A class of nonparametric procedures for testing the statistical identity of treatments in randomized block experiments is suggested and discussed. The suggested procedures are squarely based on experimental within-block randomizations, and they may be chosen so as to have special power against particular alternatives. The blocks are assumed to be statistically independent but no assumption is made concerning dependence within the various blocks. The basic idea is to obtain from each block a statistic that is, under the null hypothesis, symmetrically distributed about zero and then to apply to the set of these statistics a nonparametric test of symmetry about zero. The observational data can be of any quantitative type.