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 (firstname.lastname@example.org)