372 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



assigned ranges in such a way that each associated variable is set an 

 eciiial number of times at each of its possible values. This will cause 

 any effect of the associated variable to be balanced out with respect 

 to the chosen variable. That is, the average response of the system to 

 the chosen variable can be evaluated because the contributions to the 

 response from the associated variables are balanced out with respect to 

 their variations. 



Mathematically stated, the purpose of the latter procedure is to allow 

 the independent evaluation of each variable over the observed range of 

 its variation in the presence of the other variables. 



Until recent years the standard experimental procedure was to make 

 measurements for several values of one variable while taking great pre- 

 cautions to hold everything else constant. It was early recognized that 

 such a techniciue was expensive but until the recent development of 

 experimental designs in the field of Statistics there was no known al- 

 ternative. In the class of designs treated here,^ the set of numbers repre- 

 senting the respective sums of the measurements taken at the selected 

 values of a given variable has the following properties: 



1 . If there are K discrete values of the given variables and N measure- 

 ments made, then each sum contains N/K measurements. 



2. If there are Ki values of the i^^ remaining variable then N/K must 

 be divisible by K; , for all i. 



3. Within each sum, for any given variable, each of the discrete 

 values of the remaining variables must occur the same number of times. 



4. The set of values of any of the remaining variables occurring in 

 any sum for a given variable must be identical. 



These properties imply that the logical subgroups for the discrete 

 values of any given variable all contain the same number of measure- 

 ments balanced with respect to the values of all the remaining variables. 



The joint simultaneous evaluation of the specified variables can thus 

 be made since it can be shown that the logical subgroups with respect 

 to a given variable are independent of the logical subgroups of any 

 other variable. 



One of the difficulties in the use of this new technique is that both an 

 engineer and statistician are required, and only rarely are both these 

 professions found in an individual. It therefore becomes the respon- 

 sibility of the engineer to outhne the major and minor variables of the 

 experiment, the description of the measuring devices to be employed, 

 the accuracies desired in the results and his budget. The statistician 

 must then propose the types of designs that will be appropriate together 

 with their costs, methods of analysis, and salient features. The engineer 

 and statistician must then select the design which best fits the situation. 



