Statistics and Its Interface

Volume 16 (2023)

Number 3

Testing attributable effects hypotheses with an application to the Oregon Health Insurance Experiment

Pages: 349 – 361



Mark M. Fredrickson (Department of Statistics, University of Michigan, Ann Arbor, Mich., U.S.A.)

Yuguo Chen (Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Il., U.S.A.)


Following a randomized trial, the sum of the differences in the outcomes for the treated units compared to the outcome that would have been observed if the same units had been assigned to the control condition is known as the attributable effect. Most previous methods on testing hypotheses about the attributable effect require the outcome to be binary or ordinal. In this paper, we use a simple approximation to the distribution of a carefully selected test statistic under the hypothesis that the attributable effect is zero to expand attributable effects inference for count and continuous data. The method is efficient and performs well in a variety of simulations. We demonstrate the method using a large medical insurance field experiment.


Attributable effects, hypothesis testing, optimization, randomization inference, zero inflated outcomes

2010 Mathematics Subject Classification


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This work was supported in part by NSF grants DMS-1406455, DMS-1646108 and DMS-2015561.

Received 9 July 2021

Accepted 7 January 2022

Published 14 April 2023