# 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 effect of temperature on a chemi­cal reaction, the effect of the dosage of a drug on the response of patients, and the effect of carbon percentage on the hardness of steel are some examples of such relations. Though this is the most obvious form of a factor, factors are manifested in several other forms in experiments. The sexes of humans in a psychological test, for instance, are two levels of one qualitative factor, human. Strains of laboratory animals, varieties of wheat in a test for yield, and light bulbs made by different companies subjected to test for length of life are other examples of qualitative factors.

### 2. Random versus Fixed Factors

The worth of the published results of an experiment is measured by the extent to which generalization is possible. If the findings are restricted to the particular variety of: subject or material, time of day, and place of experimentation, then the factors so involved are said to be fixed. To facilitate generalization, there should be randomization relative to such factors. If, for instance, an experi­ment is planned to test the effect of the dosage of a pain-killing drug on human adults, ideally, randomization should be imposed relative to the sex, age, race, social, and professional varieties of the subjects, the body locations of pain, and time of day, and sev­eral replications should be done over a lengthy period in different weather and climate conditions, and so on. Out of these and many others conceivable factors, only those on which randomiza­tion was imposed in the experiment are referred to as random fac­tors; those that were not so randomized remain fixed factors in the experiment.

### 3. Constant and Phantom Factors

As mentioned above, potential factors are many; in fact, the experimenter him- or herself is a potential factor; the room where the experiment is done is also a potential factor. In any experi­ment, only a limited number of potential factors can be used as design factors. The remaining ones can be classified into two types: constant factors and phantom factors. Constant factors are those used at only one level throughout the experiment. When all experiments are done in one room, the room is a constant factor; if all replications are done by one experimenter, the experimenter is a constant factor. Phantom factors, on the other hand, are those that enter the experimental system at different levels, though unintentionally and often uncontrollably. Time of the day is a good example. Change in room temperature and humid­ity (when these are not included as design factors) are more examples. The obvious remedy against the effects of both the constant and phantom factors is randomization.

### 4. Treatment and Trial Factor

Treatment in our context means “to find the effect(s) of.” If, for instance, performance of a car in terms of miles per gallon is being tested for at speeds of fifty, sixty, and seventy miles per hour, then the speed, which is purposely varied, is a treatment factor. In the case of multifactor experiments, in which the effect of each factor, over a range, on the outcome is tested for, each is referred to as a treatment factor. When the experimenter is not sure whether a certain factor has significant or negligibly small effect on the outcome, that factor will be designed into the experiment in the preliminary stage as a treatment factor. If it is found to be an insignificant factor, from then on, it will be treated in further experiments either as a fixed or constant fac­tor, depending on the context. In contrast, when some factors— with the levels of each factor held steady—are repeatedly tested for their combined effects, and the outcome of each repetition is recorded to be averaged later for better confidence, each factor is called a trial factor (and such tests are referred to as repeated- measurement experiments’).

### 5. Blocking and Group Factors

Blocking refers to dividing subjects (before the experiment) into different groups on the basis of similarity within each group and distinction from other groups. Blocking factors may be either qualitative or quantitative. Some instances follow: If humans (or any other animals) are to be experimented on, blocking them into “male” and “female” groups is qualitative. Occupation and ethnic origin are other examples. If adult men are the subjects, blocking by age, say twenty to forty, forty-one to sixty, sixty-one to eighty years, is quantitative. Years of college education and yearly income are other examples. In contrast, forming groups among subjects by arbitrary assignment leads to group factors. Suppose a given drug is to be tested on humans for its effect at a given dosage and also at twice that dosage with a subject popula­tion of twenty adults. Forming two groups of ten with random­ization and testing the single dosage on one group and the double dosage on the other does not constitute a group factor. On the other hand, suppose a class of ten students is arbitrarily divided into two groups of five (say, those in the first bench and those in the second bench), and each group is required as a team to work out a solution on a collaborative basis to the same prob­lem given to both the groups. A talented individual in one group or a disruptive individual in the other is enough to make a con­siderable difference between the two groups’ performances. As a way of being fair to the students, this possibility calls for a group factor: students included in the group deprived of the proven advantage need to be given an extra boost in evaluation.

### 6. Unit Factor

The individuals in a subject group are referred to as units. If units in two or more groups are all subjected to the same test, and the score of each unit is separately recorded, it is quite possible, even likely, that the differences in scores will be considerable. Then, the average of scores within a particular group serves as an index of that experiment. Such averages are the bases for unit factors.

These are some, but by no means all, of the variations of fac­tors. By now, it should be evident to the reader that what makes a given factor random (not fixed), constant (not phantom), or treat­ment (not trial), and so on, is not the nature of the factor as such but the circumstances that bring the factor into the experimental scheme, as perceived and decided upon by the experimenter. Based on the answers to such questions as the following, a set of factors will first be selected by the experimenter:

• What are all the potential variables that may influence the effect to be studied?
• Which of these variables are to be included—now termed factors in the experiment—and which, if any, may be ignored?
• Each of these will, in turn, be subjected to more intrusive ques­tions, such as
• Is this factor of direct interest as a cause? If the answer is yes, it will become one of the treatment factors.
• May this factor modify the effect of one or more of the treatment factors? If the answer is yes, the presence or absence of interaction between factors will be focused on.
• Is this factor a part of the experimental technique (e.g., varieties of rice in the study of the effect of a given fertilizer on the yield of rice)?
• Is this factor required because of the need for classification (e.g., men and women in an experiment on the effect of a given drug for headache relief)?
• Does the presence or absence of this factor make a differ­ence in the effect to be studied (e.g., a certain vitamin pro­posed to have catalytic value when taken with a given miracle weight-loss drug)?

As the experimenter answers these questions, each selected factor will fall into any one, but usually more than one, of the various classification(s) discussed above.

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