This workflow teaches design-led evaluation when educational programs were not randomly assigned. Four separate synthetic examples cover propensity-score adjustment, difference-in-differences, regression discontinuity, and interrupted time series. Each module defines its own estimand and assumptions; no adjustment is described as recreating a randomized experiment.
Before modeling, state the intervention, assignment process, target population, potential outcomes, estimand, comparison condition, eligibility date, follow-up window, interference risks, attrition, and clustering. A plausible design requires knowledge that cannot be recovered from the dataset alone.
| design | assignment | estimand | central_assumption |
|---|---|---|---|
| Propensity weighting/matching | Observed covariates | ATE or ATT | No important unmeasured confounding plus overlap |
| Difference-in-differences | Group and time | Change attributable to adoption | Parallel untreated trends |
| Regression discontinuity | Threshold rule | Local effect at cutoff | Continuity and no precise manipulation |
| Interrupted time series | Known intervention time | Level/slope change | No concurrent cause with same timing |
| variable | unweighted | weighted |
|---|---|---|
| prior | 0.669 | 0.058 |
| ses | -0.425 | -0.037 |
| attendance | 0.072 | 0.008 |
## Weighted and matched estimates
| method | estimate | std_error |
|---|---|---|
| ATE weighting | 2.919 | 0.507 |
| Nearest-neighbor ATT matching | 3.168 | 0.519 |
Overlap, balance, weight concentration, and sensitivity to specifications matter more than propensity-model classification accuracy. The estimate remains conditional on no consequential unmeasured confounding.
| estimate | std_error | p_value |
|---|---|---|
| 2.454 | 0.282 | 0 |
## Event-study diagnostic
Pretrend coefficients can reveal problems but cannot prove parallel
counterfactual trends. Staggered timing and heterogeneous effects
require modern group-time estimators rather than a simple two-way
fixed-effects model.
| bandwidth | estimate | std_error | p_value |
|---|---|---|---|
| 8 | 4.9 | 1.288 | 0 |
| bandwidth | estimate | std_error |
|---|---|---|
| 5 | 4.997 | 1.731 |
| 8 | 4.900 | 1.288 |
| 12 | 4.681 | 1.007 |
The effect is local to the cutoff. Investigate sorting, other rules at the same threshold, functional form, bandwidth, and covariate continuity before making a causal claim.
| term | Estimate | Std. Error | t value | Pr(>|t|) |
|---|---|---|---|---|
| (Intercept) | 70.741 | 0.423 | 167.102 | 0.000 |
| month | 0.133 | 0.027 | 4.872 | 0.000 |
| intervention | 1.753 | 0.855 | 2.051 | 0.045 |
| time_after | 0.044 | 0.037 | 1.185 | 0.241 |
Check seasonality, autocorrelation, changes in measurement, concurrent
events, anticipation, and sufficient pre/post observations. A single
series offers weak protection against coincident shocks; add a
comparison series when possible.
The weighted synthetic comparison estimated an average program effect of 2.92 points. The difference-in-differences estimate was 2.45 points (p < .001), and the local regression-discontinuity estimate at the eligibility threshold was 4.90 points (p < .001). These estimates answer different causal questions and should not be treated as interchangeable replications.
Use randomized assignment when feasible. Instrumental variables need a defensible instrument and a local estimand. Synthetic controls require credible donor units and longer panels. Staggered adoption, fuzzy thresholds, multiple cutoffs, few clusters, and latent outcomes need specialized extensions. Statistical adjustment cannot repair an unknown assignment process or a comparison group with no credible counterfactual role.