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

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. It is convenient to introduce a standard terminology. –Cox (1958, p. 2) The users of statistics encounter a frustrating problem: statisticians seem inconsistent in the definitions they attach to certain words and in their use of symbols. –Urquhart (1981) Is the subject of statistics to lead to different terminologies in different areas of application? This reviewer suggests not. If this be accepted then the onus is on the latter‐day workers, e.g., in psychology, to read the prior literature and try to follow usage or at the very least, give also the nomenclature that is standard to the statistics profession. –Kempthorne (1982) Conceptual and inferential errors may arise because of vague and imprecise definitions and formulations. –Federer (1993) Unfortunately, the terminology for error reduction designs using the split‐unit principle is not quite uniform. –Hinkelmann and Kempthorne (2008) In conclusion, reform and standardization of terminology in statistics, experimental design and sampling design is badly needed, is possible, and would improve statistical practice. –Hurlbert (2009)