A METHOD OF GRAPHICAL ANALYSIS 99 



portion factor (ratio of the average message use to the -message al- 

 lowance) might be used in deriving a revised setup of normal dis- 

 tribution curves. 



In certain cases it may be found that some expedient such as that 

 described above may be used to eliminate or take account of the effect 

 of an outside factor. Whether this is done or a separate set of curves 

 is derived for different values of that factor, the process of deriving 

 the detail and cumulative distribution curves would in general be the 

 same as that described above. 



Some of the processes involved in studying averages and distri- 

 butions of subscribers by message use have been described because 

 they are typical and illustrate what have been found to be satis- 

 factory methods of analysis for problems of this type. It is clearly 

 impossible, however, to set up any rigid methods for such studies. 

 Any economic problem which permits of analysis by these methods 

 must be treated in the manner best suited to the data available, the 

 purposes of the study, the degrees of accuracy necessary, etc. Where 

 these methods can logically be employed the results obtained, an im- 

 portant part of which are the background and sidelights, on the 

 problem, disclosed during the process of building up the normal 

 relationships, will generally be found superior to those obtained 

 through the use of more rigorous methods. 



Application 



Before final results are obtained, there will naturally be developed 

 by those concerned in the study a very definite conception of the field 

 of their usefulness and their limitations. It is important that a 

 knowledge of these limitations be extended to those who may have 

 occasion to use the results. Given a set of smooth curves from which 

 quantitative estimates can be made, there is a great temptation to 

 make estimates under any and all circumstances, and often to give 

 such estimates an undue appearance of accuracy. The final results 

 are merely the general expression of the information contained in the 

 original data logically developed according to the knowledge and 

 judgment of the investigator. It is always necessary in applying 

 such results to consider the effect of special and local conditions. 

 Where it is known that actual conditions in a specific case are far 

 from normal, it is often possible to estimate the effect of a proposed 

 change by applying differences based on the normal experience. 



Care must also be taken in extrapolation estimates, i.e., estimates 

 where the value of one or more factors lies beyond the limits of the 

 original data. Such estimates, of course, are always subject to con- 



