Re: t-distribution, was Geiger ...

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

John Denker wrote:

> ... I'm not sure the Geiger counter is the best pedagogical approach.  Unlike
> drawing numbers from an urn, where the numbers are imagined to pre-exist,
> the Geiger-counter numbers are themselves some sort of average of a
> statistical process.  This complicates the terminology (what "mean" are you
> talking about?  which "process" are you talking about?) and makes the
> concepts look more complicated than they really are.  And Geiger tubes (and
> radioactive sources) are not available to the typical science teacher.
>
> Following the spirit of Gosset, why not just do a Monte Carlo with a
> spreadsheet?  That's available to the typical science teacher.

As far as I can see, the Geiger counter is a very good instrument to produce
rally random events, even when nothing is known about the source causing
the clicking. We were very successful here in demonstrating the Binomial,
Pascal and Student's distributions. The histogram of experimental t-values
(for 60000 counts used to create 20000 samples of size 3) agrees with the
Student's distribution very well, as far away from the center as 9 standard
deviations, under each tail. After that numbers of occurrences become
single digits (for 20000 samples). Amazing. A Cauchy distribution
(samples of size 2), for which the standard deviation is infinity, can also
be observed with experimentally measured numbers of counts.

In my mind a Monte Carlo simulation belongs to theory. A validation of
something by the Monte Carlo method is not equivalent, at least in principle,
to a validation by experiments. Drawing tickets from an urn is an experiment,
producing them with with pseudorandom numbers is not. Yes, I know that
the outcomes are indistinguishable but a line between theory and experiments
has to be drawn somewhere.