kennesaw
burglaries were increasing before the law.

Here is the sequence:
41 21 22 35 35 54

I computed a Spearman rank correlation for this sequence (If the
sequence increased monotonically this would be 1.)  The result was
0.40, so you could say that there was un upward trend.  However,
chance would produce a value this large 42% of the time, so this
result is NOT statistically significant.

What about after the law?
35 35 29 32 70

Spearman rank correlation is 0.15, with p=.80.  No significant trend
here either.

Tim