SEX DETERMINATION IN CATTLE. 211 



where p denotes the proportion of "successes," q the proportion 

 of "failures," and n the number in the sample. 



Remembering that between two uncorrclated events the prob- 

 able error of a difference is the square root of the sum of the 

 squares of the probable errors of the quantities between which 

 the difference is taken, we have the results set forth in Table II' 

 From this table it is possible to form a first judgment as to the 

 statistical significance of the raw data of Table I. 



TABLE II. 



SHOWING THE PROBABLE ERRORS OF THE DIFFERENCES BETWEEN CERTAIN OF 



THE SEX-RATIOS OF TABLE I. 



From this table we note that in the case of the extreme groups 

 the difference is 2.9 times its probable error. This means 1 that 

 if the time of coitus in relation to oestrus were absolutely without 

 influence on sex an excess of n per cent, of males such as is 

 observed in the extreme case would only happen 5 times in 

 every hundred that the matter was tested with statistical 

 samples of the present size. Or, put in another way, the odds 

 are 19 to I against the excess of cf births in "late in heat" 

 matings being due to "chance" (i. e., to errors of sampling) 

 on the basis of probable errors here used. These are distinctly 

 "long odds." 



Can the probable errors calculated by the formula used above 

 be relied upon to give correct results on data like the present? 

 They assume normality of the error distributions. This as- 

 sumption is practically justified in the present instance. The 

 material may, however, be dealt with according to the method 

 given by Pearson. 2 The present case may be regarded as falling 



1 This statement regarding probabilities assumes that the errors of sampling for 

 this material follow substantially the normal or Gaussian curve of error See below. 



2 Pearson, K., "On the Influence of Past Experience on Future Expectation," 

 Phil. Mag., March, 1907, pp. 365-378. 



