Extent of the Problem

Every problem may be visualized as a journey to be undertaken by the researcher. There is a point of departure and a point of destination. Even at the point of departure, when the researcher is likely to begin, there may be a number of uncertainties relative to the preparation necessary. The longer the journey,

Problem: Qualitative or Quantitative?

It is desirable for the experimenter to reflect on what kind of inputs and outputs he is likely to deal with in the proposed research problem. Is he going to deal with qualities or properties known to have been measured, or is he left to deal anew with qualities whose measurement is not well

Can the Problem Be Reshaped?

When we talk about reshaping a problem, we are not talking of exchanging one problem for another. If this were possible with­out obligation, the researcher’s life would be a picnic. Changing jobs where jobs are plentiful is fairly common; one is not required to explain the event. We are talking here about the pos­sibility

Proverbs on Problems

A fitting conclusion for this chapter may be a few passages taken from a very interesting little book (now a classic) by G. Polya,1 which any student of science, particularly researchers, should find instructive and interesting. Among hundreds of passages one can find worthy of using as proverbs, only twelve are given below in

The Place of Hypothesis in Research

In view of the fact that a hypothesis is central to any scientific investigation, theoretical or experimental, it is necessary to study hypotheses in more detail. In this chapter, we will see, among other things, the “provisional” nature of hypotheses, meaning that there is nothing permanent, nothing final, about any hypothesis. But without hypotheses,

Desirable Qualities of Hypotheses

The use of hypotheses are as widespread and their varieties are large. Isaac Newton’s Laws of Motion were hypotheses he set himself to prove. Finding my lost set of keys also requires hypotheses. Some qualities serve as criteria to distinguish great hypotheses from trivial ones and, to an extent, to judge the soundness of

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,

Treatment Structures in Designing Experiments

1. Placebo Placebo means something to please. It is not rare that some patients experience relief from a sickness on using a medicine given by a doctor, even if the medicine is nothing more than an inert substance given to the patient, without his knowledge, in the form (shape and color) of a medicinal

Many Factors at Many Levels, but One Factor at a Time

Let us first illustrate a case in which two or more factors have a combined influence but are experimented with one factor at a time. Example 7.1 We call our experimenter here “coffee lover.” He guessed that “great” coffee is the result of adding to the fresh brew of a given strength of a

Factorial Design, the Right Way

When two or more factors, each in two or more levels, are to be tested for their combined effect on the quality characteristic—the dependent variable—-factorial design is appropriate. The follow­ing is an example of three factors at two levels. Example 7.2 In a sheet metal press, it is the intention to measure the quantity

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Too Many Factors on Hand?

Efficient as it is, even factorial design can get choked with too many treatments in industrial experiments, where it is not uncommon to face as many as ten to fifteen factors threatening to act simultaneously on the outcome. Consider an experiment in which there are six factors—this is not too many in several industrial

“Subjects-and-Controls” Experiments

Situations wherein several causes acting together result in one or more noticeable effects are not rare. Our coffee lover’s experiment was but one example. If the intention of the experiment is to study the effect of a new cause in addition to the existing ones, then a comparison between two cases, one with the

Combined Effect of Many Causes

In the preceding example of an experiment on the benefit of a new plant food, it was agreed by implication that the addition of the plant food to the nourishment protocol of a subject plant did not, by its presence, in any way influence the other items of care. Suppose that a particular plant’s

Unavoidable (“Nuisance”) Factors

In the context of many factors acting together, some uninten­tional, often unperceived or unavoidable, factors that cannot be accounted for may influence, to an unknown extent, the quality characteristic. For example, vibrations in the building, noise, illu­mination, room temperature, humidity, and so forth, can have an effect when the experiment involves only inanimate objects.

Designing Factors

The most striking feature that distinguishes experiments with designed factors from those without them is that, in the former, all the factors are simultaneously designed into the experiment, whereas in the latter, experiments are done one factor at a time, like experiments with only one independent variable. That designing factors is more efficient than

Experiments with Designed Factors

Consider the following eight experiments with combinations: Out of these, each of the following four pairs provides results for comparing the effect of ^2 with that of ap The other four pairs serve to compare the effect of b>2 with that of bp Finally, the following four pairs provide the bases to compare the

Matrix of Factors

The situation of having three variables, each at two levels, can be represented pictorially, as shown in Figure 8.1. Each factor combination of the eight combinations we have dealt with as “designed factors” is represented by a vertex of the orthorhom­bic volume; the space represented by this shape is often referred to as the

Remarks on Experiments with Two-Level Factors

In multifactor experiments, particularly when the number of fac­tors is high, testing at two levels of factors is quite adequate to decide (1) if one or more of the factors is ineffective, (2) the rela­tive extent of effectiveness of each factor, and (3) if two or more of the factors interact, meaning that their

Response of Multifactor Experiments

Whereas results of single-factor or one-factor-at-a time experi­ments can usually be compiled as y = fx), the response to multi­factor experiments needs a different treatment for analysis. We will start in this chapter with the simplest situation: two factors, at two levels each. We further assume that the factors are quanti­tative. But to keep

Experiments with More Factors, Each at Two Levels

As a way of preparing for factorial experiments with more than two factors, let us slightly modify the data in Table 8.5, using the “-1” and “+1” symbolism in place of “low” and “high” for the factor levels. The modification results in Table 8.6. An explanation of the last two rows of this table