1. More About Factorial Design
Suppose experiment tests whether taking a game theory class causes a person to get more papers published
We cannot simply examine whether people who took a game theory class had more papers published due to possible effect of self-selection into game theory class.
Therefore, we should randomly assign people to game theory class.

2. Does Game Theory Lead to More Articles?
DV: Number of papers published 4 years later
IV: Took game theory class or not
Two groups:
Take game theory class
Did not take game theory class

3. Does Class on Experiments Lead to More Articles?
We also may want to determine whether taking a class on experiments helps a person get more articles published.
Now we randomize whether a person takes a class on experiments

4. 2 x 2 Factorial Design Class Taken Game Theory No Game Theory
Experiments
No Experiments
Now we Have 4 groups in the experiment, randomly assigned.
Each cell should have equal numbers of subjects

5. 2 x 2 x 3 Factorial
Now we randomly assign whether a person studies international relations, public policy, or economics.
This is now a 2 x 2 x 3 factorial design with 12 groups

6. Economics
Game Theory
No Game Theory
Experiments
No Experiments
Public Policy
Game Theory
No Game Theory
Experiments
No Experiments
International
Relations
Game Theory
No Game Theory
Experiments
No Experiments

7. Power Analysis: How Many Subjects Needed?
Example: G*Power (free!)
Hypothesize the magnitude of the effect (such as one additional paper published)
Calculate sample size needed for two independent samples difference in means (average number of articles published for each of two groups)
Answer will be number of subjects needed in each group

8. Exploiting Randomization When It Occurs
Natural Experiments
Exploiting Randomization When It Occurs

9. Natural Experiments Experimenter does not pre-plan experiment
Experimenter finds a naturally-occurring random assignment mechanism that serves as a treatment

10. Why Randomization?
Randomization allows comparison across groups by controlling for differences in other variables.
The expected values of other variables are the same between across randomly-assigned treatment groups.
If other variables have equal expected values across treatments, then differences in outcomes must be due to treatment variable

11. Dartmouth Roommate “Experiment”
First-year roommates at Dartmouth College assigned randomly within “like-groups” based on gender and whether student
Smokes
Listen to music while studying
Stay up late
Are neat or messy
Assignment random within 25=32 different groups

12. Treatment=Roommate
In this case, the treatment variable is a student’s roommate
The experiment does not have a true “control group” but many different treatments in the form of roommates
Also in this case, the roommates are “treatments” for each other

13. First Step: Is Assignment Truly Random?
Are there any variables that determine one’s assigned roommate other than
Gender
Smoking
Late night habits
Cleanliness
Listening to music

15. DV’s and IV’s The DV in this case is a student’s GPA
The most important IV is the roommate’s GPA
Other IV’s included as control variables are a student’s own academic index (entrance exam scores and high school grades) and roommate’s academic index

16. Statistical Model

22. Conclusions Roommates influence each other’s performance in school
Top performers reinforce each other
Bottom performers reinforce each other
Roommates also influence choice of social group such as fraternity or sorority
Roommates do not influence each other’s choice of major

23. Other Examples of Natural Experiments