252 TRANSACTIONS LIVERPOOL BIOLOGICAL SOCIETY. 



Dealing first with the small sub-samples of Manx herrings 

 taken during 1914 (Table I), the general result based on 

 character D supports the view that the differences are most 

 likely due to errors of random sampling, except in the two cases 

 where June 3rd is compared with June 13th, and June 13th 

 with June 25th. In these two cases the odds against the 

 differences being due to random sampling are 333 to 1 and 19 

 to 1. In all the other cases they are less than 10 to 1. 



Comparing these results calculated on D with results 

 calculated on l.cp.l., we find confusing discrepancies. The 

 lowest odds against the differences being due to random sampling 

 are about 14 to 1, in the case of June 25th compared with 

 July 9th. This is becoming unsatisfactory ; and they even 

 become as high as 1,000 to 1 when June 3rd is compared with 

 June 13th. So that, with the exception of June 3rd and 

 June 13th, the result based on character D is negatived by 

 that calculated on l.cp.l. 



The lumped samples are next compared (Table II) and the 

 three characters, D, 7, and l.cp.l. taken. Only in one case 

 out of four, the summer season of 1914 compared with the 

 summer season of 1920, do we get agreement on all three 

 characters, the odds against the differences being due to random 

 sampling being more than 1,000 to 1, as computed on each of 

 the three characters. 



In the other three examples D and V show odds of 10 to 1 

 or less against the differences being due to random sampling, 

 yet l.cp.l. shows these odds to be so increased that they are 

 either in the region of doubt or improbability. 



The examination of the Welsh herrings (Table III) reveals 

 a high probability that the differences are due to reasons other 

 than random sampling. But one confusing result occurs which 

 is unexplained. Winter 1913 compared with Winter 1921 — 

 character V gives odds of 1-1 to 1 against the differences being 

 due to random sampling. On l.cp.l. for these same samples 



