Ixxviii 



Tables for Statisticians and Biometricians [VIII IX 



Illustration (xvi). To test whether the following contingency table for Stature 

 in Father and Son may reasonably be considered normal. 



Stature of Father 



o 



H-H 



O 



I 



02 



This table has been reduced to broad categories from a much larger table where 

 the categories were all quantitatively given. The ten cell contents to which an 

 asterisk is attached were found with great ease by means of formula (a) from the 

 section of the Table for positive r. The contents of six further cells those in which 

 a dagger is placed were found by the like formula from the section of the Table 

 for negative r. The contents of the remaining nine cells could then be found from 

 the marginal totals and a knowledge of the sixteen cell contents already found. 



The actual correlation coefficient of this table as found by the product-moment 

 method on the original data was r = '5189. The result would have been practically 

 the same had the value obtained by mean square contingency corrected for class 

 indices, namely r=-5l79, been used. The following table gives the computed 



frequencies: 



Stature of Father 



o 

 CQ 



The method of determining the cell contents from the table is easily indicated. 

 Take for example the cell for "Tall" Sons and "Tall" Fathers. We have from 

 Table XXIX of Part I of this work for 



l(l-a A ) = -129, t (!-*)= -139, 

 the values h= 1-13113 and k = 1-08482. Thus 



</> = '6887, x = -8482, and ^= 



