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

Fractional Factorials

Having arrived at the logical end point for discussing full-facto­rial experiments with four factors, we need to reflect on what lies ahead. We mentioned early in this chapter that in many contexts, for example, manufacturing, confronting a large number of fac­tors is not uncommon. If the number of factors is ten, for instance, even

Varieties of Factors

1. Quantitative versus Qualitative Factors For convenience, we have so far considered a factor as an inde­pendent variable in a function of the kind y = fx). In this equa­tion, for every different numerical value of x, there is a corresponding numerical value of y. Therefore, x, then, is obvi­ously a quantitative factor. The

Levels of Quantitative and Qualitative Factors

Considerations, of quantity or quality levels, is an inseparable part of the selection of factors. First of all, the difference relative to a given variable may be taken either as a distinction between (or among) factors or as different levels of one factor. Men and women, in an experiment dealing with physical strength, may

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Limitations of Experiments with Factors at Two Levels

Chapter 8 dealt with designing many factors together, all at only two levels. When we are beset with a large number of factors, it is possible that one or more among those are spurious. It is desir­able to eliminate those early in planning the experiment. If the main effect of a particular factor is

Four-Level Factorial Experiments

We take the two factors as a and b, and designate the levels of The sixteen combinations can be lined up as follows: We notice in the above matrix that In the first column, the factor is common, and the only variables are the levels of b: bi, b>2, b3, and b4. In the

Interactions in Experimental Research

In most cases of research, particularly with quantitative parame­ters, data as depicted in Figure 9.1, with absolutely parallel lines, are rather rare. A set of data as shown in Figure 9.3, instead, is one of many possibilities. We will examine Figure 9.3 for interac­tion and for main effects. We notice in this figure some

Main Effects in Experimental Research

For observation of the main effects, we import the data in Table 9.1, augmented with some derived, additional information, now shown in Table 9.2. We observed in Figure 9.1 that there is practically no interac­tion between the factors a and b, but that has no bearing what­ever on the presence or absence of the

More on Interactions in Experimental Research

Interactions between factors, when there are only two, are easy to identify in two-way tables, as in Table 9.1, or even make visible in figures such as Figures 9.1 to 9.3. The presence of interactions complicates the inter­pretation of the experimental results relative to the benefits or harmful effects of individual factors. If there

More Factors at More Than Two Levels

When dealing with more than two factors, each at more than two levels, the significance of main effects and interactions remains unchanged. Now we need to analyze the experimental responses for main effects and interactions with three or more factors. For instance, with three factors instead of the previously analyzed two, the main effects

Searching through Published Literature

1. Researcher and Scholar Research scientists, of necessity, need to become scholars. The best scholars are not necessarily the best researchers, and vice versa. Knowledge in science and technology is so diversified that a pro­fessor, an expert in his own area of specialization, is nearly a novice in regard to the knowledge of other

Diversity to Match the Need

Perhaps no other aspect of experimental research, as an orga­nized activity, has so much diversity as the setup, often referred to as the apparatus, used for carrying out the experiment. With some reservation, we may say that there are as many setups as there are researchers. Notable exceptions are the standard equip­ment used repeatedly,

Designing the Apparatus of Experimental Research

To design is to contrive for a purpose; purpose is the all-impor­tant consideration. The first question any researcher needs to ask, as a way of designing the apparatus is, What do I want to observe? The answer to this question is part of the hypothesis. To the extent that the answer to the above

Simplicity, Compactness, and Elegance of Experimental Research

Guided by the hypothesis, one may visualize the kind of arrange­ment among several pieces of equipment to constitute the setup. It is worth one’s while to review each conceived piece of equip­ment individually, asking oneself crucial questions: Is it possible to eliminate a given piece of equipment and still accomplish the purpose? Is there

Measuring Instruments in Experimental Research

There are very few experiments in science and technology, even when only an object or a phenomenon is to be observed, in which no measuring instruments are involved. And when the change in a measurable quantity constitutes the effect (sometimes referred to as outcome or quality characteristic) part of the hypoth­esis, the need for

Calibration of Experimental Research

For most of the primary and secondary measures, there are mea­suring instruments, like rulers for lengths, balances for weights, and thermometers for temperatures. In daily routines, we take such measuring instruments for granted. If a person’s tempera­ture is noticed to be 104°F on a newly bought thermometer, one does not react with complacence, wondering,

Researcher as Handyman

The circumstances in which an experimenter finds himself deter­mine the variety and degree of skill demanded of him. To researchers in humanities, mathematics, and “theoretical” sci­ences, this concern for building the experimental setup is just hearsay. At the other extreme, almost all areas of engineering and technology require, for experimental research, some kind of

Cost Considerations in Experimental Research

The cost of an experimental setup may be considered against two items: (1) the cost of the various pieces of equipment, and (2) the cost of the experimenter’s time. In places where research is part of the tradition, several items, like motors, gear trains, pulleys, tubes, and clamps, may be available, waiting to be

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The Subject, Logic of Scientific Research

Philosophy is a typical subject of liberal arts. Logic is a part of philosophy; either at undergraduate or graduate level, it is taught by professors in the Department of Philosophy, unless there is a Department of Logic at the particular college. For the purpose of delimiting the scope of this book, we may act