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Several branches of the potential outcome causal inference literature have discussed the merits of blocking versus complete randomization. Some have concluded it can never hurt the precision of estimates, and some have concluded it can hurt. In this article, we reconcile these apparently conflicting views, give a more thorough discussion of what guarantees no harm, and discuss how other aspects of a blocked design can cost, all in terms of estimator precision. We discuss how the different findings are due to different sampling models and assumptions of how the blocks were formed. We also connect these ideas to common misconceptions; for instance, we show that analyzing a blocked experiment as if it were completely randomized, a seemingly conservative method, can actually backfire in some cases. Overall, we find that blocking can have a price but that this price is usually small and the potential for gain can be large. It is hard to go too far wrong with blocking.

Evaluating blocked randomized experiments from a potential outcomes perspective has two primary branches of work. The first focuses on larger blocks, with multiple treatment and control units in each block. The second focuses on matched pairs, with a single treatment and control unit in each block. These literatures not only provide different estimators for the standard errors of the estimated average impact, but they are also built on different sets of assumptions. Neither literature handles cases with blocks of varying size that contain singleton treatment or control units, a case which can occur in a variety of contexts, such as with different forms of matching or poststratification. In this article, we reconcile the literatures by carefully examining the performance of variance estimators under several different frameworks. We then use these insights to derive novel variance estimators for experiments containing blocks of different sizes. [For the corresponding grantee submission, see ED599248.]

Analyses that reveal how treatment effects vary allow researchers, practitioners, and policymakers to better understand the efficacy of educational interventions. In practice, however, standard statistical methods for addressing heterogeneous treatment effects (HTE) fail to address the HTE that may exist "within" outcome measures. In this study, we present a novel application of the explanatory item response model (EIRM) for assessing what we term "item-level" HTE (IL-HTE), in which a unique treatment effect is estimated for each item in an assessment. Results from data simulation reveal that when IL-HTE is present but ignored in the model, standard errors can be underestimated and false positive rates can increase. We then apply the EIRM to assess the impact of a literacy intervention focused on promoting transfer in reading comprehension on a digital assessment delivered online to approximately 8,000 third-grade students. We demonstrate that allowing for IL-HTE can reveal treatment effects at the item-level masked by a null average treatment effect, and the EIRM can thus provide fine-grained information for researchers and policymakers on the potentially heterogeneous causal effects of educational interventions.

Randomized controlled trials (RCTs) admit unconfounded design-based inference – randomization largely justifies the assumptions underlying statistical effect estimates – but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT nonparticipants. For example, data from A/B tests conducted within an educational technology platform exist alongside historical observational data drawn from student logs. We outline a design-based approach to using such observational data for variance reduction in RCTs. First, we use the observational data to train a machine learning algorithm predicting potential outcomes using covariates and then use that algorithm to generate predictions for RCT participants. Then, we use those predictions, perhaps alongside other covariates, to adjust causal effect estimates with a flexible, design-based covariate-adjustment routine. In this way, there is no danger of biases from the observational data leaking into the experimental estimates, which are guaranteed to be exactly unbiased regardless of whether the machine learning models are “correct” in any sense or whether the observational samples closely resemble RCT samples. We demonstrate the method in analyzing 33 randomized A/B tests and show that it decreases standard errors relative to other estimators, sometimes substantially.

We are sometimes forced to use the Interrupted Time Series (ITS) design as an identification strategy for potential policy change, such as when we only have a single treated unit and cannot obtain comparable controls. For example, with recent county- and state-wide criminal justice reform efforts, where judicial bodies have changed bail setting practices for everyone in their jurisdiction in order to reduce rates of pre-trial detention while maintaining court order and public safety, we have no natural and available comparison group other than the past. In these contexts, it is imperative to model pre-policy trends with a light touch, allowing for structures such as autoregressive departures from any pre-existing trend, in order to accurately and realistically assess the uncertainty of our projections. We aim to provide a methodological approach rooted in commonly understood and used modeling tools to achieve this. We quantify uncertainty with simulation, generating a distribution of plausible counterfactual trajectories to compare to the observed; this approach naturally allows for incorporating seasonality and other time-varying covariates, and provides confidence intervals along with point estimates for the potential impacts of policy change. We find simulation provides a natural framework to capture and show uncertainty in the ITS designs. It also allows for easy extensions such as nonparametric smoothing in order to handle multiple post-policy time points.

Researchers face many choices when conducting large-scale multisite individually randomized control trials. One of the most common quantities of interest in multisite RCTs is the overall average effect. Even this quantity is non-trivial to define and estimate. The researcher can target the average effect across individuals or sites. Furthermore, the researcher can target the effect for the experimental sample or a larger population. If treatment effects vary across sites, these estimands can differ. Once an estimand is selected, an estimator must be chosen. Standard estimators, such as fixed-effects regression, can be biased. We describe 15 estimators, consider which estimands they are appropriate for, and discuss their properties in the face of cross-site effect heterogeneity. Using data from 12 large multisite RCTs, we estimate the effect (and standard error) using each estimator and compare the results. We assess the extent that these decisions matter in practice and provide guidance for applied researchers.

For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. In addition to the classical method of moments, we also introduce model-free likelihood and Bayesian methods based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment-based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach that allows for the characterization of the impact of the association between the potential outcomes on statistical inference.

The injunction to “analyze the way you randomize” is well known to statisticians since Fisher advocated for randomization as the basis of inference. Yet even those convinced by the merits of randomization-based inference seldom follow this injunction to the letter. Bernoulli randomized experiments are often analyzed as completely randomized experiments, and completely randomized experiments are analyzed as if they had been stratified; more generally, it is not uncommon to analyze an experiment as if it had been randomized differently. This article examines the theoretical foundation behind this practice within a randomization-based framework. Specifically, we ask when is it legitimate to analyze an experiment randomized according to one design as if it had been randomized according to some other design. We show that a sufficient condition for this type of analysis to be valid is that the design used for analysis should be derived from the original design by an appropriate form of conditioning. We use our theory to justify certain existing methods, question others, and finally suggest new methodological insights such as conditioning on approximate covariate balance.

Analyses that reveal how treatment effects vary allow researchers, practitioners, and policymakers to better understand the efficacy of educational interventions. In practice, however, standard statistical methods for addressing heterogeneous treatment effects (HTE) fail to address the HTE that may exist within outcome measures. In this study, we present a novel application of the explanatory item response model (EIRM) for assessing what we term "item-level" HTE (IL-HTE), in which a unique treatment effect is estimated for each item in an assessment. Results from data simulation reveal that when IL-HTE is present but ignored in the model, standard errors can be underestimated and false positive rates can increase. We then apply the EIRM to assess the impact of a literacy intervention focused on promoting transfer in reading comprehension on a digital assessment delivered online to approximately 8,000 third-grade students. We demonstrate that allowing for IL-HTE can reveal treatment effects at the item-level masked by a null average treatment effect, and the EIRM can thus provide fine-grained information for researchers and policymakers on the potentially heterogeneous causal effects of educational interventions. [ABSTRACT FROM AUTHOR]

A benefit of randomized experiments is that covariate distributions of treatment and control groups are balanced on average, resulting in simple unbiased estimators for treatment effects. However, it is possible that a particular randomization yields covariate imbalances that researchers want to address in the analysis stage through adjustment or other methods. Here we present a randomization test that conditions on covariate balance by only considering treatment assignments that are similar to the observed one in terms of covariate balance. Previous conditional randomization tests have only allowed for categorical covariates, while our randomization test allows for any type of covariate. Through extensive simulation studies, we find that our conditional randomization test is more powerful than unconditional randomization tests and other conditional tests. Furthermore, we find that our conditional randomization test is valid (1) unconditionally across levels of covariate balance, and (2) conditional on particular levels of covariate balance. Meanwhile, unconditional randomization tests are valid for (1) but not (2). Finally, we find that our conditional randomization test is similar to a randomization test that uses a model-adjusted test statistic.

Although multiple interventions to remediate physical blight have been found to reduce urban firearm violence, there is limited evidence for demolishing vacant buildings as a violence reduction strategy. Starting in 2014, Detroit, MI launched a large-scale program that demolished over 10,000 buildings in its first 3 years. We analyzed the pre-post effects of this program on fatal and nonfatal firearm assaults and illegal drug violations at the U.S. Census block group level, using propensity score matching and negative binomial regression. Receiving over 5 demolitions was associated with a 11% reduction in firearm assaults, relative to comparable control locations, 95% CI [7%, 15%], p = 0.01. The program was associated with larger reductions in firearm assaults for the locations receiving moderate numbers of demolitions (between 6 and 12) than for locations receiving high numbers of demolitions (13 and over). No effects were observed for illegal drug violations and no evidence of spatial crime displacement was detected. These findings suggest that vacant building demolitions may affect gun violence., Author(s): Jonathan Jay [sup.1] [sup.2] , Luke W. Miratrix [sup.3] , Charles C. Branas [sup.1] [sup.4] , Marc A. Zimmerman [sup.1] [sup.5] , David Hemenway [sup.1] [sup.2] Author Affiliations: (Aff1) [...]

Risk-limiting post-election audits limit the chance of certifying an electoral outcome if the outcome is not what a full hand count would show. Building on previous work, we report on pilot risk-limiting audits in four elections during 2008 in three California counties: one during the February 2008 Primary Election in Marin County and three during the November 2008 General Elections in Marin, Santa Cruz and Yolo Counties. We explain what makes an audit risk-limiting and how existing and proposed laws fall short. We discuss the differences among our four pilot audits. We identify challenges to practical, efficient risk-limiting audits and conclude that current approaches are too complex to be used routinely on a large scale. One important logistical bottleneck is the difficulty of exporting data from commercial election management systems in a format amenable to audit calculations. Finally, we propose a bare-bones risk-limiting audit that is less efficient than these pilot audits, but avoids many practical problems.

There are two general views in causal analysis of experimental data: the super population view that the units are an independent sample from some hypothetical infinite population, and the finite population view that the potential outcomes of the experimental units are fixed and the randomness comes solely from the treatment assignment. These two views differs conceptually and mathematically, resulting in different sampling variances of the usual difference-in-means estimator of the average causal effect. Practically, however, these two views result in identical variance estimators. By recalling a variance decomposition and exploiting a completeness-type argument, we establish a connection between these two views in completely randomized experiments. This alternative formulation could serve as a template for bridging finite and super population causal inference in other scenarios.

“M-Bias,” as it is called in the epidemiologic literature, is the bias introduced by conditioning on a pretreatment covariate due to a particular “M-Structure” between two latent factors, an observed treatment, an outcome, and a “collider.” This potential source of bias, which can occur even when the treatment and the outcome are not confounded, has been a source of considerable controversy. We here present formulae for identifying under which circumstances biases are inflated or reduced. In particular, we show that the magnitude of M-Bias in linear structural equation models tends to be relatively small compared to confounding bias, suggesting that it is generally not a serious concern in many applied settings. These theoretical results are consistent with recent empirical findings from simulation studies. We also generalize the M-Bias setting (1) to allow for the correlation between the latent factors to be nonzero and (2) to allow for the collider to be a confounder between the treatment and the outcome. These results demonstrate that mild deviations from the M-Structure tend to increase confounding bias more rapidly than M-Bias, suggesting that choosing to condition on any given covariate is generally the superior choice. As an application, we re-examine a controversial example between Professors Donald Rubin and Judea Pearl.

To identify links among professional development, teacher knowledge, practice, and student achievement, researchers have called for study designs that allow causal inferences and that examine relationships among features of interventions and multiple outcomes. In a randomized experiment implemented in six states with over 270 elementary teachers and 7,000 students, this project compared three related but systematically varied teacher interventions--"Teaching Cases, Looking at Student Work, and Metacognitive Analysis"--along with no-treatment controls. The three courses contained identical science content components, but differed in the ways they incorporated analysis of learner thinking and of teaching, making it possible to measure effects of these features on teacher and student outcomes. Interventions were delivered by staff developers trained to lead the teacher courses in their regions. Each course improved teachers' and students' scores on selected-response science tests well beyond those of controls, and effects were maintained a year later. Student achievement also improved significantly for English language learners in both the study year and follow-up, and treatment effects did not differ based on sex or race/ethnicity. However, only Teaching Cases and Looking at Student Work courses improved the accuracy and completeness of students' written justifications of test answers in the follow-up, and only Teaching Cases had sustained effects on teachers' written justifications. Thus, the content component in common across the three courses had powerful effects on teachers' and students' ability to choose correct test answers, but their ability to explain why answers were correct only improved when the professional development incorporated analysis of student conceptual understandings and implications for instruction; metacognitive analysis of teachers' own learning did not improve student justifications either year. Findings suggest investing in professional development that integrates content learning with analysis of student learning and teaching rather than advanced content or teacher metacognition alone. (Contains 1 figure and 4 tables.)

This article develops design-based ratio estimators for clustered, blocked randomized controlled trials (RCTs), with an application to a federally funded, school-based RCT testing the effects of behavioral health interventions. We consider finite population weighted least-square estimators for average treatment effects (ATEs), allowing for general weighting schemes and covariates. We consider models with block-by-treatment status interactions as well as restricted models with block indicators only. We prove new finite population central limit theorems for each block specification. We also discuss simple variance estimators that share features with commonly used cluster-robust standard error estimators. Simulations show that the design-based ATE estimator yields nominal rejection rates with standard errors near true ones, even with few clusters. [ABSTRACT FROM AUTHOR]

Several branches of the potential outcome causal inference literature have discussed the merits of blocking versus complete randomization. Some have concluded it can never hurt the precision of estimates, and some have concluded it can hurt. In this article, we reconcile these apparently conflicting views, give a more thorough discussion of what guarantees no harm, and discuss how other aspects of a blocked design can cost, all in terms of estimator precision. We discuss how the different findings are due to different sampling models and assumptions of how the blocks were formed. We also connect these ideas to common misconceptions; for instance, we show that analyzing a blocked experiment as if it were completely randomized, a seemingly conservative method, can actually backfire in some cases. Overall, we find that blocking can have a price but that this price is usually small and the potential for gain can be large. It is hard to go too far wrong with blocking. [ABSTRACT FROM AUTHOR]

Evaluating blocked randomized experiments from a potential outcomes perspective has two primary branches of work. The first focuses on larger blocks, with multiple treatment and control units in each block. The second focuses on matched pairs, with a single treatment and control unit in each block. These literatures not only provide different estimators for the standard errors of the estimated average impact, but they are also built on different sets of assumptions. Neither literature handles cases with blocks of varying size that contain singleton treatment or control units, a case which can occur in a variety of contexts, such as with different forms of matching or poststratification. In this article, we reconcile the literatures by carefully examining the performance of variance estimators under several different frameworks. We then use these insights to derive novel variance estimators for experiments containing blocks of different sizes. [ABSTRACT FROM AUTHOR]