Many students of statistics and econometrics express frustration with the way a problem known as "bad control" is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is…

Regression discontinuity (RD) designs have gained significant popularity as a quasi-experimental device for evaluating education programs and policies. In this paper, we present a comprehensive review of RD designs, focusing on the continuity-based framework, the most widely adopted RD framework. We first review the fundamental aspects of RD…

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…

We provide tools for identification and exploration of data with very large variability having power law tails. Such data describe extreme features of processes such as fire losses, flood, drought, financial gain/loss, hurricanes, population of cities, among others. Prediction and quantification of extreme events are at the forefront of the…

Social scientists are often interested in estimating the marginal effects of a time-varying treatment on an end-of-study continuous outcome. With observational data, estimating these effects is complicated by the presence of time-varying confounders affected by prior treatments, which may lead to bias in conventional regression and matching…

A common motivation for adding control variables to statistical models is to reduce the potential for spurious findings when analyzing non-experimental data and to thereby allow for more reliable causal inferences. However, as I show here, unless "all" potential confounding factors are included in an analysis (which is unlikely to be…

Treatment effect estimates from a "regression discontinuity design" (RDD) have high internal validity. However, the arguments that support the design apply to a subpopulation that is narrower and usually different from the population of substantive interest in evaluation research. The disconnect between RDD population and the…

The central purpose of this article is to provide an overview of the many ways in which special educators can generate and think about causal inference to inform policy and practice. Consideration of causality across different lenses can be carried out by engaging in multiple method and mixed methods ways of thinking about inference. This article…

Many teachers of required secondary school mathematics classes are introducing statistics and probability topics traditionally relegated to college or AP Statistics courses. As a result, they need guidance in preparing lesson plans and orchestrating effective classroom discussions. In this article, the authors will describe the students' learning…

Mediation is usually assessed by a regression-based or structural equation modeling (SEM) approach that we refer to as the classical approach. This approach relies on the assumption that there are no confounders that influence both the mediator, "M", and the outcome, "Y". This assumption holds if individuals are randomly…

In education, most naturally occurring data are clustered within contexts. Students are clustered within classrooms, classrooms are clustered within schools, and schools are clustered within districts. When people are clustered within naturally occurring organizational units such as schools, classrooms, or districts, the responses of people from…

In Shadish (2010) and West and Thoemmes (2010), the authors contrasted 2 approaches to causality. The first originated in the psychology literature and is associated with work by Campbell (e.g., Shadish, Cook, & Campbell, 2002), and the second has its roots in the statistics literature and is associated with work by Rubin (e.g., Rubin, 2006). In…

This report summarizes the complex research literature on quantitative methods for assessing how impacts of educational interventions on instructional practices and student learning differ across students, educators, and schools. It also provides technical guidance about the use and interpretation of these methods. The research topics addressed…

In behavioral research, interest is often in examining the degree to which the effect of an independent variable X on an outcome Y is mediated by an intermediary or mediator variable M. This article illustrates how generalized estimating equations (GEE) modeling can be used to estimate the indirect or mediated effect, defined as the amount by…

This article examines some of the difficulties frequently encountered by students when analyzing bivariate data and suggests how they might be overcome. (Author)