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 conducting one-factor-at- a-time experiments is the first point we need to underscore. The number of many factors and number of levels at which each should be tested, of course, depend on the particular experimen­tal requirement. For our purpose, we will start with three factors, each to be tested at two levels. We will call the factors a, b, and c. When used at low levels, we will designate these as a^ b1 and q, and at high levels, as a2, b2 and C2. Functions of the three inde­pendent variables, when all are used at low levels, may be expressed as

nd when all are used at high levels, as

In this designation, “high” and “low” do not necessarily mean that a2 > a1, with both expressed in the same units. Instead, it means that by changing a from a1 to aj, an improvement is expected in the dependent variable y. Improvement, again, does not mean that yj > yi, with both expressed in the same units. For instance, if y is the profit in a business, when y₂ is numerically higher than yi, there is an improvement, whereas if y is the loss in the business, when yj is numerically higher than yi, there is not an improvement; it would then be desirable that yj be numeri­cally less than yi. Similar considerations hold good for the inde­pendent variables b and c as well.

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