One of the original questions on this thread had to do with the origin of the
".05" cutoff. I suggested that if naive subjects were placed in a situation in
which they had to detect whether a coin was fair or not, it would correspond
closely to the commonly used .05 level. I just did it with 65 naive subjects
(Intro Psych - mostly freshmen). Three were discarded for not following
instructions or having unreadable answers. I flipped a double-headed coin 10
times, and subjects indicated where in the sequence of Heads they would challenge
the fairness of the coin. The results are as follows - expressed as % and
cumulative % of the 63 I scored.
AFTER this This % of my
number of sample challenged
Heads: fairness: Cumulative %
1 0 0
2 1.61 1.61
3 11.29 12.90
4 22.58 35.48
5 25.81 61.29
6 24.19 85.48
7 9.68 95.16
8 3.23 98.39
9 1.61 100.00
10 0 100.00
-----------------------------------------
>From the binomial, 5 heads in 5 flips is .031, 6 heads in 6 flips is .016. So, a
majority challenged after I got 5 heads in a row.
I suggested that the .05 may be rooted in human cognitive heuristics that evolved
to serve everyday decision making - such as catching cheaters (as opposed to
formal statistical trainig). "Evolutionary psychologists" have marshalled quite a
bit of evidence that many of our cognitive abilities (including deductive logic)
did not evolve "context-free" but to meet the needs people in everyday decisions
. It's a speculative, but not unreasonable, hypothesis.
I learned a few things doing the demo. Because these were my students, they
expressed great reluctance challenging the coin I suggested was fair. After I
detected their reluctance I toned down the "challenge" language and simply asked
them to indicate where in the sequence you'd suspect a non-fair coin. It would be
fun (but alot of work) to have both heads and tails drawn - but in different
proportions. There are a host of other contextual features (including the cost of
making a Type I vs. Type II error) that should matter too.
--
---------------------------------------------------------------
John W. Kulig [EMAIL PROTECTED]
Department of Psychology http://oz.plymouth.edu/~kulig
Plymouth State College tel: (603) 535-2468
Plymouth NH USA 03264 fax: (603) 535-2412
---------------------------------------------------------------
"What a man often sees he does not wonder at, although he knows
not why it happens; if something occurs which he has not seen before,
he thinks it is a marvel" - Cicero.
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