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 zero or close to zero, it should draw our attention as a possibly ineffective factor. We need to see if that factor has any noticeable interaction with other factors, particularly with the prime factor (assuming that it is possible, either by previous experience or by intention, to designate one as such). If the interaction is also negligible, the particular factor should be counted out in all further steps of the design. The more such spurious factors we can identify, the less complex the planning and analysis of the responses from the experiment becomes. Two-level experiments are ideally suited for that. Besides, data from two-level experiments provide an idea of the direction of the correlation curve. What such data cannot pro­vide is the correlation itself. To get a suggestion for the shape of the correlation curve, even if it turns out to be linear, we need at least three data points, which calls for testing factors at three lev­els. To render the correlation more dependable, we need to test factors at more than three levels. But the limitation is the number of experimental runs to be planned and the concomitant resources for the experiment itself, followed by the analysis of the data. Thus, the number of levels for testing factors in most cases will be the “most we can afford,” not “all we can do.”

The effect of two factors acting together at three levels on a dependent variable is the simplest in this category of factorial design. The number of combinations of factors is given by I^f = 3² = 9. But, three points, each an outcome (recorded as a num­ber) of the dependent variable, may not be adequate for observ­ing the trend—the shape of the curve—of the relation between the dependent variable and the independent variable(s). Testing each factor at four levels will provide a better definition, which, of course, is made possible at the cost of increasing the number of required runs to 4² = 16. After running the experiment, we will have sixteen numbers to deal with, each recorded as the effect caused by one of the sixteen combinations of the two indepen­dent variables. Assuming fictitious values for the dependent vari­able, we will attempt some possible observations in the following.

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