Write R for the unobservable array with N rows and j GLYPH<10> j columns having entries r$_{bi}$$_{z}$ . The unobservable R describes what would happen under all possible treatment assignments z 2 GLYPH<10> , but R does not change when actual randomized treatment assignment Z is selected. In contrast, the observable responses r$_{bi}$$_{Z}$ are one column of R , and which one column that is does, of course, depend upon the randomized treatment assignment, Z . FisherGLYPH<146>s (1935) sharp null hypothesis H$_{0}$ of no treatment e⁄ect asserts that r$_{bi}$$_{z}$ = r$_{bi}$$_{z}$ 0 for all z , z 0 2 GLYPH<10> and all b; i , so within each row bi of R all j GLYPH<10> j columns have the same value for r$_{bi}$$_{z}$ . No interference between units means that r$_{bi}$$_{z}$ = r$_{bi}$$_{z}$ 0 whenever z$_{bi}$ = z 0 $_{bi}$, that is, the response in block b at trial i depends on the treatment z$_{bi}$ assigned in block b at trial i , but it does not depend on the treatments z assigned at other trials. As discussed in §1.3, no interference between units is not plausible in Figure 1, and because of the overlapping of HRF functions is virtually impossible in Figure 2 if H$_{0}$ is false. By a randomized block experiment, we mean that Pr ( Z = z j R ; n ; m ) = 1 j GLYPH<10> j for each z 2 GLYPH<10> . (1) In §1, the timing of trials and hence also the number N$_{b}$ of trials was determined by a random process; then, with probability 1 4 the trial was a GLYPH<147>stop trialGLYPH<148>and with probability 3 4 the trial was a GLYPH<147>go trial;GLYPH<148> hence, n and m were random variables, but the conditional probabilities given R ; n ; m of particular patterns of stop or go trials was completely ran- domized within each block in the sense that (1) was true. Importantly, (1) says treatment assignments were determined by a truly randomized mechanism that ensured the unob- servable potential responses R were not predictive of treatment assignment Z ; this is, of course, the essential element of randomized treatment assignment. In a randomized exper- iment, any association between treatment assignment Z and the observed responses, r$_{bi}$$_{Z}$ , is due to an e⁄ect caused by the treatment expressed in R ; because of (1), an association 12