"People have erroneous intuitions about the laws of chance. In particular, they regard a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. The prevalence of the belief and its unfortunate consequences for psychological research are illustrated by the responses of professional psychologists to a questionnaire concerning research decisions." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"Significance levels are usually computed and reported, but power and confidence limits are not. Perhaps they should be." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"The emphasis on significance levels tends to obscure a fundamental distinction between the size of an effect and its statistical significance." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"[...] the statistical power of many psychological studies is ridiculously low. This is a self-defeating practice: it makes for frustrated scientists and inefficient research. The investigator who tests a valid hypothesis but fails to obtain significant results cannot help but regard nature as untrustworthy or even hostile." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"[...] too many users of the analysis of variance seem to regard the reaching of a mediocre level of significance as more important than any descriptive specification of the underlying averages Our thesis is that people have strong intuitions about random sampling; that these intuitions are wrong in fundamental respects; that these intuitions are shared by naive subjects and by trained scientists; and that they are applied with unfortunate consequences in the course of scientific inquiry. We submit that people view a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. Consequently, they expect any two samples drawn from a particular population to be more similar to one another and to the population than sampling theory predicts, at least for small samples." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1071)
"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." (Amos Tversky & Daniel Kahneman, "Judgment Under Uncertainty: Heuristics and Biases", Science Vol. 185 (4157), 1974)
"Intuitive judgments of probability are based on a limited
number of heuristics that are usually effective but sometimes lead to severe
and systematic errors. Research shows, for example, that people judge the
probability of a hypothesis by the degree to which it represents the evidence,
with little or no regard for its prior probability. Other heuristics lead to an
overestimation of the probabilities of highly available or salient events, and
to overconfidence in the assessment of subjective probability distributions.
These biases are not readily corrected, and they are shared by both naive and
statistically sophisticated subjects." (Amos Tversky, "Assessing Uncertainty", Journal
of the Royal Statistical Society B Vol. 36 (2), 1974)
"The theory of expected utility is formulated in terms of an abstract set of consequences, that are the carriers of utilities. The axiomatic theory, by its very nature, leaves the consequences uninterpreted. Any application of the theory, of course, is based on a particular interpretation of the outcomes. Thus, the theory could be valid in one interpretation and invalid in another. The appropriateness of the interpretation, however, cannot be evaluated within the theory." (Amos Tversky, "A Critique of Expected Utility Theory: Descriptive and Normative Considerations", Erkenntnis Vol. 9 (2), 1975)
"A significant property of the value function, called loss
aversion, is that the response to losses is more extreme than the response to
gains. The common reluctance to accept a fair bet on the toss of a coin suggests
that the displeasure of losing a sum of money exceeds the pleasure of winning
the same amount. Thus the proposed value function is (i) defined on gains and
losses, (ii) generally concave for gains and convex for losses, and (iii)
steeper for losses than for gains."
"An essential condition for a theory of choice that claims
normative status is the principle of invariance: different representations of
the same choice problem should yield the same preference. That is, the
preference between options should be independent of their description. Two
characterizations that the decision maker, on reflection, would view as
alternative descriptions of the same problem should lead to the same
choice-even without the benefit of such reflection."
"Effective learning takes place only under certain
conditions: it requires accurate and immediate feedback about the relation
between the situational conditions and the appropriate response. The necessary
feedback is often lacking for the decisions made by managers, entrepreneurs,
and politicians because (i) outcomes are commonly delayed and not easily attributable
to a particular action; (ii) variability in the environment degrades the
reliability of the feedback, especially where outcomes of low probability are
involved; (iii) there is often no information about what the outcome would have
been if another decision had been taken; and (iv) most important decisions are
unique and therefore provide little opportunity for learning."
"The modern theory of decision making under risk emerged from a logical analysis of games of chance rather than from a psychological analysis of risk and value. The theory was conceived as a normative model of an idealized decision maker, not as a description of the behavior of real people." (Amos Tversky & Daniel Kahneman, "Rational Choice and the Framing of Decisions", The Journal of Business Vol. 59 (4), 1986)
"The assumption of rationality has a favored position in
economics. It is accorded all the methodological privileges of a self-evident
truth, a reasonable idealization, a tautology, and a null hypothesis. Each of these
interpretations either puts the hypothesis of rational action beyond question
or places the burden of proof squarely on any alternative analysis of belief
and choice. The advantage of the rational model is compounded because no other
theory of judgment and decision can ever match it in scope, power, and
simplicity."
"Theories of choice are at best approximate and incomplete. One reason for this pessimistic assessment is that choice is a constructive and contingent process. When faced with a complex problem, people employ a variety of heuristic procedures in order to simplify the representation and the evaluation of prospects. These procedures include computational shortcuts and editing operations, such as eliminating common components and discarding nonessential differences. The heuristics of choice do not readily lend themselves to formal analysis because their application depends on the formulation of the problem, the method of elicitation, and the context of choice." (Amos Tversky & Daniel Kahneman, "Advances in Prospect Theory: Cumulative Representation of Uncertainty" [in "Choices, Values, and Frames"], 2000)
"Whenever there is a simple error that most laymen fall for, there is always a slightly more sophisticated version of the same problem that experts fall for." (Amos Tversky)
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