Re: Order being created from disorder?

[LUDWIK KOWALSKI <kowalskil@alpha.montclair.edu>]

Earlier today Ludwik asked:

> Would the "non-acceptable" conclusion drawn by Brian Whatcott change if
> all frequencies were multiplied by a large factor, such as 10000, to
> "improve statistical significance"?

That was a silly question; the probabilities f_r/sum(f_r) do not change 
when all frequencies are multiplied. The question should have been asked
differently. Can the discrepancies (between the values of D1 and D2, as
calculated by Brian, and our knowledge of the probability distribution) 
be due to statistical fluctuations in frequencies invented to represent 
real data. Here the value of the "large factor" does become important. 
A frequency of 4 (out of 10 throws) can be purely accidental but the 
frequency of 40000 (out of 100000 throws) can not fluctuate by more than 
about 1%. (To be pedantically correct the low level of fluctuations 
should have been matched by the number of digits in table 1, for example, 
probability=0.400 instead of 0.4, etc.)

Thus the Brian's question remains valid; we must assume that each 
realization involved a vary large number of throws. THE DIFFERENCE 
BETWEEN D1 AND D2 DOES NOT REFLECT THE OBVIOUS FACT THAT THE SECOND 
DISTRIBUTION OF OUTCOMES WAS VERY COMMON WHILE THE FIRST ONE WAS HIGHLY 
UNLIKELY. WHY IS THIS NOT REFLECTED IN SHANON'S ENTROPIES?
                                                         Ludwik kowalski