## Statistical Science

- Statist. Sci.
- Volume 32, Number 3 (2017), 469-485.

### Models for the Assessment of Treatment Improvement: The Ideal and the Feasible

P. C. Álvarez-Esteban, E. del Barrio, J. A. Cuesta-Albertos, and C. Matrán

#### Abstract

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in statistics through natural questions such as “Is the the new treatment significantly better than the old?” However, this is only partially answered by some of the usual statistical tools for this task. More importantly, often practitioners are not aware of the real meaning behind these statistical procedures. We analyze these troubles from the point of view of the order between distributions, the stochastic order, showing evidence of the limitations of the usual approaches, paying special attention to the classical comparison of means under the normal model. We discuss the unfeasibility of statistically proving stochastic dominance, but show that it is possible, instead, to gather statistical evidence to conclude that slightly relaxed versions of stochastic dominance hold.

#### Article information

**Source**

Statist. Sci., Volume 32, Number 3 (2017), 469-485.

**Dates**

First available in Project Euclid: 1 September 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1504253127

**Digital Object Identifier**

doi:10.1214/17-STS616

**Mathematical Reviews number (MathSciNet)**

MR3696006

**Zentralblatt MATH identifier**

06870256

**Keywords**

Stochastic dominance similarity two-sample comparison trimmed distributions winsorized distributions Behrens–Fisher problem index of stochastic dominance

#### Citation

Álvarez-Esteban, P. C.; del Barrio, E.; Cuesta-Albertos, J. A.; Matrán, C. Models for the Assessment of Treatment Improvement: The Ideal and the Feasible. Statist. Sci. 32 (2017), no. 3, 469--485. doi:10.1214/17-STS616. https://projecteuclid.org/euclid.ss/1504253127