Techniques described in an earlier paper (Kastenbaum, Hoel Bowman, 1970), are used to generate tables of sample size requirements for testing treatment effects in a randomized block design. Maximum values of the standardized range of the treatment means are tabulated for k = 2, 3, 4, 5, 6 treatments; b = 2, 3, 4, 5 blocks; 1 ≤ N ≤ 5 observations per cell; and α = 0.01, 0.05 and β = 0.005, 0.01, 0.05, 0.1, 0.2, 0.3 levels of risk. To simplify the determination of sample sizes necessary in a one-way analysis of variance, we have presented (Kastenbaum, Hoel & Bowman, 1970) tables of maximum values of the standardized range which apply when the means of k groups, each containing N* observations, are being compared at α and β levels of risk. Use of the standardized range in this situation was first elaborated on by Pearson & Hartley (1951), who also proposed extensions of the procedure to the randomized block design. Their model for the double classification with N observations in each cell is yijl = μ + li + bj+(tb)ij + ɛijl' where ti is the ith treatment effect, bj is the jth block effect, (tb)ij is the interaction effect of treatment i with block j and ɛijl is the effect due to the lth observation on the ith treatment in block j (i = 1,…, k; j = 1,…, b; l = 1,…, N). Here the ɛijl are assumed to be independent normal variables with mean zero and variance σ2. In this situation the sample size, N, necessary to test the absence of a treatment effect(ti = 0 for all i = 1,…, k) for specified values of k, b, α and β may be achieved through an iterative process involving Pearson and Hartley's charts of the power function. These charts are given in terms of Tang's noncentrality parameter ø, α, β, v1 = k − 1 and v2 = bk(N − 1). Table 1 provides direct answers to this question without requiring iteration. For the randomized block design the standardized maximum difference between any two treatment means is T = (tmax-tmin)/σ. It can easily be shown that T≤ ø{(2k)/(bN)}1/2 with equality if and only if ti = 0, Σti = 0, for all ti other than tmsx and tmin. Maximum values of the standardized range of the treatment means, ø{(2k)/(bN)}½, were calculated as described by Kastenbaum et al. (1970) and are tabulated for situations in which k treatment means are being compared at α and β levels of risk, in a randomized block design containing b blocks and N observations per cell, for aα = 0.01, 0.05; β = 0.005, 0.01, 0.05, 0.1, 0.2, 0.3; k 2(1)6; b = 2(1)5; 1 ≤ N ≤ 5. More extensive tables may be obtained from the authors.