Causal Inference from Experiments and Observational Data

The route

1. 01

   Module 1: Potential outcomes and the causal estimand

   Potential outcomes, individual treatment effects, and population causal estimands. Defines the quantity an experiment is designed to estimate and why no individual effect is observable.

   • 1
     Potential Outcomes and the Fundamental Problem

     • Given a description of units, an assignment, and observed data, the learner can write each unit's potential outcomes and observed outcome, state which quantities are known and which are missing, and explain why no individual treatment effect can be computed from the data.
2. 02

   Module 2: How assignment determines what a comparison means

   The assignment mechanism determines what a later comparison identifies. The arithmetic of a difference in means is the same whether or not the design supports a causal reading of it.

   • 1
     Randomized Assignment

     • Given a description of how treatment was assigned, the learner can identify the mechanism, state whether it is known and independent of the potential outcomes, say what causal claim it supports, and explain why observed imbalance in a single realisation is not evidence against it.
3. 03

   Module 3: Variance, intervals, and design-based refinements

   An estimate that would differ under another allocation requires a variance, and a claim that treatment had no effect requires a reference distribution. Both are derived from the design. Once an interval can be constructed, the refinements that narrow it, grouping before assignment and covariates in the regression, can be assessed by their effect on it.

   • 1
     Neyman Repeated-Sampling Inference

     • Given summary data from a completely randomized experiment, the learner can compute the difference in means, compute its conservative variance and standard error, form a confidence interval, and explain which term of the exact variance has been omitted and why that makes the result conservative rather than incorrect.
   • 2
     Fisher Randomization Inference

     • Given a small experiment and its assignment mechanism, the learner can state the sharp null, enumerate or sample the permitted allocations, compute the randomization p-value, and explain what rejecting or failing to reject establishes, distinguishing it from a claim about the average effect.
   • 3
     Blocked and Paired Randomized Experiments

     • Given a description of units and a design, the learner can decide whether blocking or pairing is warranted, compute the estimator the design requires, and identify analyses that ignore the design structure.
   • 4
     Regression Adjustment in Experiments

     • Given an experiment and a proposed regression, the learner can say what adjustment contributes, judge whether the covariates are admissible, and state what the specification cannot repair.
4. 04

   Module 4: Identification from observational data

   Estimating an effect when nothing was assigned: unconfoundedness and overlap as the assumptions adjustment requires, the propensity score, inverse-probability weighting, and matching.

   • 1
     Unconfoundedness and Overlap

     • Given an observational study, the learner can state the assumptions adjustment requires, judge which of them the data can speak to, and say what the comparison would estimate if an assumption failed.
   • 2
     Propensity Scores

     • Given an observational study, the learner can say what the propensity score is for, judge a fitted score by balance and overlap rather than by predictive accuracy, and state what it does not repair.
   • 3
     Inverse Probability Weighting

     • Given estimated propensity scores, the learner can form inverse-probability weights, compute the weighted estimate, and diagnose what extreme weights indicate about the comparison.
   • 4
     Matching for Causal Inference

     • Given a described matching procedure, the learner can say which estimand it targets, how its design choices change the population described, and what it does not establish.

What finishing means

Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.

10 required skills. If you reach a lesson without the background it assumes, you are pointed at the prerequisite first, and returned here afterwards.