[From Rick Marken (941115.2220)]
Bruce Abbott (941115.1830 EST) --
O.K., let's try geometry:
Oh god, no. Not GEOMETRY.
Apparently the laws of probability, the ones that make p = 0.50 in all
these scenarios according to your calculations, are DIFFERENT in
California than they are here in Indiana....?
I sure hope so.
Must be some strange new way of defining "better" and "worse."
Why don't you give my way a try? Use:
Nutrient Rate of Change Before a Tumble - Nutrient Rate of Change
After a Tumble. Positive is better, negative is worse. Notice that
Nutrient Rate of Change is what is being compared, not Nutrient
Level.
OK. I ran a simulation where I determined the probability that
Nutrient Rate of Change (dNut in your program) is better (or worse)
after a tumble. If dNut was negative before the tumble and positive
after then Nutrient Rate of Change got better; my estimate of the
probability of this happening (over 2560 instances in which dNut was
negative before the tumble) was .48. If dNut was positive before the
tumble and negative after then Nutrient Rate of Change got worse; my
estimate of the probability of this happening (over 2440 instances in
which dNut was positive before the tumble) was .52. So the actual
probability of Nutrient Rate of Change getting better after a tumble was
slightly less than .5; given more samples I think we could have pulled
it up to chance. And the probability of Nutrient Rate of Change getting
worse was actually better than chance.
These are not the kind of results that encourage one to believe that
reinforcements (a positive change in Nutrient Rate of Change after a
tumble) can shape behavior.
You know. I'm gettin' the impression that you might be one of those
aliens yourself. You seem to attribute rather remakable powers to
random consequences of behavior. Maybe you've just been in Indiana
too long. Be careful, now. Look what happened to B.F. Skinner and
Dan Quayle.
Best
California Rick