The Experimental Unit in Statistical Analysis

healthy skepticism toward their own work, because the validity of any statistical analysis for any experiment depends upon how nearly the data and components of the experiment approximate the conditions of the mathematical model employed. The mathematical statistician is largely concerned with the development of &dquo;theoretical&dquo; experiments; the researcher employs models developed by the theoretician to assist him in making an objective and, hopefully, correct interpretation. Some situations closely parallel the models but other situations are only rough approximations, at best. The &dquo;success&dquo; of gambling casinos in Las Vegas rests on the premise that the assumptions of their mathematical models are almost perfectly met. Conversely, the probability-calculated assuming fair dice-of 15 straight &dquo;passes&dquo; is irrelevant in a crap game with loaded dice. Perfect isomorphism between models and reality is rarely possible in the behavioral sciences, yet the accuracy of our conclusions and inferences is contingent, at least in part, upon the degree of correspondence between the model and the experimental processes and data. A researcher needs