THE INHERITANCE OF DURATION 169 



or direction of its variation. The significance of a cor- 

 relation coefficient is always to be judged, in any partic- 

 ular case, by the magnitude of a constant associated 

 "with it called the probable error. A correlation coeffi- 

 cient may be regarded as certainly significant when it has 

 a value of 4 or more times that of its probable error, 

 which is always stated after the coefficient with a com- 

 bined plus and minus sign between the two. The coeffi- 

 cient is probably significant when it has a value of not 

 less than 3 times its probable error. By "significant" 

 in this connection is meant that the coefficient probably 

 is not merely a random chance result. 



In Table 18 are the numerical results from the first 

 study based upon the "Peerage" and "Landed Gentry." 



TABLE 18 



Inheritance of duration of life in male line. Data from 

 "Landed Gentry." (Beeton and Pearson). 



'Peerage" and 



It is seen at once that all of the coefficients are signifi- 

 cant in comparison with their probable eirors. The 

 last column of the table gives the ratio of the coefficient 

 to its probable eiror, and in the worst case the 

 coefficient is 4.7 times its probable error. The odds 

 against such a correlation having arisen from chance 

 alone are about 655 to 1. Odds such as these may 

 be certainly taken as demonstrating that the results rep- 



