Appendix 189 



time-saver for the student. As Durkheim points out, it obviates 

 the necessity of discussing minutely each of the possible causes. 

 After their relative importance has been measured, attention can 

 be centered on the forces which have the closest relationship 

 to the change. 



The task of the Chapter on "Migrations of Countrymen" is 

 of the kind which Durkheim had in mind when he outlined this 

 method. At that time, however, the statistical method was 

 relatively undeveloped. What he described was little more than 

 a modification, by a more liberal use of mass data, of the logic- 

 ians methods of reasoning. Since that date material contribu- 

 tions have been made to the use of mathematical methods for 

 attaining exactitude, and scientists have demonstrated the lvalue 

 of the methods in Biology, Psychology, and Economics. Mod- 

 ern sociologists are insistent that knowledge of the statistical 

 method of induction is the most useful tool of the student of 

 social science, but as yet, the application of statistics to social 

 problems is in its infancy. 



Since the chapter on Movements of Countrymen demonstrates 

 the practical use of correlation in measuring social relationships, 

 it was thought advisable to include the fundamental steps in 

 the logic of this method and a condensed mathematical deriva- 

 tion of the Pearsonian coefficient in this appendix. 



Correlation 



General Measures — A method of measuring the relation be- 

 tween two variables, or, to keep the terminology of the previous 

 section,— of measuring the extent to which the presence or ab- 

 sence of a certain element of a situation is coincident with cer- 

 tain changes in the population, is herewith outlined. (For more 

 technical treatments of the mathematics of correlation, see bib- 

 liography,-«tatistics.) 



1. The most widely known measure of a variable series is 

 the arithmetic average, which is the sum of the individual mem- 

 bers of the series divided by the number of cases. In Table 

 17, the method of guessing the average was used. This is 

 valid because the sum of a series of deviations from any quan- 

 tity which we may guess, when divided by the number of cases 

 in the series and added to the quantity guessed is equal to the 

 true average. This makes it possible to guess a round number 

 which greatly facilitates the calculation of deviations, and later 



