434 



Journal of Agricultural Research 



It is evident from mere inspection of Tables I to VI that the correla- 

 tion between these two variables is very high and that the regression is 

 linear. Calculating the coefl&cients of correlation by the usual Bravais 



formula, r= ^ ' > with a probable error of r given by the expression 



PEr- 



±.67449 "~7^' we have the results set forth in Table VII. 



Table VII. — Coefficients of correlation between (a) egg production to March I and (b) 

 egg production to joo days of age 



Coefficient of corre- 

 lation. 



1911. . 

 1911. . 

 1912. . 

 1912. . 

 1913.., 

 1913.., 



Barred Plymouth Rock 



Total 



Barred Plymouth Rock 



Total 



Barred Plymouth Rock 

 Total 



95S±o. 004 

 939± -004 



923 ± 

 9i5± 

 949 ± 



92I± 



007 

 005 

 005 

 COS 



These coefficients are clearly of a high order of magnitude. They fall 

 in the same class, for example, as coefficients measuring the correlation 

 between homologous organs on the two sides of bilaterally symmetrical 

 organisms. These values in the present case lead unequivocally to the 

 conclusion that with the flocks of birds here considered there certainly 

 is no definite or marked superiority of either of these measures of the 

 mnter cycle of productivity over the other. These high correlations indi- 

 cate that the two measures can be employed interchangeably so far as 

 practical statistical work is concerned. This does not mean that the rec- 

 ords to March i and to 300 days will be identical for a particular hen. 

 What the high correlations do mean is that if an individual, A, has a 

 higher record to March i than another individual, B, the probability is 

 so high as to amount nearly to certainty that A will also have a record to 

 300 days which will be higher than the corresponding record of indi- 

 vidual B and by an amount in proportion to the difference exhibited by 

 the records to March i . 



It will be noted that the correlation for the total flock is lower than 

 that for the Barred Plymouth Rock flock in every case. No biological 

 significance appears to attach to these differences, which are small in 

 amount. 



The three years here dealt with are entirely typical, and an exami- 

 nation of our data indicates clearly that precisely the same result would 

 be reached if we used the material from other years of the trap-nest rec- 

 ords of the Maine Station. There was felt to be no point in piling up 

 further correlation coefficients, all showing the same thing. The figures 

 given above are quite sufficient to show that there is no warrant what- 



