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.
"A Non-Parametric Test of Whether Two Simple Regression Lines are Parallel." Ann. Statist. 2 (2) 295 - 310, March, 1974. https://doi.org/10.1214/aos/1176342664