A Comparison of Sample Sizes for the Analysis of Means and the Analysis of Variance

AbstractTables of sample sizes for the analysis of means necessary for detecting differences among k treatments when two of the treatment means differ by at least a specified amount Δ (measured in units of the process standard deviation) for fixed level of significance α and fixed power P are 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.KeywordsAnalysis of MeansMultiple ComparisonsPowerSample Sizes Additional informationNotes on contributorsPeter R. NelsonDr. Nelson is a Senior Statistician. He is a Senior Member of ASQC.