Randomized A/B tests allow causal estimation without confounding but are often under-powered. This paper uses a new dataset, including over 250 randomized comparisons conducted in an online learning platform, to illustrate a method combining data from A/B tests with log data from users who were not in the experiment. Inference remains exact and…

After explicit instruction on how to give possible bidirectional (two-way) causality explanations for a correlation, 240 students from eight sections of social psychology and research methods courses wrote "reverse causality" explanations on various test questions, creating a total of 882 answers. Averaging across multiple graded…

A valuable extension of the single-rating regression discontinuity design (RDD) is a multiple-rating RDD (MRRDD). To date, four main methods have been used to estimate average treatment effects at the multiple treatment frontiers of an MRRDD: the "surface" method, the "frontier" method, the "binding-score" method, and…