A METHOD OF GRAPHICAL ANALYSIS 89 



After deriving a series of final charts estimates are made of the 

 value of the dependent variable for all the cases on which the study 

 was based. Consideration of the differences between the estimated 

 and the actual values is an excellent general criterion of the accuracy 

 of the normals. In general, the positive deviations should be ap- 

 proximately equal to the negative both in number and in the sum of 

 their numerical values. If either positive or negative deviations are 

 decidedly predominant, it is probable that the general level of the 

 normal curves is too low or too high. 



When the deviations (without regard to sign) are plotted as a 

 frequency curve, the curve should be fairly smooth. It need not be 

 and usually is not a bell shaped curve, but if there are sudden and de- 

 cided breaks, it is probable that either certain portions of the data 

 have not been given proper consideration or that the data were not 

 originally essentially homogeneous. The cumulative frequency curve 

 based on the deviations makes possible the easy reading of the median 

 or probable error of estimate. The probable error may be used as a 

 general criterion of the value of future estimates made from these 

 normals and the ratio of the probable error to the median value of 

 the dependent variable forms a basis for comparison of the relative 

 accuracy of different sets of normals. 



The deviations (sign being taken into account) when plotted against 

 the various factors included in the study should be fairly evenly 

 scattered and show no trend or relationship. If a consistently oc- 

 curring variation is discovered between the deviations and any of the 

 independent variables it indicates that the relationship of that variable 

 to the dependent variable has not been properly taken into account 

 in deriving the normals. If this variation appears in connection with 

 the dependent variable, it indcates that some of the curves are not of 

 proper shape. For instance, if a straight line is fitted to data having a de- 

 cided non-linear trend, the errors plotted against the dependent variable 

 will fall along a well defined U-shaped (or inverted U-shaped) curve. 



Additional information may also be obtained by plotting the 

 deviations against factors not included in the study. Relationships 

 will sometimes become apparent which previously were obscured 

 by the effect of the more important factors. The influence of such 

 factors may account for seemingly abnormal cases and their inclusion 

 would tend to reduce the mean and to a lesser extent the median 

 deviation. 



Frequency Distributions 



Normal curves, such as those described above, form a basis for 

 estimates of an average value for a group of items comprising a unit such 



