MEASUREMENTS OF RELATIONSHIPS 



41 



Let us call the four series of inaccurate measures obtained with 

 the four errors, Xa, Xb, Xc, Xd, and Ya, Yb, Yc, Yd. 



Call the series obtained by averaging each member of Xa with 

 its correspondent in Xb, Xab. 



Let Xcd, Yob and Ycd have similar meanings. 



Call the series obtained by averaging each member of Xa with 

 the corresponding Xb, Xc and Xd, Xabcd. 



Let Yabcd have a similar meaning. 



We have then 4 very inaccurate measures of X in every one of 

 the 100 pairs; so also of Y. We have two less inaccurate measures 

 Or X and also of Y in each pair. We have one still better measure, 

 the best obtainable from our data. 



We may then calculate the corrected r according to Spearman, 

 using many different combinations of the r's obtained from the 

 above series. The combinations which I have used and the results 

 follow in Table XVI. 1 



The correspondence of the coefficients corrected by Spearman's 

 formulas with the actual coefficient from accurate measures is satis- 

 factory. 



TABLE XVI. 

 rxowithxi =.731 



rxawlth,. =.142 



rx6with, =.208 



rxJwithya =.243 



r t ( the average 



of the four) =.169 



rxabwltoyab =.212 



r xcd with ycd =.221 



Txab with ycd =.239 



Txcdwlthyab =.170 



r 2 ( the average 



of the four) =.2105 



Txabcd with yabcd =.260 



= .260 



= .289 



== =.277 



rxabw.xcdryabv.ycd 



fxab with xcd 

 Tyab with ycd 



= .803 

 = .717 



t. c. 



r s 



MEI-i 



Average by all for- 



mulae 

 Median by all for- 



mulae 

 True relationship 



9. Minor Advice to Students of Mental and Social Relationships 



As a rule nothing should be taken for granted about any relation- 

 ship and the result of any calculation should be to express, not to 

 replace, the comprehension of a fact about the series of individual 

 relationships. 



1 In all the calculations I have assumed the original as the central tend- 

 ency from which to reckon deviation values. To have turned each of the 200 

 values of each of the fourteen series into a new deviation measure would have 

 added practically nothing to the general result in the way of accuracy. The 

 labor of 2,800 little sums in addition and 2,800 copyings of numbers could be 

 more profitably spent. My figures are on this basis. 



