Kari Lock Morgan | Searcharxiv

arXiv2022

Examining the role of context in statistical literacy outcomes using an isomorphic assessment instrument

The central role of statistical literacy has been discussed extensively, emphasizing its importance as a learning outcome and in promoting a citizenry capable of interacting with the world in an informed and critical manner. Our work contributes to the growing literature on assessing and improving people's statistical literacy vis-a-vis contexts important in their professional and personal lives. We consider the measurement of contextualized statistics literacy - statistical literacy as applied to relevant contexts. We discuss the development of an isomorphic instrument modifying an existing assessment, design of a pilot study, and results which conclude that 1) the isomorphic assessment has comparable psychometric properties, and 2) test takers have lower statistical literacy scores on an assessment that incorporates relevant contexts.

stat.OT↗

arXiv2018

Sequential rerandomization

The seminal work of Morgan and Rubin (2012) considers rerandomization for all the units at one time. In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result, Theorem 3, that given the same number of rerandomizations (in expected value), under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.

stat.AP↗

arXiv2017

Reallocating and Resampling: A Comparison for Inference

Simulation-based inference plays a major role in modern statistics, and often employs either reallocating (as in a randomization test) or resampling (as in bootstrapping). Reallocating mimics random allocation to treatment groups, while resampling mimics random sampling from a larger population; does it matter whether the simulation method matches the data collection method? Moreover, do the results differ for testing versus estimation? Here we answer these questions in a simple setting by exploring the distribution of a sample difference in means under a basic two group design and four different scenarios: true random allocation, true random sampling, reallocating, and resampling. For testing a sharp null hypothesis, reallocating is superior in small samples, but reallocating and resampling are asymptotically equivalent. For estimation, resampling is generally superior, unless the effect is truly additive. Moreover, these results hold regardless of whether the data were collected by random sampling or random allocation.

math.ST↗

arXiv2016

Balancing Covariates via Propensity Score Weighting

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.

stat.ME↗

arXiv2016

Balancing Covariates via Propensity Score Weighting

Covariate balance is crucial for unconfounded descriptive or causal comparisons. However, lack of balance is common in observational studies. This article considers weighting strategies for balancing covariates. We define a general class of weights---the balancing weights---that balance the weighted distributions of the covariates between treatment groups. These weights incorporate the propensity score to weight each group to an analyst-selected target population. This class unifies existing weighting methods, including commonly used weights such as inverse-probability weights as special cases. General large-sample results on nonparametric estimation based on these weights are derived. We further propose a new weighting scheme, the overlap weights, in which each unit's weight is proportional to the probability of that unit being assigned to the opposite group. The overlap weights are bounded, and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing weights. The overlap weights also possess a desirable small-sample exact balance property, based on which we propose a new method that achieves exact balance for means of any selected set of covariates. Two applications illustrate these methods and compare them with other approaches.

stat.ME↗

arXiv2012

Rerandomization to improve covariate balance in experiments

Randomized experiments are the "gold standard" for estimating causal effects, yet often in practice, chance imbalances exist in covariate distributions between treatment groups. If covariate data are available before units are exposed to treatments, these chance imbalances can be mitigated by first checking covariate balance before the physical experiment takes place. Provided a precise definition of imbalance has been specified in advance, unbalanced randomizations can be discarded, followed by a rerandomization, and this process can continue until a randomization yielding balance according to the definition is achieved. By improving covariate balance, rerandomization provides more precise and trustworthy estimates of treatment effects.

math.ST↗