Open Access
December 2018 Rank tests in unmatched clustered randomized trials applied to a study of teacher training
Peng Ding, Luke Keele
Ann. Appl. Stat. 12(4): 2151-2174 (December 2018). DOI: 10.1214/18-AOAS1147


In the Teacher and Leader Performance Evaluation Systems study, schools were randomly assigned to receive new measures of teacher and principal performance. One outcome in the study, measured at the teacher level, was truncated at zero, and displayed a long tail. Rank-based statistics are one natural method to apply to such outcomes, since inferences will be robust and exact, and we can avoid assumptions about the model that generated the data. We investigate four different possible rank statistics that vary in the form of weighting applied to clusters. Each test statistic has the correct level but may vary in terms of the power to detect departures from the null. We conduct simulations for power comparing to linear mixed models with Normal, $t$, and Cauchy errors. We obtain a point estimate and construct confidence intervals by applying the Tobit model of effects, which assumes that treatment increases the outcome by a constant amount but only if the response under control would be positive. We also develop a formal randomization-based method for testing the appropriateness of the Tobit model of effects. In the data from the study, we find no evidence against the Tobit model of effects.


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Peng Ding. Luke Keele. "Rank tests in unmatched clustered randomized trials applied to a study of teacher training." Ann. Appl. Stat. 12 (4) 2151 - 2174, December 2018.


Received: 1 May 2017; Revised: 1 October 2017; Published: December 2018
First available in Project Euclid: 13 November 2018

zbMATH: 07029450
MathSciNet: MR3875696
Digital Object Identifier: 10.1214/18-AOAS1147

Keywords: clustered randomization , Fisher randomization test , model checking , rank statistic , Tobit model

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.12 • No. 4 • December 2018
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