In expositions of the scientific use of experimentation it is frequent to find an excessive stress laid on the importance of varying the essential conditions only one at a time.… to study the effects of this single factor, is the essentially scientific approach to an experimental investigation. This ideal doctrine seems to be more nearly related to expositions of elementary physical theory than to laboratory practice in any branch of research.…
The modifications possible to any complicated apparatus, machine or industrial process must always be considered as potentially interacting with one another, and must be judged by the probable effects of such interactions. If they have to be tested one at a time this is not because to do so is an ideal scientific procedure, but because to test them simultaneously would sometimes be too troublesome, or too costly. In many instances, as will be shown in this chapter, the belief that this is so has little foundation. Indeed, in a wide class of cases an experimental investigation, at the same time as it is made more comprehensive (by including multiple determinants], may also be made more efficient … [so that] … more knowledge and a higher degree of precision are obtainable by the same number of observations.
Seventy years later, however, we read:
One-factor-at-a-time experiments and similar “common sense” design strategies continue to be prevalent in industrial experiments in spite of the strong emphasis in statistics courses that these design strategies should be avoided. In justifying the avoidance of such design strategies, technical criteria such as design efficiency and confounding … routinely are over-looked by experimenters in industry. (Gunst & McDonald, 1996, p. 44.)
Actually, factorial design may be considered an ideal form of varying one variable at a time. Each row in a two-factor, A × B design varies only B, for one fixed level of A. Each additional row is thus a systematic replication of the B effect, but at a different level of A. From this perspective, factorial design conjoins the rule of one-variable-at-a-time with the principle of replication.