32 STATISTICAL METHODS. 



In studying correlation one (either one) of the characters is 

 regarded as subject and the other as relative. A correlation 

 table is then arranged as in the example on page 29, which 

 gives data for determining the correlation between the num- 

 ber of Miillerian glands on the right (subject) and left (rela- 

 tive) legs of male swine. 



METHODS OF DETERMINING COEFFICIENT OF CORRELATION. 



Galton's graphic method. On co-ordinate paper 

 draw perpendicular axes X and T '; locate a series of points 

 from the pairs of indices of abmodality of the relative and sub- 

 ject corresponding to each subject class. The indices of the 

 subjects are laid off as abscissae ; the indices of the relatives 

 as ordinates, regarding signs. Get another set of points by mak- 

 ing a second correlation table, regarding character B as subject 

 and character A as relative. Then draw a straight line through 

 these points so as to divide the region occupied by them into 

 halves. The tangent of the angle made by the last line with 

 the horizontal axis XX (any distance yp, divided by xp) is the 

 index of correlation. 



A more precise method is given by Pearson as follows: 

 Sum of products (deviation subj. class X deviation each assoc. 

 rel. class X no. of cases in both) 



total no. ofludivs. X Stand. Dev. of subject x Stand. Dev. 



of relative ; 



or, expressed in a formula : 



2 (dev. x X dev. y X /) 

 p = 



This method requires finding many products in the numera- 

 tor, as many sets of products as there are entries in the body of 

 the correlation table. A portion of the pioducts to be found 

 is indicated below ; 



(- 3.540 X 8 



- 3.547 X !- 2.540 X 5 



(- 1.540 X 2 



f_ 3.540 X 4 

 | - 2.540 X 151 



- 2.547 X -{ - 1-540 X 58 



| - 0.540 X 9 



L_ o.460 x 3 



etc. 



