Affirmation of the Classical Terminology for Experimental Design via a Critique of Casella’s Statistical Design

Published in Agron. J. 105:412–418 (2013) doi:10.2134/agronj2012.0392 Copyright © 2013 by the American Society of Agronomy, 5585 Guilford Road, Madison, WI 53711. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. T in statistics, as in other fields, cannot be irrevocably fixed and evolves with the subject. Nevertheless, where there is a firmly established set of concepts and definitions encapsulating important concepts, it is regrettable to see these definitions abandoned without good reason. This seems to have happened frequently in treatises on the design of experiments, and again in the recent book Statistical Design (Casella, 2008). This book rejects some of the widely used terms of experimental design, redefines others inappropriately or incompletely, and accepts other confusing usages long adopted by others. The purpose of this essay is to identify these conflicts and call attention to existing, more suitable terminology. The essay might serve as a supplement to Statistical Design for researchers and students who wish to use it but who are discomfited or confused by its terminology. Because Statistical Design is just one example from the large number of texts with similar terminological problems, this essay should have wider value as well. Over the years a few statisticians have called for improving the clarity with which statistical concepts and methodologies are communicated to researchers and students. The aim has been to improve statistical practice. In particular, there are good grounds for defending the core classical terminology of experimental design and for arguing that this terminology is suitable for adoption by all disciplines in which experimental work is carried out. On the other hand, many statisticians and scientists have not been much concerned with the lack of standardized terms and definitions for even core concepts. Statisticians have sometimes been heard to say, for example, that a common terminology is not important as long as researchers make clear how they define the terms they use or as long as they select the right model. This unkindness toward, especially, non-statistician users of the statistics literature is not often put into print. At the beginning of his classic monograph on factorial experiments, Yates (1935), however, did so in particular reference to the term experimental unit: ABSTRACT In many disciplines, basic and applied, a high frequency of errors of statistical analysis has been documented in numerous reviews over the decades. One insufficiently appreciated source of this has been the failure of statisticians, individually and collectively, to provide clear definitions for many of the terms they use—and failure to adhere to those definitions across time and across disciplines. The field of experimental design is one area where such problems have become acute. This essay documents that phenomenon via analysis of the terminology used in a recent text in that field, Statistical Design by G. Casella, but the problems identified are widespread and of ancient lineage. There exists a clearer, more consistent terminology, most of it well established more than half a century ago. Key issues are the tripartite structure of the design of an experiment, the need for experimental units to be physically independent of each other, the definition of pseudoreplication, and confusion about the meaning of split-unit designs. The problems identified seem to reflect a long-standing conflict between the classical, experiment-focused approach to design and the model-focused approach to the topic. Proponents of the latter have tended to stray from the classical terminology of experimental design, redefining terms in a somewhat casual fashion and thereby considerably confusing non-statisticians in particular. Wider understanding of these matters should lead to better textbooks, better teaching, and better statistical practice.