A METHOD OF GRAPHICAL ANALYSIS 83 



of curves is drawn to fit the data as closely as practicable and still be 

 logical and consistent. 



On Fig. 2, the number of data points on which each average is 

 based has been noted as an aid to judgment and a set of rough 

 preliminary curves has been drawn. These, of course, are not 

 necessarily the most accurate curves which could be constructed 

 from these data. A method of progressing to final curves is 

 described below. 



Curve Smoothing 



The first set of curves constructed from the data may not be an 

 entirely consistent and reasonable family. The relation between 

 different curves on the same chart or between different charts indi- 

 cates the influence of factors other than the one plotted and must, 

 therefore, be made consistent and logical. The process of trans- 

 forming the preliminary curves into the final normals is known as 

 smoothing. 



The original curves are first studied for reasonableness. Their 

 general shape (whether straight line, convex or concave, having maxi- 

 mum or minimum points, being asymptotic to a certain line, etc.) is, 

 in so far as practicable, determined on logical grounds. If a large 

 majority of the curves, or the curves based on the greatest amount 

 of data, have a certain clearly defined trend, the remainder of the 

 curves are made to conform to this trend, if it is reasonable, at the 

 same time keeping as closely in line with the data as possible. 



Each chart will usually have one independent variable plotted 

 against the dependent variable and another independent variable 

 coded. Each curve, therefore, indicates the relationship between the 

 dependent variable and one independent variable for a certain con- 

 stant value or range of values of a second independent variable. If 

 the relative positions of the curves of a family on one chart are ad- 

 justed, the relationship of the coded variable to the other two is 

 altered. The effect of this alteration may be seen by plotting the 

 coded variable against the dependent variable and coding the one 

 which previously was plotted, all values being read from the pre- 

 liminary curves. This is sometimes called cross-sectioning. The 

 families of curves formed by cross-sectioning are then smoothed until 

 they are reasonable and consistent. In doing this, the original 

 curves are automatically departed from, and when the original 

 curves are replotted from the cross-sections, it may be found that the 

 resulting family of curves is not smooth, consistent or reasonable. 



