## The Annals of Statistics

- Ann. Statist.
- Volume 2, Number 2 (1974), 295-310.

### A Non-Parametric Test of Whether Two Simple Regression Lines are Parallel

#### Abstract

This paper provides a means for testing the hypothesis that two simple regression lines are parallel, when the two sets of error terms have two arbitrary unknown continuous distributions. The non-parametric test which is developed here is analogous to the two-sample Wilcoxon test. At the end of the paper, two additional problems in non-parametric regression analysis are briefly referred to.

#### Article information

**Source**

Ann. Statist., Volume 2, Number 2 (1974), 295-310.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342664

**Digital Object Identifier**

doi:10.1214/aos/1176342664

**Mathematical Reviews number (MathSciNet)**

MR362692

**Zentralblatt MATH identifier**

0277.62054

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 62J05: Linear regression 62G15: Tolerance and confidence regions

**Keywords**

Non-parametric test parallelism Wilcoxon-Mann-Whitney test simple regression $U$-statistics

#### Citation

Potthoff, Richard F. A Non-Parametric Test of Whether Two Simple Regression Lines are Parallel. Ann. Statist. 2 (1974), no. 2, 295--310. doi:10.1214/aos/1176342664. https://projecteuclid.org/euclid.aos/1176342664