CHUCu} cL EISENEART University of Wi200nsin and the National Bureau of Standards 1. Introductory Remarks. The statistical technique known as' analysis of variance," developed more than two decades ago by RA Fisher to facilitate the analysis and interpretation of data from field trials and laboratory experiments in agricultural and biological research, today constitutes one of the principal research tools of the biological scientist, and its use is spreading rapidly in the social sciences, the physical sciences, and in engineering. Numerous textbooks (or, should I say" manuals"?) have been published-and, I dare say, many more are being written-that aim to provide their readers with a working knowledge of the steps of analysis-of-variance procedure with a minimum exposure to mathematical formulas and mathematical thinking. Designed expressly for the" non-mathematical reader", whose mathematical equipment is presumed to be a reasonahle competence in arithmetic and elementary algebra-mere previous exposure to these subjects is not enough. The method of instruction adopted in these books consists chiefly in guiding the reader by easy stages through a series of worked examples that are typical of the more common problems amenable to analysis of variance that arise in the scientific or engineering field with which the author of the book concerned is con-versant."* An expository address delivered at a joint session of the Biometrics Section of the American Statistical Association and the Institute of Mathematical Statistics, held on December 28, 1946, in conjdnction with the 113th Annual Meeting of the American Aso-ciation for the Advancement of Science, Boston, Massachusetts. IThe author has found the discusslons and examples of analysis-of-variance procedures given in the following four books especially valuable both for reference and for purposes of Instruction: CH Goulden, Methods oJ Statistical Analysit; GW Snedecor, Cale-ulatlon and It erpretation of Analysis of Variance and Corariance; GW Snedecor Statietical Method8; LHC Tippett, The Methods of Statistics. See full bibliographica references at the end of this paper.