Speaking of normal distributions and cancer clusters, does anybody (a)
agree with me that the human race in general has a better "feel" for the
normal distribution than the binomial distribution, and the Poisson is
still worse - and (b) know of any experimental evidence for this?
That is, my conjecture is that if an untrained human thinks that there
is an unusually large collection of tall people, or larger-than-usual
apples, or whatever, in a collection, they are probably right; but there
is a tendancy to expect more uniformity in Bernoulli and Poisson
processes than should be there. People tend to see clusters of things
and streaks of events when they are not really there.
There is probably a reverse trend in the extreme tail; people probably
overestimate the probability of getting (say) red fifty times in a row
at Roulette simply because we don't have a good feel for really large
and small numbers.
-Robert Dawson
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