In article <[EMAIL PROTECTED]>,
Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote:
>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?
There is plenty of evidence that humans have a poor
understanding of probability. In one study of the
behavior, college students exposed to decision problems in
which a probability of 1/4 (four clearly equally likely
alternatives) was involved, their behavior corresponded to
treating it as about .2. When it comes to smaller ones,
it is even worse.
>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.
Very definitely so. They do not expect anywhere near the
lack of uniformity.
>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.
This is because they consider getting red fifty times in a
row to be on the order of 1/50 the probability of read.
They cannot handle rare events at all. In fact, can we
do it correctly without computing? Intuition is VERY
dangerous.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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