XXXIV 



Tables for Statisticians and Bio metricians 



[XVII 



Table XVII (p. 31) 



Values of (— log P) correspondinrj to (jiven values of x' ^" '^ fourfold table. 

 (K. Pearson : On a Novel Method of regarding the Association of two Variates 

 classed solely in Alternate Categories. Drapers Company Research Memoirs, 

 Biometric Series, VIII. Dulau & Co.) 



If individuals be claisscd by the characters into A and not-^^i, B and not-i?, we 

 form a tetrachoric table of the form 





A 



Not-J 



Totals 



B ... 

 Not-5 



a b 



d 



a + b 

 c+d 



Totals 



a + c 



b + d 



N 



For such a table : 



X' 



N{ab-cdy 



{a + b) {c + d) (b + d) (a + c)' 



.(xxxi), 



gives a measure of the probability of independence, and, if the two attributes are 

 highly associated, p^" will be large and P the probability of independence very 

 small and largely outside Palin Elderton's Table XII. Table XVII provides for 

 such cases. 



Illustrations. The following tables are given by Mr G. U. Yule in his Theory 

 of Statistics*. His conclusions with regard to them are : 



1. Datura : " No Association." 



2. Eye Colour in Father and Son : " Shows the tendency to resemblance." 



3. Houses in course of erection, Urban and Rural : " Distinct Positive 

 Association." 



4. Imbecility and Deaf-Mutism : " High Degree of Association." 



5. Developmental Defects and Dullness : " Very high indeed." 



It is required to measure the degree of probability that the variates in these 

 five cases are independent. 



(1) Datura. 

 Colour of Flower. 



(2) Ei/e-Golour in Father and Son. 

 Father. 







Violet 



White 



Totals 





Prickly ... 

 Smooth ... 



47 

 12 



21 

 3 



68 

 15 





Totals ... 



59 



24 



83 



a 



o 





Light 



Not Light 



Totals 



Light 



Not Liglit ... 



471 148 

 1.^.1 230 



619 

 .381 



Totals ... 



622 



378 



1000 



* Pp. 37, 34, 62, 83, 34 and 45 respectively. 



