1. Repetition I Attribution theory: ANOVA model of Kelley.
Ignoring relevant causes: Halos, anchors, consensus information.
Overestimation of irrelevant causes: Reassurance.
Fundamental attribution error.
Attributional asymmetry.
Problems of explanation by means of saliency.

2. Repetition II Causal reasoning in science
Confounding and hidden common causes prevent the inference of causes from observations.
Model of factor analysis is based on hidden (latent) common causes.
Experimental method as a possibility to prevent confounding and hidden com-mon causes by means of randomization and balancing.

3. Causal reasoning: Method
Conclusion: It is impossible to establish causal relations without doubt (David Hume).
Alternative Approach (Karl Popper):
Inferring causal relations is but a specific case of inductive inference.
Inductive inference cannot be justified.
Causal theories and assumptions can be tested.

4. Causal reasoning: Method
Assessing causal theories / assump-tions /models:
Causal models implicate pattern of cor-relations (that can be observed).
Specifically: Causal models implicate missing (conditional) correlations.

5. Causal reasoning: Method
Assessing causal theories / assump-tions /models:

6. Causal reasoning: Method
Assessing causal theories / assump-tions /models:
Important Problem: Equivalent causal models: Models the make the same predictions (or no predictions at all). X1 X3 X2 X4 X1 X3 X2 X4 X1 X3 X2 X4

7. Causal reasoning: Method
Principle of equivalent causal models: Unshielded collider rule
Arrows may be reoriented as long as no »unshielded collider« is destroyed or generated. X1 X3 X2 X4 X1 X3 X2 X4 X1 X3 X2 X4

8. Causal reasoning: Method
Example of equivalent causal models: The three variable moderator model

9. Causal reasoning: Method
Bad practice in causal modeling (as well as other branches):
Explorative models are termed as confirmatory in publications.

10. Simpson’s Paradox: Example 1
Death sentence
Group
Yes No 
%Yes
Yule’s Q
Black 59
2448
2507
2.4
-0.16
White 72
2185
2257
3.2
131
4633
4764

11. Simpson’s Paradox: Example 1
Color
Death sentence
Victim
Delinquent
Yes No 
%Yes
Yule’s Q
Black 11
2209
2220
0.5
1.00
White
111
0.0 48
239
287
16.7
0.71 72
2074
2146
3.4
131
4633
4764

12. Simpson’s paradox: Example 1: Paik Diagram
Blacks kill Blacks: 2220 vs 287.
Whites kill Whites: 2146 vs. 111.
Killing a Black is less risky than killing a White: 0.5% vs. 4.9%.

13. Simpson’s Paradox: Example 2
A psychologist has developed a new treatment for couples. She compares her new treatment with a conventional one in two small towns: Cow-city and Goat-town.
She gets the following results:

14. Simpson’s Paradox: Example 2
Successful 
Locality
Treatment
Yes No
% Success
Yule’s Q
Goat-town
New 20
180
200
10%
0.36
Old 5 95
100 5%
Cow-city 90 10
90%
0.50
150 50
75%
265
335
600

15. Simpson’s Paradox: Example 2
The new treatment turns out as being superior to the conven­tional one in both towns.
Enthusiastically our psychologist sends a report to the news­papers of both towns. The editor of the Cow-city News in­structs the volunteer who had to write a short article: »Present a single table only. Otherwise readers will be confused«.
Consequently the volunteer adds the data of both towns and gets the following result:

16. Simpson’s Paradox: Example 2
Successful 
Treatment
Yes No
% Success
Yule’s Q
New
110
190
300
37%
-0.30
Old
155
145
52%
265
335
600

17. Simpson’s Paradox: Example 2
Apparently, the new treatment is less successful than the conventional one: 37% vs. 52%. The volunteer writes a furious article: The nasty statistical tricks of the Psycho- lobby.

18. Simpson’s paradox: Example 2: Paik Diagram
The new therapy has been applied predomi nantly in Goat-town: 200 vs. 100.
The old therapy has been applied mostly in Cow-city: 200 vs. 100.
Overall Success rate in Cow-city higher than in Goat-town: 80% vs. 8.3%

19. Simpson’s Paradox: Example 3
An educationalist investigates in here Bachelor thesis the study success of male and female students at the University of Freecastle for two branches: Social work and psychology. She gets the following data:

20. Simpson’s Paradox: Example 3
Success
Field
Sex
Yes No 
% Success
Yules Q
Social work
Man
127 35
162
78%
-0.20
Woman 27 5 32
84%
Psychology 17 42 59
29%
-0.14 92
170
262
35%
263
252
515

21. Simpson’s Paradox: Example 3
Obviously, women are more successful in both fields:
84% vs. 78% in social work
35% vs. 29% in psychology.
The women’s representative of the Uni-versity would like to publish these results in ReflectUni, the journal of the University. In order to simplify the presentation she pools the results from the two branches and gets:

22. Simpson’s Paradox: Example 3
Success
Sex
Yes No 
% Success
Yules Q
Man
144 77
221
65%
0.47
Woman
119
175
294
40%
263
252
515

23. Simpson’s Paradox: Example 3
Obviously men are more successful than women (65% vs. 40%). The women’s representative writes a forceful article: Discrimination of women at the University of Freecastle.

24. Simpson’s paradox: Example 3: Paik Diagrams
Women study predomi- nately psychology: 262 vs. 59.
Men study predomi- nately psychology: 126 vs. 32.
Success rate in psychology is lower: 34.0% vs. 79.4%.

25. Simpson’s paradox: The problem of summing over variables in tables
When is it allowed to sum over vari-ables without changing the association between the variables in the resulting marginal table (i.e. associations are identical to those in the full table)?
The summation over a variable X does not change the associations between the remaining variables (in the marginal table) if X is associated with only one of the remaining variables.

26. Simpson’s paradox: The problem of summing over variables in tables
Lines denote associations
It is allowed to sum over variables X or Y but not over variable Z.

27. Simpson’s paradox: The problem of summing over variables in tables
Example death sentences:
It is not allowed to sum over any of the three variables.

28. Ecological Fallacy: Example
Treatment of clustered (grouped) data:
A study investigates the association between achievement and inclination to aggression in High School. The whole sample is made up of three different classes of a single school.

29. Ecological Fallacy: Example
Treatment of clustered (grouped) data:

30. Ecological Fallacy: Example
Treatment of clustered (grouped) data:
The clustered nature of the data can hide the correct relationship: The negative relation between aggression and achievement (within classes).
Thus, the clustered structure has to be taken into account.

31. Exercises:
Exercise 2-4, 2-5 & 2-6 (new manuscript).