Evaluating Assumptions

Motivating Assumptions

• Previously, we learned how to estimate $ATE$ with $SDO$
• In turn, we learned how to estimate causal effects

• We learned that $SDO$ makes some assumptions about $ATE$

  • We must verify there isn't any selection bias or other biases
• Let's summarize those assumptions now and introduce a few more

Verifying for Independent Assignment

• Assigning an $i^{th}$ observation to a treatment and control group $t_{i}$ shouldn't be made based on their potential outcomes $Y^{0}_{i}$ or $Y^{1}_{i}$
• Another way of saying this is that potential outcomes do not depend on the particular group assignment; they are independent
• In other words, treatment and control assignment must be independent of any potential outcomes

• Examples of violations of the independence assumption include:

  • A doctor assigning certain patients to a treatment group who he/she thinks will react more positively compared to the patients he/she assigns to the control group
• These assumptions must hold in order to make accurate estimations about causal effects

Verifying SUTVA Assumptions

• There are two similar assumptions coined as SUTVA assumptions:

  1. Observations are homogeneous between the control and treatment groups
  2. Spillover (or externalities) don't exist between observations

• Examples of violations of the homogeneity assumption include:

  • Doctors applying surgery in the control group are more skilled or higher quality compared to the treatment group
  • The IQ of one group is higher than the other group

• Examples of violations of the spillover assumption include:

  • Students assigned to attend a tutoring program to improve their grades might interact with other students in their school who were not assigned to the tutoring program and influence the grades of these control students
  • Social media users in a control group may influence users in a treatment group
• These assumptions must hold in order to make accurate estimations about causal effects

References

• Causal Inference Textbook
• Python Causality Handbook
• Comprehensive Causal Inference Textbook
• Causal Inference Slides