Many generalization studies in education are typically based on a sample of 30-70 schools while the inference population is at least twenty times larger. This small sample to population size ratio limits the precision of design-based estimators of the population average treatment effect. Prior work has shown the potential of small area estimation…

This study examines informal hypothesis testing in the context of drawing inferences of underlying probability distributions. Through a small-scale teaching experiment of three lessons, the study explores how fifth-grade students distinguish a non-uniform probability distribution from uniform probability distributions in a data-rich learning…

This study aimed to explore how prospective middle school mathematics teachers think critically about a newspaper article that reported the findings of a statistical research. Participants of the study were four fourth-year students enrolled at the mathematics teacher education program of a public university. To investigate the research question…

Recent methods to improve generalizations from nonrandom samples typically invoke assumptions such as the strong ignorability of sample selection, which is challenging to meet in practice. Although researchers acknowledge the difficulty in meeting this assumption, point estimates are still provided and used without considering alternative…

This paper reports on the results of a study investigating the potential to embed Informal Statistical Inference in statistical investigations, using TinkerPlots, for assisting 8th grade students' informal inferential reasoning to emerge, particularly their articulations of uncertainty. Data collection included students' written work on a…

Questions regarding the generalizability of results from educational experiments have been at the forefront of methods development over the past five years. This work has focused on methods for estimating the effect of an intervention in a well-defined inference population (e.g., Tipton, 2013; O'Muircheartaigh and Hedges, 2014); methods for…

The main result of an experiment is typically an estimate of the average treatment effect (ATE) and its standard error. In most experiments, the number of covariates that may be moderators is large. One way this issue is typically skirted is by interpreting the ATE as the average effect for "some" population. Cornfield and Tukey (1956)…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…