Dude, Where’s My Treatment Effect? Errors in Administrative Data Linking and the Destruction of Statistical Power in Randomized Experiments

Objective
The increasing availability of large administrative datasets has led to an exciting innovation in criminal justice research—using administrative data to measure experimental outcomes in lieu of costly primary data collection. We demonstrate that this type of randomized experiment can have an unfortunate consequence: the destruction of statistical power. Combining experimental data with administrative records to track outcomes of interest typically requires linking datasets without a common identifier. In order to minimize mistaken linkages, researchers often use stringent linking rules like “exact matching” to ensure that speculative matches do not lead to errors in an analytic dataset. We show that this, seemingly conservative, approach leads to underpowered experiments, leaves real treatment effects undetected, and can therefore have profound implications for entire experimental literatures.

Methods
We derive an analytic result for the consequences of linking errors on statistical power and show how the problem varies across combinations of relevant inputs, including linking error rate, outcome density and sample size.

Results
Given that few experiments are overly well-powered, even small amounts of linking error can have considerable impact on Type II error rates. In contrast to exact matching, machine learning-based probabilistic matching algorithms allow researchers to recover a considerable share of the statistical power lost under stringent data-linking rules.

Conclusion
Our results demonstrate that probabilistic linking substantially outperforms stringent linking criteria. Failure to implement linking procedures designed to reduce linking errors can have dire consequences for subsequent analyses and, more broadly, for the viability of this type of experimental research.