Re: Statistical test for equality ?

[ghaverla]

I threw in a blurb early in this, and watched this thread grow.

You can't use statistics to prove or disprove anything.  You can assign
probabilities (which may themselves have error) to decisions.  People
may at some point decide the probability is close enough to 0 or 1 to
prove a fact.

I lived a highly unlikely event.  I had a room to work out of at the
university in my B.Sc in my latter years.  One day, my sister who was
on campus at the time, came to visit and have a coffee.  I was working
away on an assignment, and my sister wanted a stir stick to incorporate
the chemical whitener in her coffee.  So, I took a clean stir stick
from the box next to me (I don't remember why it wasn't next to the
coffee machine, I didn't use whitener) and through it towards her.  She
tried to catch it, and missed.  That stir stick ended up very close to
the center of her cup of coffee, standing straight up.  Zero horizontal
momentum.  It stood up in the center for at least a minute.  To my
sister, it was just a freak event.  I had been studying quite a lot of
statistics, and realized just how rare an event that was.

There are libraries that will do math with variables defined as ranges,
not values.  There are rules about propagation of error, where are of
enough importance in physics, that a physicist wrote the Perl module
Number::WithError.  And this properly propagates error through most
problems, allowing for the fact that these calculations will have
roundoff error of their own, and depending on the calculation in
question, the final estimate of error may be largely due to roundoff in
attempting to propagate the error.

I don't do economics problems, my bank does economics problems on me.
You pay some programmer $2000 for some action which happens millions of
times, and you charge me $0.50  every time you do this?  Banks don't
operate now as banks operated originally.  Not your problem.

You need to choose reasonable random number generators for solving any
problem of a stochastic nature.  Totally unrelated to your problem, do
NOT use a RNG which draws from /dev/random to examine your problem.
Perl has a Mersenne Twister replacement to rand, which works fine (it
has a LONG period).

Most of the world thinks Gaussian is Normal.  Gaussian is not
normal, Gaussian is just common. If you have reason to believe the
inputs to your problem are close to Guassian, try testing them with a
Cauchy RNG.  A Cauchy PDF has undefined variance (infinite).

Gord