SPECIAL TECHNIQUES 83 



verifiably accurate. The description and analysis of a pop- 

 ulation is one of those problems that must first be analyzed 

 precisely on a morphological level before we can choose the 

 best methods with which to analyze it on a mathematical 

 level. The most effective methods so far achieved are of 

 various sorts, but they share one feature so universally that 

 they may be grouped under the general name of polygraphic 

 analysis. That is to say that they are all more or less graph- 

 ical and that they all in one way or another summarize the 

 variation in two or more characters in a population. These var- 

 ious methods of polygraphic analysis may be listed as follows : 



1. Scatter diagrams. 



2. Pictorialized scatter diagrams. 



3. Ideographs. 



4. Hybrid indices. 



5. Radiate indicators. 



6. Standardized photographs. 



SCATTER DIAGRAMS 



Scatter diagrams are the simple alignment of dots in a 

 two-dimensional field, such as were used in Chapter 3 in 

 describing the possible relationships of flower color and pu- 

 bescence. Since one of the steps sometimes employed in cal- 

 culating the correlation coefficient is the preparation of a 

 scatter diagram, it may be well to point out specifically that 

 for population analysis scatter diagrams are greatly superior 

 to the correlation coefficient as well as much easier to pre- 

 pare. It is unfortunately not generally realized by most 

 biologists that scatter diagrams may show various kinds of 

 relationships that are ignored or distorted in the calcula- 

 tion of correlation coefficients (see Walker, 1943, pp. 237, 

 238). 



PICTORIALIZED SCATTER DIAGRAMS 



For all their excellencies, scatter diagrams are a somewhat 

 limited form of polygraphic analysis because the relation- 

 ships of only two characters can be considered at a time. 



