Several Problems, Several Causes in Designing Experiments

The association of one cause with one effect has historically been considered “obvious”; hence, the logic of Mill’s Methods of Inquiry (see Chapter 4). Boyle’s law (1662), for example, associates the pressure (P) of a gas with its volume (V): P o 1/V Another law, attributed to Charles (1746—1823) and Gay (1778—1850) Lus- sac, associates pressure (P) with (absolute) temperature (T): P o T. It is implied, though, that in the verification of P o 1/V, the temperature is to be maintained constant, and in the verification of P o T, the volume is to remain unaltered. If, for instance, we consider the experiment in which the effect of pressure on vol­ume is being verified, with increasing pressure, the temperature concomitantly increases; to keep the temperature constant, the heat generated needs to be removed concurrently. To make this happen, the systems of insulation, temperature monitoring, and heat removal have to be perfect and instantaneous, which is, in terms of experimental control, unattainable. The laws were for­mulated disregarding such realities, that is, by “idealizing” the experiments. In terms of systems associated with an effect driven by several causes simultaneously, the above example is only the tip of the iceberg.

Instances where close to a dozen or more causes simulta­neously determine the end effect are not rare. The yield of an agricultural crop and the quality of a manufactured piece of hard­ware are but two examples. That yield in agriculture is a result of many variables—seed quality, field preparation, rain fall, sun­shine, fertilizer, pest control, and so forth—functioning together, has long been known to the farmer. To bring the benefit of scien­tific research to agriculture, experiments entailing many causes acting simultaneously are required. R. A. Fisher and his contem­porary investigators, starting in the early twentieth century, initi­ated a systematic study with the application of statistical principles to such experiments, which, in fact, laid the founda­tion for later analysis of experiments involving more than one factor. Many more vigorous developments have since been taking place in extending this aspect of statistics to experimental research in such areas as medicine, psychology, education, manu­facturing, athletics, and so on. Such developments came to be collectively known as “Design of Experiments.”

Though Design of Experiments has found applications in diverse areas, it is very often expounded in terms of plants and agriculture, perhaps owing to its origin. But analogies have been found, and extensively used, in all other fields of application. Conforming to this practice, Design of Experiments can be broadly divided into two aspects: (1) designing the block struc­ture, and (2) designing the treatment structure.

The first of these, the block structure, refers to dividing a cer­tain area of an experimental site for agriculture into so many blocks, and each block into so many plots, the purpose being to assign each plot to a different treatment. The second, the treat­ment structure, consists of subjecting different varieties of plants to the effect(s) of a combination of more than one cause, each cause referred to as a factor. Both structures are created using well-known principles of statistics and in ways that conform to randomization. Block structure and randomization are discussed in Chapter 16. The design of treatment structures, or factorial design, is discussed in this chapter. A few terms, often used as equivalents owing to their entry from different fields of applica­tion, need to be mentioned:

• Factor: also referred to as a cause, input, treatment, parameter
• Result: also referred to as an effect, yield, response, output, quality characteristic, dependent variable
• Treatment: also referred to as a given combination of fac­tors at given levels
• Test: also referred to as trial, replication, experiment, and so forth

The design referred to, obviously, is the preparatory work of the experimenter, in purpose and function similar to a blueprint for an engineer before execution of a project. The basic question that the experimenter needs to ask in designing an experiment is, What question(s) should the result(s) of the test(s) help me to answer? A careful, detailed answer to such a question determines what treatment—inclusion and/or variation of one or many independent variable(s), to act as cause—is required This consti­tutes the treatment structure, which has several variations; some of the better-known ones are briefly described as follows.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.