Improving Experiments by Optimal Blocking: Minimizing the Maximum Inter-Block Distance

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Michael Higgins*+ and Jasjeet S. Sekhon
• Companies: and University of California, Berkeley
• Keywords: Blocking ; Optimization ; Bottleneck Graph ; Design of Experiments ; Causal Inference

Abstract

We develop a new method for blocking in randomized experiments that works for an arbitrary number of treatments. We analyze the following problem: given a threshold for the minimum number of units to be contained in a block, and given a distance measure between any two units in the finite population, block the units so that the maximum distance between any two units within a block is minimized. This blocking criterion can minimize covariate imbalance, which is a common goal in experimental design. Finding an optimal blocking is an NP-hard problem. However, using ideas from graph theory, we provide the first polynomial time approximately optimal blocking algorithm for when there are more than two treatment categories. In the case of just two such categories, our approach is more efficient than existing methods. We derive the variances of estimators for sample average treatment effects under the Neyman-Rubin potential outcomes model for arbitrary blocking assignments and an arbitrary number of treatments.