1. Recapitulation I Epistemic vs. instrumental rationality.
Problems of application of formal rules or models:
Risk aversion example
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. Recapitulation 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. Recapitulation IV
Cognitive mechanism: Subjective [plausible] folk theories.
Psychology as a source of erroneous psychological theories:
Traumatic experiences are repressed.
People tend to incestuous behavior.
Acting out one’s aggression has a cathartic effect.

5. Recapitulation V
Cognitive mechanism: Subjective [plausible] folk theories.
Neuropsychology as a source of erroneous psychological theories:
We use only 10% of our brain.
»Mirror neurons« are the basis of empathic behavior.

6. Recapitulation VI 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 & neuropsychology: Localization of cognitive functions in the brain.

7. 2. Contingency and Causality X
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.
Required shift probability: about .6 to .7
Representativeness and randomness: Mini-theory about random sequences.
Belief in the Law of small numbers:

8. 2. Contingency and Causality XI
Law of small numbers:
Allusion to the »law of large 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].

9. 2. Contingency and Causality XII
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.

10. 2. Contingency and Causality XIII
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.

11. 2. Contingency and Causality XIV
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.

12. 2. Contingency and Causality XV
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.

13. 2.4 Regression to the mean I
History of Science: Francis Galton.
Extreme values of characteristics are not transferred from the parents to their children. For example, sons of very tall or very short fathers are predominantly of mean size.
Erroneous interpretation of results: Children’s characteristics are determined by parents as well as early ancestors.
Problem: The pattern was also found in the opposite direction.

14. 2.4 Regression to the mean II
Example: Results in subsequent tests.
A group of students has to take an exam with multiple choice questions.
After the test the upper and lower 10 percent (with respect to their scores in the test) are submitted to a second test compri­sing questions from the same pool of questions.
Result:
In general, students from the upper 10% will perform less well in the second test compared to the first round.
On the other hand, students from the lower 10% will, in general, get higher scores in the second test compared to the first one.

15. 2.4 Regression to the mean III
Everyday examples:
Daniel Kahneman: Flight instructor
Explanations in sports, profession and medicine
Fairness toward members of disadvantaged groups: Herrnstein & Murray (1994): Black students had privileged access to Colleges and Universities [This is no longer the case].

16. 2.4 Regression to the mean IV
Fairness toward members of disadvantaged groups:
Hypothesis of overachievement (Alan Zaslavsky): Black students with scores located in the upper range with respect to their own group but in the lower range with respect to the White candidates should reveal an excellent academic performance.
Regression to the mean: The academic development promoted Black students should be inferior to that of their White col­leagues

17. 2.4 Regression to the mean VI

18. 2.4 Regression to the mean V
Fairness toward members of disadvantaged groups: Results (Wainer & Brown, 2007):
46’000 students from 38 colleges: The SAT (Scolastic Aptitude Test) was used for predicting the HS-GPA (High School Grade Point Average).
A clear regression to mean was observed: Students from Asia as well as White students exhibited an increase of the HS-GPA with respect to SAT whereas for Black and Hispanic students a decrease was observed.
Same pattern for students of medicine.

19. 2.5 Information in cross tables I
Information in contingency tables:
Information of cells is weighted differentially:(a) > (b) > (c) > (d)
 Treatment
Success
No success
New method
200 (a)
75 (b)
No treatment
50 (c)
15 (d)

20. 2.5 Information in cross tables II
Effect
 Cause
Present
Absent
(a)
(b)
(c)
(d)
Quick assessment of direction of the relationship: a·d - b·c
Yules Q:

21. 2.5 Information in cross tables III
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).