On a Class of Rank Order Tests for the Parallelism of Several Regression Lines

For the regression model $Y_{\nu i} = \alpha + \beta C_{\nu i} + \epsilon_{\nu i}, i = 1, \cdots, N_\nu$, where the $\epsilon_{\nu i}$ are independent and identically distributed random variables (iidrv), optimum rank order tests for the hypothesis that $\beta = 0$ are due to Hoeffding (1950), Terry (1952) and Hajek (1962), among others. In the present paper, the theory is extended to the problem of testing the homogeneity of the regression coefficients from $k(\geqq 2)$ independent samples. Allied efficiency results are also presented.