Tables of sample sizes for the analysis of means necessary for detecting differences amongktreatments when two of the treatment means differ by at least a specified amountΔ(measured in units of the process standard deviation) for fixed level of significanceαand fixed powerPare given forα= 0.1, 0.05, 0.01P= 0.5, 0.6, 0.7, 0.75, 0.8, 0.9, 0.95, 0.99Δ= 1, 1.25, 1.5, 1.75, 2, 2.5, 3k= 3(1)20, 24, 30, 40, 60.A comparison of these sample sizes with previously published sample sizes for the analysis of variance does not reveal any substantial differences. Examples of the use of the tables are given.