## The Annals of Statistics

### On the Use of Ranks for Testing the Coincidence of Several Regression Lines

#### Abstract

For several linear regression lines $Y_{ij} = \alpha_i + \beta_i(x_{ij} - x{_i.}) + Z_{ij}, i = 1,\cdots, k; j = 1, \cdot, n_i$, a statistic for testing $\alpha_i = \alpha, \beta_i = \beta$ is constructed based on the simultaneous ranking of all the observations. The asymptotic properties of the criterion are also studied. The results are, however, not directly applicable to the general design model $Y_{ij} = \alpha_i + \beta_i x_{ij} + Z_{ij}$, unless it is assumed that the group means $x_i$. are all equal.

#### Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 521-527.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343083

Digital Object Identifier
doi:10.1214/aos/1176343083

Mathematical Reviews number (MathSciNet)
MR373144

Zentralblatt MATH identifier
0305.62026

JSTOR