At 11:23 PM 3/2/00 -0700, you wrote:
>From: Brian D Harper
><<mailto:bharper@postbox.acs.ohio-state.edu>bharper@postbox.acs.ohio-state.edu>
> > Seriously, it seems obvious to me that the agreement suggested above
> > between supposed
> > random numbers would be sufficient proof that they are not random. Random
> > means without
> > pattern. If two lists agree, this establishes a pattern. What am I
>missing?
> > Could you possibly fill in
> > some details of Woodmorappe' analysis for those of us who do not have
> > access to the book?
>
>He used to a common random number generator used in scientific circles. The
>lists of number were generated separately. The agreements were to the same
>accuracy to which radiometric dates are commonly found. I loaned the book
>to a friend so I don't have it in front of me at the moment. However I
>believe that two numbers were considered in agreement if they were within a
>percentage of error common with radiometric dating accuracy. For instance,
>assuming an accuracy of 0.15% then 256813 +/- 385 is in agreement with
>256600 +/- 384.
>
>Not every number in the list agrees. But he found that the first agreement
>occurred within the first 20 to 30 number pairs from each list by comparing
>pair by pair down the list. Other agreements occurred randomly throughout
>the rest of the lists.
Thanks for this clarification. The puzzling thing for me is why his readers
are not skeptical enough about this seemingly extraordinary result to
check it. Its easy to do. For simplicity, I generated two lists of numbers
with three digits each. I chose three because in the above one has to get the
first three correct. Then I went through and compared the lists. The closest
agreement within the first 30 rows was 3%. I had to go through 332 rows
before getting a match to within 1 in the last number (i.e. 886 vs 885). I
did not
get a match in all three digits even after 1000 rows.
So, did Woodmorappe actually get a match within the first 30? Perhaps, but if
so it just illustrates the danger in basing a statistical conclusion upon a
single experiment.
Another puzzling thing is why Woodmorappe even bothers with doing this
experiment. The statistics of the situation is very simple. What is the
probability of getting the same three digits after 30 trials? About 0.03.
So, even if Woodmorappe did this little experiment, it is meaningless since
his result is not typical of what one should expect.
Of course, the another obvious question to ask is why allow 30 trials
instead of one? In the situation we are modeling, one gets only one
chance for agreement. This chance is, of course, 0.001 to get the first
three digits correctly. Since this number is so easy to calculate, why
bother comparing tables of random numbers?
Sidelight: I haven't shown the details of the calculation of 0.03 above
as this number is not quite as easy to compute as the case when
there is only one trial. Let me just say that it is not as easy as multiplying
the number of trials times the probability of success in one trial.
If this were the case one would have 100% certainty of getting a match
within 1000 trials, which we all know is not the case. In fact, I didn't get
a match in the first 1000 trials in my little experiment.
Final conclusion: Woodmorappe is simply wrong. One cannot dismiss the
agreement between different measuring methods in such a trivial manner.
Do you agree?
Brian Harper | "If you don't understand
Associate Professor | something and want to
Applied Mechanics | sound profound, use the
The Ohio State University | word 'entropy'"
| -- Morrowitz
This archive was generated by hypermail 2b29 : Fri Mar 03 2000 - 17:52:31 EST