1. Recapitulation I  Epistemic vs. instrumental rationality.  Problems of application of formal rules: e.g. Bayes Rule.  Hot vs. cold cognition:  Hot cognition: self-serving biases  Cold cognition: Biases due to cognitive mechanisms

2. Recapitulation II  Chapman & Chapman (1969):  People are unable to learn valid con- tingencies in the presence of invalid features.  People »see« non-existing relations.  Significance of (erroneous) personal theories.

3. 2. Contingency and Causality III  Cognitive mechanism: Subjective [plausible] folk theories.  Acquisition of subjective theories.  Cultural learning / tradition: Common sense.  Role of similarity.  Vagueness of subjective theories.  Barnum effect.

4. 2. Contingency and Causality III  Barnum (Forer) effect: Strategies:  Truisms.  Flattery.  Statements that are partly true.  Statements with restricting remarks.  The feeling to be seen through.  Problem of vague theories in psychology & neuro-psychology: E.g. »place neurons«, »mirror neurons«.

5. 2. Contingency and Causality IV  Pattern recognition capabilities: Observing patterns in random sequences:  Binary Sequences with shift probability of.50 are not regarded as random since they may contain longer regular subsequences.  Representativeness and randomness: Mini-theory about random sequences.  Belief in the Law of small numbers:

6. 2. Contingency and Causality V  Law of small numbers:  Overestimation of how well small samples resemble the population (they are drawn from)  Unjustified generalizability from small samples to populations.  Random processes as self-correcting: gambler’s fallacy [Erroneous conception of the nature of random processes].

7. 2. Contingency and Causality VI  Hot hand in Basketball:  Belief: A hit increases the probability of a subsequent hit (Similarly, a miss increases the probability of a further miss).  The belief is held up by professionals and ex- perts.  The belief in a hot hand is wrong: Neither the hot hand nor hot or cold nights do exist.  Sequences with a shift probability of.50 were not regarded as random.

8. 2. Contingency and Causality VII  Hot hand and Gambler’s fallacy:  Hot hand: Overestimation of small series of events of the same kind.  Gambler’s fallacy: Self correcting randomness.  Problem:  Hot hand: Belief in an increase of the probability for an event of the same kind.  Gambler’s fallacy: Self-correcting probability.

9. 2. Contingency and Causality VIII  Rationality of the Hot hand:  Is the belief in the Hot hand (instrumentally) rational?  Strategies based on the Hot hand might be rational (Maximizing the expected score of the team).  Confusion: Players with a high average score vs. players with a hot hand.

10. 2. Contingency and Causality IX  Rationality of the Gambler’s fallacy:  Is the belief in the Gambler’s fallacy (instrumentally) rational?  In everyday life there do not exist truly independent events. Rather, the probability of an event of the same kind decreases (due to limited resources).  The argument does not apply to gambles and lotteries where independence is nearly perfect.

11. 2.4 Regression to the mean  History of Science: Francis Galton.  Example: Results in subsequent tests.  Everyday examples:  Flight instructor  Explanations in sports and profession  Fairness toward members of disadvantaged groups

12. 2.4 Regression to the mean

13. 2.5 Information in cross tables  Information in contingency tables:  Information of cells is weighted differentially:(a) > (b) > (c) > (d) TreatmentSuccessNo success New method200 (a)75 (b) No treatment50 (c)15 (d)

14. 2.5 Information in cross tables Quick Assessment of  Quick assessment of direction of the relationship: a·d - b·c  Yules Q: Effect CausePresentAbsent Present(a)(b) Absent(c)(d)

15. 2.5 Information in cross tables A supplement of the Swiss newspaper »Tagesanzeiger« of December 2012 contained an article of Wiebke Toebelmann titled Was schon die Kräuterweiber wussten [What the herb women already knew]: »For example, at the University of Bern that disposes of a ho­meopathic research department it was found how effective na­turopathic treatments can be with respect to the treatment of children with an attention deficit syndrom (ADHS). The result of the study conducted was as follows: For 80 percent of the children with this illness the clinical picture was improved by means of an individually adjusted homeopathic treatment at a rate of 50 percent. The study that had been published already in 2005 has, how­ever, received not enough attention as complained by Klaus von Ammon, the chief of the homeopathy research« (translated by the author).