SEX DETERMINATION IN CATTLE. 213 



This means that a random sample of the size of this "late in 

 heat" groups, from a population having the sex ratio exhibited 

 by the "early in heat" sample, would be expected as often as 

 not to give a male sex percentage within the limits 45.7 and 53-5- 



The observed percentage of male births in the "late in heat' 

 lot was 60.75. This value is well outside the- limits, and the 

 probability against its being a result of random sampling is 

 considerable. It is not, however, so great as to amount to 

 certainty. The standard deviation of the error distribution for 

 random samples of the size of this "late in heat" lot is approxi- 

 mately 6.2. Taking the rough rule that for practical purposes 

 the half range as either side of the mean is 3 a, it would give an 

 upper limit to the curve of 67.9. The observed 60.75, while 

 getting well out towards the range end, still lacks something 

 of actually reaching that point, to say nothing of going beyond. 



In general, the data presented appear to warrant the following 

 conclusions : So far as the present statistics are concerned there is 

 an increasing proportion of male births as the time of service ap- 

 proaches the termination of the cestrons period. This increase 

 amounts to approximately 10 per cent, in the extreme case, and 

 to not quite half this in the intermediate case. Statistically 

 considered the difference in the extreme case is probably significant 

 (i. e., not due to errors of random sampling). The probability 

 that the observed increase in the proportions of male births is 

 a real and biologically significant phenomenon, while not enor- 

 mously great, is nevertheless of an order which one would not 

 hesitate to act upon in the practical affairs of life. 



So much for the bare facts. We have now to consider the 

 possibilities as to the cause of the observed relation. Apparently 

 the increase in male births is associated with time of service, 

 but before accepting such a conclusion it is important to deter- 

 mine whether some other variable factor may not be influencing 

 the results. The first possibility which suggests itself is that 

 there may be a difference in age distribution of the animals in 

 the three lots and that in some manner this has affected the 

 result. In the ideal experiment of this sort of course the parents 

 used should be of the same average age in the different groups. 



The age distribution of the animals involved in these statistical 



