40 



0.3 there is probably no association. A few examples of correlation co- 

 efficients actually obtained in the course of this study are given to illus- 

 trate the method of calculation. 



The principle of correlation should not be applied indiscriminately 

 to collections of data for systematic purposes. Certain characters and 

 properties have been universally accepted as reliable and appropriate for 

 bacterial differentiation; thus, staining reactions such as the Gram and 

 acid fast stains, spore formation, and aerobiosis and anaerobiosis, hardly 

 need to be bolstered up by correlation with other characters to justify their 

 taxonomic value. On the other hand the significance of such characters 

 as motility, indol production, and fermentation of certain substances, is 

 still debatable. 



Motility is regarded by many as a highly variable property. Perhaps 

 it is in reality a reliable morphological difference. Certainly if it could 

 be shown that this character goes hand in hand with several others, more 

 reliance and attention should and would be given to motility. The same 

 is true of the indol test. In dealing with gas formation from carbohydrates, 

 alcohols, or polysaccharids, the question naturally arises as to which 

 substance should be given preference for subdivision, or whether all are 

 to be considered of equal taxonomic value. The lack of a criterion for 

 determining the most significant fermentable substances has led to con- 

 siderable confusion. It has already been pointed out how subdivision 

 on every character studied results in an infinite number of varieties. Where 

 we are dealing with a number of characters each of which is assumed to 

 be of equal taxonomic significance, it would certainly be desirable and 

 advantageous to subdivide on that character which gives the greatest amount 

 of information as to the manner in which the resulting subgroups react 

 with respect to other characters. It is under such circumstances that the 

 principle of correlation of characters may be legitimately, conveniently, 

 and advantageously employed. 



The Method of Selecting the Best Correlating Character. The 

 following example will illustrate the method of selecting the best correlated 

 character for the purpose of subdivision of a group of organisms. Let 

 us take for instance a group of 89 strains of the coli section, which were 

 found to be non-fermenters of sucrose, and which it is required to further 

 divide on one of the following characters: motility, indol production, 

 dulcitol, glycerol, or salicin fermentation. Tabulation is first made, as 

 indicated below, so as to show the relation of each character to every 

 other character and also to facilitate the calculation of correlation coefficient 

 which are then determined for each pair of characters and recorded as in- 

 dicated in Table XVIII. 



For subdivision that character is selected which gives the highest co- 

 efficient of correlation with the greatest number of other characters. Thus, 

 in the group under consideration, motility is not well correlated with any 

 other character. Dulcitol and glycerol each have a high correlation co- 

 efficient with salicin but not with any other character. Salicin fermenta- 

 tion, on the other hand, is well correlated with three characters glycerol, 



