4.23 Independence assumption & random assignment

  • Random assignment
    • = a statistical solution (Holland 1986, 948f)
    • Units randomly assigned to treatment/control have identical distributions of covariates/potential outcomes in both groups ((infinite) long run!)25
    • Random assignment induces independence between treatment status and potential outcomes
    • Q: What does in the long run mean?
      • Contrast a randomized experiment here in the class (e.g., N = 4) with a bigger sample (e.g., N = 1000).
    • Compare average outcome among treatment units with average outcome among control units

References

Holland, Paul W. 1986. “Statistics and Causal Inference.” J. Am. Stat. Assoc. 81 (396): 945–60.

  1. “When units are assigned at random either to cause t or to cause c, certain physical randomization processes are carried out so that the determination of which cause (t or c) u is exposed to is regarded as statistically independent of all other variables, including Yt and Yc. This means that if the physical randomization is carried out correctly, then it is plausible that S [= treatment D] is independent of Y, and Y, and all other variables over U. This is the independence assumption” (Holland 1986, 948).↩