Randomized Experiments

Motivating Physical Randomization in Experiments

• In order to make accurate estimations $SDO$ about $ATE$ to determine causal effects, we must remove the following biases:

  • Selection bias
  • Heterogenous treatment effect bias
• Conducting randomized experiments will successfully eliminate biases

• To verify that an experiment is randomized, we must verify the following assumptions:

  • Independence assumption

  • SUTVA assumptions:

    • Homogeneity assumption
    • Spillover assumption

Removing Biases with Physical Randomization

• Biases are eliminated by randomly assigning observations to a treatment group and control group

  • Assignment is random if the treatment and control groups are as balanced as if they were assigned by flipping a coin

• Specifically, randomization of the treatment assignment would eliminate both selection bias and heterogeneous treatment effect bias

  • Thus, $SDO$ no longer suffers from selection bias
• Mathematically, randomization of the treatment assignment ensures:

$$E[Y^{0} | t = 1] - E[Y^{0} | t = 0] = 0$$

• Again, randomization of the treatment assignment also eliminates any heterogeneous treatment effect bias
• Since, randomization of the treatment assignment also ensures:

$$E[Y^{1} | t = 1] - E[Y^{1} | t = 0] = 0$$

References

• Course about Causality
• Programming Book about Randomized Experiments
• Causal Inference Textbook
• Python Causality Handbook
• Comprehensive Causal Inference Textbook