Executive Summary
Causal treatment effect estimate (ATT) after propensity score matching
After propensity score matching, the estimated Average Treatment Effect on the Treated (ATT) is 7.541 (95% CI: [4.598, 10.483]), which is statistically significant (p < 0.05). 74 treated units (23.9%) were successfully matched to controls within the specified caliper. Matching improved covariate balance by -251.1%, with post-matching SMD for the pre-treatment variable reduced substantially.
Group Descriptive Statistics
Pre-matching comparison of treated and control groups
| Group | N Obs | Mean Outcome | Mean Pre Treatment |
|---|---|---|---|
| Treated | 309 | 20.9 | 20.43 |
| Control | 75 | 21.1 | 23.38 |
Before matching, there are 309 treated and 75 control units. The treated group has a mean outcome of 20.9 versus 21.1 for controls (raw difference: -0.2). The mean pre-treatment value is 20.43 for treated and 23.38 for controls, indicating substantial pre-treatment imbalance that motivates matching.
Covariate Balance Before Matching
Standardized mean difference before matching — higher values indicate more imbalance
Before matching, the standardized mean difference (SMD) for Pre Treatment Value is -0.276, indicating large imbalance between treated and control groups. An SMD above 0.1 is the standard threshold for meaningful imbalance requiring adjustment. This value reflects the initial selection bias that propensity score matching is designed to remove.
Covariate Balance After Matching
Standardized mean difference after matching — values below 0.1 indicate adequate balance
After matching, the SMD for Pre Treatment Value is 0.968, which still exceeds the 0.1 threshold — consider adjusting the caliper or using regression adjustment. The balance improved by -251.1% relative to the pre-matching SMD.
Propensity Score Distribution by Group
Distribution of estimated treatment probability by group — overlap is required for valid matching
The treated group has a median propensity score of 0.816 versus 0.81 for the control group. Overlap between the two distributions indicates the region of common support — units where matching is valid. Treated units with very high propensity scores and control units with very low scores fall outside the common support region and are typically excluded by the caliper.
Average Treatment Effect on the Treated (ATT)
Point estimate and 95% confidence interval for the causal treatment effect
The estimated ATT is 7.541 (95% CI: [4.598, 10.483]), indicating that treatment increases the outcome by approximately 7.541 units on average. This effect is statistically significant (p = 0.000). The ATT is interpreted as the expected change in outcome for treated units had they instead been in the control condition.
Matched Pair Outcomes
Treated vs. matched control outcomes — points above the diagonal indicate a positive treatment effect
Each point represents one matched pair, with the treated unit's outcome on the y-axis and its matched control's outcome on the x-axis. Across 74 matched pairs, 73% of treated units have higher outcomes than their matched controls. The average within-pair difference is 7.541, consistent with the ATT estimate. A systematic vertical offset above the diagonal confirms a positive treatment effect.
Match Quality and Sensitivity Summary
Diagnostics on units matched, caliper trimming, and ATT robustness
| Metric | Matched Value | Unmatched Value |
|---|---|---|
| Treated Units (Total) | 74 | 309 |
| Control Units (Total) | 74 | 75 |
| Treated Units Matched | 74 | 235 |
| Control Units Used | 74 | 1 |
| Proportion Treated Matched (%) | 23.9 | 76.1 |
| Caliper Width | 0.1 | |
| ATT Estimate | 7.54 | |
| ATT p-value | 0 |
Of 309 treated units, 74 (23.9%) were successfully matched within the caliper of 0.1. The remaining 235 treated units could not be matched and are excluded from the ATT estimate. A high proportion of unmatched treated units (>20%) may indicate poor common support or an overly restrictive caliper. Sensitivity to hidden bias can be assessed by varying the caliper parameter.