For block designs with one observation per cell, the model often used is the linear model in which the observations $X_{i\alpha} (i = 1, \cdots, r; \alpha = 1, \cdots, n)$ can be written \begin{equation*}\tag{1.1} X_{i\alpha} = v + \xi_i + \mu_\alpha + Y_{i\alpha} (\sum \xi_i = \sum \mu_\alpha = 0)\end{equation*} where the $\xi's$ are the parameters of interest (treatment effect) the $\mu's$ are nuisance parameters (block effect), and the $Y's$ are independent with common continuous distribution $F$. The purpose of this note is to discuss some new robust test statistics (e.g. 2.14 and 2.16) of the null-hypothesis $H_0 : \xi_1 = \xi_2 = \cdots = \xi_r$, and to discuss a new robust estimate (3.3) of the contrast $\theta = \sum c_i\xi_i$.