Analyzing block randomized studies: the example of the Jersey City drug market analysis experiment

Objectives: While block randomized designs have become more common in place-based policing studies, there has been relatively little discussion of the assumptions employed and their implications for statistical analysis. Our paper seeks to illustrate these assumptions, and controversy regarding statistical approaches, in the context of one of the first block randomized studies in criminal justice—the Jersey City Drug Market Analysis Project (DMAP). Methods: Using DMAP data, we show that there are multiple approaches that can be used in analyzing block randomized designs, and that those approaches will yield differing estimates of statistical significance. We develop outcomes using both models with and without interaction, and utilizing both Type I and Type III sums-of-squares approaches. We also examine the impacts of using randomization inference, an approach for estimating p values not based on approximations using normal distribution theory, to adjust for possible small N biases in estimating standard errors. Results: The assumptions used for identifying the analytic approach produce a comparatively wide range of p values for the main DMAP program impacts on hot spots. Nonetheless, the overall conclusions drawn from our re-analysis remain consistent with the original analyses, albeit with more caution. Results were similar to the original analyses under different specifications supporting the identification of diffusion of benefits effects to nearby areas. Conclusions: The major contribution of our article is to clarify statistical modeling in unbalanced block randomized studies. The introduction of blocking adds complexity to the models that are estimated, and care must be taken when including interaction effects in models, whether they are ANOVA models or regression models. Researchers need to recognize this complexity and provide transparent and alternative estimates of study outcomes.