Planning Experiments

Abstract

This chapter highlights the importance of thorough experimental planning and provides a step-by-step guide for this process. The purpose and significance of the guide is illustrated with real experiments. The chapter also briefly introduces some standard experimental designs, such as completely randomized designs, block designs, and split-plot designs, whose detailed descriptions are provided in later chapters.

Exercises

Exercises 1–7 refer to the list of experiments in Table 2.10.

• 1. Table 2.10 gives a list of experiments that can be run as class projects. Select a simple experiment of interest to you, but preferably not on the list. Complete steps (a)–(c) of the checklist with the intention of actually running the experiment when the checklist is complete.

• 2. For experiments 1 and 7 in Table 2.10, complete steps (a) and (b) of the checklist. There may be more than one treatment factor. Give precise definitions of their levels.

• 3. For experiment 2, complete steps (a)–(c) of the checklist.

• 4. For experiment 3, complete steps (a)–(c) of the checklist.

• 5. For experiment 4, list sources of variation. Decide which sources can be controlled by limiting the scope of the experiment or by specifying the exact experimental procedure to be followed. Of the remaining sources of variation, decide which are minor and which are major. Are there any blocking factors in this experiment?

• 6. For experiment 6, specify what measurements should be made, how they should be made, and list any difficulties that might be expected.

• 7. For experiment 8, write down all the possible sources of variation. In your opinion, should this experiment be run as a completely randomized design, a block design, or a design with more than one blocking factor? Justify your answer.

• 8. Read critically through the checklists in Sect. 2.5. Would you suggest any changes? Would you have done anything differently? If you had to criticize these experiments, which points would you address?

• 9. The following description was given by Clifford Pugh in the 1953 volume of Applied Statistics.

  “The widespread use of detergents for domestic dish washing makes it desirable for manufacturers to carry out tests to evaluate the performance of their products. $\ldots$ Since foaming is regarded as the main criterion of performance, the measure adopted is the number of plates washed before the foam is reduced to a thin surface layer. The five main factors which may affect the number of plates washed by a given product are (i) the concentration of detergent, (ii) the temperature of the water, (iii) the hardness of the water, (iv) the type of “soil” on the plates, and (v) the method of washing used by the operator. $\ldots$ The difficulty of standardizing the soil is overcome by using the plates from a works canteen (cafeteria) for the test and adopting a randomized complete block technique in which plates from any one course form a block $\ldots$ . One practical limitation is the number of plates available in any one block. This permits only four $\ldots$ tests to be completed (in a block).”

  Draw up steps (a)–(d) of a checklist for an experiment of the above type and give an example of a design that fits the requirements of your checklist.