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Topic: ABS Streaky Behavior
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KINGB@WCSUB.CTSTATEU.EDU

Posts: 144
Registered: 12/6/04
ABS Streaky Behavior
Posted: Dec 28, 1996 8:17 AM
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ABS "Streaky Behavior: Runs in Binomial Trials" activity (_Student
Guide_, p.65):

There are lots of interesting things about this activity. Although
(a) Length_Of_Longest_Run

is the easiest variable to use to try to discriminate between the two
sequences of Hs and Ts in the _Student Guide_ (p.66), my students have
suggested at least two others:
(b) Average_Run_Length
and
(c) Number_Of_Runs.

So I wrote a Minitab macro (a local macro, which runs in Release 11, if
anyone wants it) that can be used to simulate, say, 100 experiments
consisting of 200 flips of a fair coin. (The macro is quite slow, but
you can be doing something else while it's running.) It outputs
histograms for all three variables mentioned above. And when you compare
the values of these variables for the two sequences in the _Student
Guide_ with the histograms, it not only becomes obvious which sequence is
the human-generated one, but it also becomes pretty obvious which of the
three variables seems to best discriminate between these two sequences.
(I don't think I want to claim yet that (a) is the best discriminator in
general.)

For the record, here are the values of these variables for the two
sequences in SGWW:

Sequence (a) (b) (c)

1 9 2.04 98

2 4 1.88 106

(Incidentally, the second sequence, as printed in the _Student Guide_,
has only 199 flips.)

One other thing: One evening, I asked my students to write for the next
class 200 Hs and Ts "at random". For the few who actually did it, the
value of (a) was never as low as 4, although their values for (a) tended
to be lower than those generated by my macro. In other words, I don't
think you can depend on human-generated sequences to have values of (a)
as low as 4 very often.

==============================================
Bruce King
Department of Mathematics and Computer Science
Western Connecticut State University
181 White Street
Danbury, CT 06810
(kingb@wcsu.ctstateu.edu)





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