222 EXPERIMENTAL DESIGN 



five different temperatures at any one level of glucose, and if these are 

 replicated five times, there will be a total of twenty-five measurements. 

 If we repeat this operation with each of five concentrations of glucose, 

 we perform a total of 125 measurements. A factorial experiment can 

 allow us to obtain the same information more easily and, at the same time, 

 to evaluate any interaction between temperature and glucose concentra- 

 tion. At 5° C, we make five measurements, each using a different con- 

 centration of glucose. At 10°, 15°, 20°, and 25° C we do the same. We 

 have performed a total of twenty-five measurements, and each tempera- 

 ture and each glucose concentration is replicated five times. Analysis of 

 variance tells us the significance of the effect of temperature, the effect 

 of glucose, and any change in the effect of temperature resulting from 

 changes in the glucose concentration. 



The factorial design is very logical. If a repetition of a measurement 

 is identical in all details to the original measurement, the same errors 

 are likely to be repeated. If several factors influence the results, one 

 might as well learn something about these other effects upon repeating 

 the measurement. 



If the number of factors is large, the factorial design can become ex- 

 ceedingly complex. Because some of the factors may prove to be unimpor- 

 tant, the complex design may provide a great deal of useless informa- 

 tion. A few preliminary measurements may simplify the design. Despite 

 its complexity, the factorial design is very useful, and it is likely that 

 more and more laboratory experiments will be performed in this manner. 



SELECTED REFERENCES 



Cochran, William G., and Gertrude M. Cox, Experimental Designs, 

 2nd ed. New York: John Wiley & Sons, Inc., 1957. One of the most 

 complete catalogues of exp)erimental designs. 



Finney, D. J., Experimental Design and its Statistical Basis. Chicago: 

 The University of Chicago Press, 1955. A useful introduction to the 

 subject. 



