Educational researchers advocate the use of an effect size and its confidence interval to assess the effectiveness of interventions instead of relying on a p-value, which has been blamed for lack of reproducibility of research findings and the misuse of statistics. The aim of this study is to provide a framework, which can provide direct evidence…

In this response, we first show that Simpson's proposed analysis answers a different and less interesting question than ours. We then justify the choice of prior for our Bayes factors calculations, but we also demonstrate that the substantive conclusions of our article are not substantially affected by varying this choice.

A recent paper uses Bayes factors to argue a large minority of rigorous, large-scale education RCTs are "uninformative." The definition of "uninformative" depends on the authors' hypothesis choices for calculating Bayes factors. These arguably overadjust for effect size inflation and involve a fixed prior distribution,…

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 non-participants. For example, data from A/B…

Educational stakeholders are keen to know the magnitude and importance of different interventions. However, the way evidence is communicated to support understanding of the effectiveness of an intervention is controversial. Typically studies in education have used the standardised mean difference as a measure of the impact of interventions. This…

Bayesian statistical methods have become more feasible to implement with advances in computing but are not commonly used in educational research. In contrast to frequentist approaches that take hypotheses (and the associated parameters) as fixed, Bayesian methods take data as fixed and hypotheses as random. This difference means that Bayesian…

Interest in variation in program impacts--How big is it? What might explain it?--has inspired recent work on the analysis of data from multi-site experiments. One critical aspect of this problem involves the use of random or fixed effect estimates to visualize the distribution of impact estimates across a sample of sites. Unfortunately, unless the…