LAUSR

The Making Pre-K Count and High 5s studies represent a recent application of a phased two-stage, multi-level design, which was used to examine the effects of two aligned math programs implemented in early childhood settings. The purpose of this paper is to describe the challenges encountered in implementing this two-stage design and to describe approaches to resolving them. We then present a set of sensitivity analyses the study team used to examine the robustness of the findings. During the pre-K year, pre-K centers were randomly assigned either to receive an evidence-based early math curriculum and associated professional development (Making Pre-K Count) or to a pre-K-as-usual control condition. In the kindergarten year, students who had been in Making Pre-K Count program classrooms in pre-K were then individually randomly assigned within schools to small-group supplemental math clubs that were designed to sustain the gains from the pre-K program, or to a business-as-usual kindergarten experience. Making Pre-K Count took place in 69 pre-K sites, comprising 173 classrooms across New York City. High 5s took place in the 24 sites that were part of the public school treatment arm of the Making Pre-K Count study and included 613 students. The study focuses on the effect of the Making Pre-K Count and High 5s programs on children's math skills at the end of kindergarten as measured by two instruments, the Research-Based Early Math Assessment-Kindergarten (REMA-K) and the Woodcock-Johnson Applied Problems test. The multi-armed design, while logistically and analytically challenging, balanced multiple considerations of power, the number of research questions that could be answered, and efficiency of resources. Robustness checks suggest that the design created groups that were both meaningfully and statistically equivalent. Decisions to use a phased multi-armed design should consider both its strengths and weaknesses. While the design allows for a more flexible, expansive research study, it also introduces complexities that need to be addressed both logistically and analytically.