Repetition I q Attribution theory q ANOVA model

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

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

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

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

Causal reasoning: Method q Assessing causal theories / assump tions /models:

Causal reasoning: Method q Assessing causal theories / assump tions /models: q Important Problem: Equivalent causal models: Models the make the same predictions (or no predictions at all). X 1 X 2 X 3 X 4 X 2 X 1 X 3 X 4 X 2 X 3 X 4

Causal reasoning: Method q Principle of equivalent causal models: Unshielded collider rule q Arrows may be reoriented as long as no » unshielded collider « is destroyed or generated. X 1 X 2 X 3 X 4 X 2 X 1 X 3 X 4 X 2 X 3 X 4

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

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

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

Simpson’s Paradox: Example 1 Color Victim Delinquent Black White Death sentence Yes No 11 2209 2220 0. 5 1. 00 0 111 0. 0 48 239 287 16. 7 0. 71 72 2074 2146 131 4633 4764 3. 4 %Yes Yule’s Q

Simpson’s paradox: Example 1: Paik Diagram q Blacks kill Blacks: 2220 vs 287. q Whites kill Whites: 2146 vs. 111. q Killing a Black is less risky than killing a White: 0. 5% vs. 4. 9%.

Simpson’s Paradox: Example 2 q 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. q She gets the following results:

Simpson’s Paradox: Example 2 Successful Locality Treatment Yes No % Success Yule’s Q Goat-town New 20 180 200 10% 0. 36 Cow-city Old New 5 90 95 10 100 5% 90% 0. 50 Old 150 50 200 75% 265 335 600

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

Simpson’s Paradox: Example 2 Successful Treatment Yes No % Success Yule’s Q New 110 190 300 37% -0. 30 Old 155 145 300 52% 265 335 600

Simpson’s Paradox: Example 2 q 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 Psycholobby.

Simpson’s paradox: Example 2: Paik Diagram q The new therapy has been applied predomi nantly in Goat town: 200 vs. 100. q The old therapy has been applied mostly in Cow city: 200 vs. 100. q Overall Success rate in Cow city higher than in Goat town: 80% vs. 8. 3%

Simpson’s Paradox: Example 3 q 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:

Simpson’s Paradox: Example 3 Success Field Sex Yes No Social work Man 127 35 162 78% -0. 20 Woman 27 5 32 84% 17 42 59 29% -0. 14 Woman 92 170 262 35% 252 515 Psychology Man 263 % Success Yules Q

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

Simpson’s Paradox: Example 3 Success Sex Yes No Man 144 77 221 65% 0. 47 Woman 119 175 294 40% 263 252 515 % Success Yules Q

Simpson’s Paradox: Example 3 q 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.

Simpson’s paradox: Example 3: Paik Diagrams q Women study predomi nately psychology: 262 vs. 59. q Men study predomi nately psychology: 126 vs. 32. q Success rate in psychology is lower: 34. 0% vs. 79. 4%.

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.

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.

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.

Ecological Fallacy: Example o 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.

Ecological Fallacy: Example o Treatment of clustered (grouped) data:

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

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