ERRORS OF JUDGMENT AND CHOICE ---- Episode 4

               OUR ERRONEOUS MODES OF REASONING 

   Misconceptions of chance.   People expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short. In considering tosses of a 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-T-T, which does not appear random, and also more likely than the sequence H-H-H-H-T-H, which does not represent the fairness of the coin. Thus, people expect that the essential characteristics of the process will be represented, not only globally in the entire sequence, but also locally in each of its parts. A locally representative sequence, however, deviates systematically from chance expectation : it contains too many alterations 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 roulette wheel, for example, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red. Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. IN FACT, DEVIATIONS ARE NOT "CORRECTED" AS A CHANCE PROCESS UNFOLDS, THEY ARE MERELY DILUTED. 

Misconceptions of chance are not limited to naive subjects. A study of the statistical intuitions of experienced research psychologists revealed a lingering belief in what may be called "the law of small numbers," according to which small samples are highly representative of the populations from which they are drawn. The responses of these investigators reflected the expectation that a valid hypothesis about a population will be represented by a statistically significant result in a sample with little regard for its size. As a consequence, the researchers put too much faith in the results of small samples and grossly overestimated the replicability of such results. In the actual conduct of research, this bias leads to the selection of samples of inadequate size and to the over-interpretation of findings. 

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