between Z and r$_{bi}$$_{Z}$ cannot result from biased selection into treated and control groups if the treatment has no e⁄ect, that is if FisherGLYPH<146>s H$_{0}$ is true. 2.2 The uniformity trial As mentioned previously, in the absence of interference, it is natural to ask how a unit would have responded if that one unit had received the treatment and or if that one unit had received the control and to deGLYPH<133>ne e⁄ect of the treatment on this unit as a comparison of these two potential responses; see Neyman (1923), Welch (1937) and Rubin (1974) for discussion of this standard way of deGLYPH<133>ning treatment e⁄ects in randomized experiments. This formulation does not work when there is interference between units because a unit may be a⁄ected by treatments applied to or withheld from other units. Some deGLYPH<133>nition of the treatment e⁄ect with interference is needed if a randomization test of the null hypothesis of no e⁄ect is to be inverted to obtain a conGLYPH<133>dence interval for the magnitude of e⁄ect. In principle, the treatment e⁄ect is characterized by the N GLYPH<2> j GLYPH<10> j array R , where j GLYPH<10> j = Q B b =1 GLYPH<0> N$_{b}$ n$_{b}$ GLYPH<1> ; however, that array is mostly not observed, and it is so large and detailed that it would be beyond human comprehension even if it were observed. We would like to deGLYPH<133>ne the treatment e⁄ect as a summary of R , but in such a way that the summary is intelligible and usable in inference. We deGLYPH<133>ne the treatment e⁄ect with reference to a uniformity trial of the type that, in a certain era, was commonly used as an aid to designing experiments; see Cochran (1937). For instance, uniformity trials were once used to study the performance of competing experimental designs, such as complete randomization or randomized blocks or randomized Latin squares. In a uniformity trial, treatment assignment Z is randomized as if an actual experiment were about to be performed, but instead Z is ignored and the standard treatment is applied in all cases. In its original use, a uniformity trial divides a farm 13