write:Hereagain intuitive judgments are dominated by the sample proportion and areessentially unaffected by the size of the sample which plays a crucial rolein the determination of the

the correct posterior odds are 8 to 1 for the 4:1 sampleand 16 to 1 for the 12:8 sample
assuming equal prior probabilities.However
most people feel that the first sample provides much strongerevidence for the hypothesis that the urn is predominantly red
because theproportion of red balls is larger in the first than in the second sample. Hereagain
intuitive judgments are dominated by the sample proportion and areessentially unaffected by the size of the sample
which plays a crucial rolein the determination of the actual posterior odds.5 In addition
intuitiveestimates of posterior odds are far less extreme than the correct values.The underestimation of the impact of evidence has been observedrepeatedly in problems of this type.6 It has been labeled “conservatism.”Misconceptions of chance. People expect that a sequence of eventsgenerated by a random process will represent the essential characteristicsof that process even when the sequence is short. In considering tosses ofa coin for heads or tails
for example
people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T- [enc. IT-T
which doesnot appear random
and also more likely than the sequence H-H-H-H-T-H
which does not represent the fairness of the coin.7 Thus
people expectthat the essential characteristics of the process will be represented
notonly globally in the entire sequence
but also locally in each of its parts. Alocally representative sequence
however
deviates systematically fromchance expectation: it contains too many alternations and too few runs.Another consequence of the belief in local representativeness is the well-known gambler’s fallacy. After observing a long run of red on the roulettewheel
for example
most people erroneously believe that black is now due
presumably because the occurrence of black will result in a morerepresentative sequence than the occurrence of an additional red. Chanceis commonly viewed as a self-correcting process in which a deviation inone direction induces a deviation in the opposite direction to restore theequilibrium. In fact
deviations are not “corrected” as a chance processunfolds
they are merely diluted.Misconceptions of chance are not limited to naive subjects. A study ofthe statistical intuitions of experienced research psychologists8 revealed alingering belief in what may be called the “law of small numbers
” accordingto which even small samples are highly representative of the populationsfrom which they are drawn. The responses of these investigators reflectedthe expectation that a valid hypothesis about a population will be