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 be two levels on one factor, humans. In another experiment dealing with family expenses for clothing and cosmetics, it is prudent to think of the two, men and women, as different factors; this deci­sion, of course, is left to the experimenter.

The presence or absence of a particular variable may be con­sidered as two levels of one factor. When the factor is quantita­tive, absence may be treated as level zero. When the factor is qualitative, there is room for confusion. For instance, it is often claimed that plants are sensitive to classical music. I am not aware of any proof for or against such a claim, but I know of a high school English teacher who, while his students were taking an examination, played records of classical music, believing in a sim­ilar claim that human performance is affected by music. If that teacher had two groups of; say; thirty students separated with randomization, and if he placed each group in identical rooms and gave all individuals the same examination at the same time, with himself functioning as proctor for both groups with equal time sharing, and if, with these factors common, he played music in one room and let silence prevail in the other, music then would be a presence-or-absence qualitative factor. Using the same criteria for judging, if the average performance of those in the group that was exposed to music was found to be better, to that extent, the belief of the teacher, the “hypothesis” of that “experi­menter,”—would be proven valid. But then, it would be a typical one-factor-at-a-time experiment, which is less meaningful. To observe the effect of music as a factor properly, the extents of its interaction(s) or noninteraction(s) with other factors, such as dif­ference^) in the subject matter for examination, teacher person­ality, time of day, duration of the examination, and so on, need to be studied.

Assuming that a list of factors has been selected, we now look at the selection of levels separately for quantitative and qualitative factors.

1. Levels of Quantitative Factors

Quantitative factors need to be specified in terms of

1. The lowest and the highest measurable value
2. The number of steps between these extremes
3. The increments (or spacing) between consecutive steps

In these respects, each factor in factorial experiments requires similar considerations to the ones in one-factor-at-a- time experiments.

The selection of extreme values is sometimes obvious. For instance, in an experiment in which temperature is a factor in measuring the productivity of shop workers, it is reasonable not to go beyond the range of 40°F to 100°F. On the other hand, if the experiment is to determine the effectiveness of a weight- increasing wonder drug, the lowest level should, of course, be zero, but the selection of the highest level is not so obvious. The guiding principles in selecting the number of steps are, on the one hand, to take as many as possible within the resources, but, on the other hand, to take as few as are sufficient for economy. In preliminary experiments, it is reasonable to use a considerably smaller number of levels than in the final experiment. Also, if the effect is known to present a linear relation, a smaller number of levels, often only two, is adequate, whereas if the effect presents a curve instead, at least three levels for the preliminary experiment, and many more for the final experiment, are required. As for the space between levels, it is preferable in most cases to keep it uni­form, but if the output presents a combination of straight and curved parts, closer spacing at the curve than at the straight part is desirable.

2. Levels of Qualitative Factors

An obvious example of a qualitative factor is different varieties of rice in testing the effectiveness of a fertilizer. The levels are the same as the varieties tested; hence, their number is the same. Another example is the case discussed above using classical music as a factor. Varieties in the music delivered based on volume, composer, instrument, and so on, can become qualitative factors with as many levels as there are variations. In both of these exam­ples, the highest and lowest levels, as well as the spacing between them, are devoid of significance.

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