No. 611] FERTILITY IN SOUTHDOWN SHEEP 665 



While both records show a higher agreement with the 

 average than probably exists in actual selections, the fact 

 that the best record is more closely in agreement with the 

 average than a random record makes high production a 

 significant selection standard. The correlation between 

 random records and the best records is presented in 

 Tal)le III. 



TABLE III 



The coefficient of correlation here is 0.6518 + 0.03665. 

 The relationship is not as great as between either of the 

 records and the average record, as shown in Tables I and 

 II. Since the correlation is not as high, and since an error 

 (false agreement with the average) is introduced into 

 each of the first two tables, it is well to determine whether 

 the difference between the first two correlation coefficients 

 is significant. Using the formula for the standard deviation 

 of the difference between the first two constants presented 

 by Pearl (10) : Error of {x — t/)=\/E.^ -\-Ey" — 2 r^y cr^ ay, 

 where E refers to the error, x to the larger constant, 

 y to the smaller, and rxy to the correlation between 

 X and y. The error of the difference between the cor- 

 relation coefficients of Tables I and II is 0.01598. 

 Since the difference is .10548, it is greater than three 

 times the probable error, hence it is justifiable to conclude 

 that the highest number at a birth is a better indication of 

 the average fertility of an animal than a random birth, 

 although on the basis of the figures presented the latter 

 relationship is high. 



Youatt (14) reports in 1837 that one ewe out of five in 

 the average English flock produced twins, which would 

 give 120 per cent, of lambs as the proportion of English 

 flocks at that time. 



