HUOOniXKSS AND FECUNDITY IX I'OWI. 59 



tion lies mainly in its use for selecting a group of lueeders and nol in the 

 selection of individual breeders. 



Tiie true eoellkicnt of correlation may only be calculated for a race pure 

 with regard to the characteristics being studied, as Harris (1915) points out. 

 False correlations result when two or more genetically different races are 

 concerned in any calculation Broody birds have been shown to i)e genetically 

 different (Hays, 19'JI-) from non-broody birds. In studying the relation of 

 broodiness to fecundity, it lias been deemed advisable to make three general 

 grou])ings: namely, (1) total jjopulation of broody and non-broody combined, 

 (2) only birds that went liroody during the pullet year, and (3) broody or 

 non-broody without regard to the degree of broodiness. The first series of 

 calculations was made for two purposes: first, to confirm that broody and 

 non-broody races are genetically different; second, to furnish evidence on the 

 intensity characteristics in relation to the_broody trait even in a mixed popu- 

 lation of broodies and non-broodies. The third series of calculations was 

 made by Yule's formula for presence and absence of a character, as given by 

 Davenport (1907). All other calculations were made by the ordinary method 

 for calcidating the correlation coefficient for fluctuating variables. 



The regression coefficient is readily calculated after the correlation coeffi- 

 cient is determined. It is useful to the breeder for selection purposes. If a 

 group of liens, each five times broody, were selected, the regression coefficient 

 might be used to estimate its probable average egg production. If the degree 

 of correlation between days broody and annual production is known, it is a 

 simple matter to calculate the probable annual egg record of hens broody for 

 25 days or for any other period of days. Thus the regression coefficient merely 

 represents the amount of change in one character with respect to a unit change 

 in another. For example, the regression coefficient of days broody on annual 

 production is — .1171, and the regression of annual production on days broody 

 is — .3295. "What should be the average annual egg yield of hens broody for 

 thirty davs? 



42 87 average days broody of all hens 

 30.00 



— 12.87 days broody below the average 



— 12.87 X— .3295 — 4.2407 + 16 1..8S5 (average production of all)=r 



169.1257, probable record of hens broody for 30 days 



The correlation ratio is comi)arable to the correlation coefficient and has a 

 similar use. The former is made use of where the correlation coefficient 

 would be false. As a measure of association in mixed races the correlation 

 ratio is reasonably accurate, but it is of less value than the correlation coeffi- 

 cient for prediction purposes. Since a con.stant is calculated for each of the 

 two variables in correlation ratio, a difference in magnitude of these two con- 

 stants sometimes occurs, probably due to genetic impurity. Correlation ratio 

 has not been used extensively in these studies because the correlation coeffi- 

 cient has been calculated on the three classes of hens with respect to broodi- 

 ness: namely, broody and non-broody, different degrees of broody, and broody 

 or non-broodv, so that regressions closely approach linearity. 



