MEASUREMENTS OF RELATIONSHIPS 



15 



may provoke some capable student to give the adequate review that 

 is so much needed. 



This report will presuppose in the reader knowledge of the bare 

 elements of the theory of measurement of variable facts such as is 

 given for instance in the writer's Introduction to the Theory of Men- 

 tal and Social Measurements. It will deal in order with the fol- 

 lowing topics : 



I. What is actually measured by typical measures of the relation- 

 ship between first and second member of a pair in a series of pairs 

 of values, each first-member value being a deviation from the central 

 tendency of one series and each second-member value being a related 

 deviation from the central tendency of a second series? 



II. What are the respective presuppositions of each of these 

 typical measures? 



III. What are the advantages and disadvantages of each of these 

 typical measures? 



The only original contributions which this discussion contains 

 are (1) the investigation of certain artificially constructed cases of 

 correlation and (2) a laborious but not very important experimental 

 testing of the comparative reliability of different measures of rela- 

 tionship, and (3) a similar experimental testing of methods for cor- 

 recting measures of relationship for the 'attenuation' due to inaccu- 

 rate original data. 



5. I. What is actually measured by typical measures of the 

 relationship between first and second member of a pair in a series 

 of pairs of values, each first-member value being a deviation from 

 the central tendency of one series and each second-member value 

 related deviation from the central tendency of a second series 



Consider the following series of paired values of A and B : 



A 



1 



5 

 3 



5 



5 



3 



1 



7 



3 



o 



3 



1 



A 



_ I 

 _ J 

 _ 1 



1 



+ 1 



+ 1 



3 



1 

 + 1 

 + 1 

 + 3 



3 



1 

 + 1 

 + 3 

 + 5 



B 



+ 7 



+ 3 - 



+ 3 

 + 3 

 + 3 

 + 5 

 + 5 

 + 5 

 + 7 



+ 1 

 + 3 

 + 5 

 1 

 + 3 

 + 3 

 + 5 



3 



1 +1 



'.+ 1 + 1 



5 +1 



Pearson Coefficient =.634. 

 Median Ratio B/A = .65. 

 Average of Ratios =.902. 



The average of ratios is valueless because it overweights positive values of 

 2 pairs, etc. A 



Per cent, unlike signs = .267, r as calculated therefrom being .665. [Mi, ff" 



