Minimum Detectable Effect Size Computations for Cluster-Level Regression Discontinuity: Quadratic Functional Form and Beyond

TL;DR

This paper extends power calculation formulas for cluster-level regression discontinuity designs to quadratic and beyond functional forms, providing practical tools and insights for researchers to determine minimum detectable effects under various conditions.

Contribution

It introduces extended formulas for power analysis assuming quadratic functional form and an empirical framework for untraceable variance, implemented in R tools.

Findings

Quadratic functional form simplifies interaction concerns.

Sample size varies with functional form and truncation symmetry.

Extended empirical framework aids power calculations when variance is unknown.

Abstract

This study extends power formulas proposed by Schochet (2008) assuming that the cluster-level score variable follows quadratic functional form. Results reveal that we need not be concerned with treatment by linear term interaction, and polynomial degree up to second order for symmetric truncation intervals. In comparison, every slight change in the functional form alters sample size requirements for asymmetric truncation intervals. Finally, an empirical framework beyond quadratic functional form is provided when the asymptotic variance of the treatment effect is untraceable. In this case, the CRD design effect is either computed from moments of the sample or approximate population moments via simulation. Formulas for quadratic functional form and the extended empirical framework are implemented in the cosa R package and companion Shiny web application.