Randomization Inference and Bias of Standard Errors

Author

Gary L. Gadbury, Missouri University of Science and Technology

Abstract

A nonparametric statistics course typically includes material regarding "distribution free" randomization based inference. However, the accuracy of reported p values and confidence intervals often relies on an unverifiable assumption of unit(subject)-treatment additivity. This assumption is not always explicitly stated in texts and, when the assumption does not hold, the implications on inference are seldom discussed. The focus of this article is the bias of standard errors of estimated mean treatment effects in the presence of nonadditivity. This bias is characterized and interpreted for a usual estimator of standard error in three common experimental designs: a two-sample completely randomized design, a matched-pairs design, and a balanced, two-period cross-over design. Even in the presence of nonadditivity, useful conservative estimates of a mean treatment effect can be obtained. This is illustrated using some previously published data.

Recommended Citation

G. L. Gadbury, "Randomization Inference and Bias of Standard Errors," American Statistician, vol. 55, no. 4, pp. 310 - 313, Taylor and Francis Group; Taylor and Francis, Nov 2001.

The definitive version is available at https://doi.org/10.1198/000313001753272268

Department(s)

Mathematics and Statistics

Keywords and Phrases

Additivity; Experiments; Nonparametric; Permutation; Potential response

International Standard Serial Number (ISSN)

0003-1305

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Taylor and Francis Group; Taylor and Francis, All rights reserved.

Publication Date

01 Nov 2001