1922.] 



Trials of New Varieties of Cereals. 



:U5 



paring the produce of a series of " control " plots of an estab- 

 lished race " C " with a corresponding series of a new race "A" 

 the result was : — 



C " = 100. " A " = 105 ± 1 per cent, 

 (where + 1 .0 stands for the calculated probable error as a per- 

 centage of " C ") we could be practically certain that the differ- 

 ence in favour of "A" was not a chance occurrence. 



The following may be taken as a rough standard of the 

 reliability of any comparison such as we are considering : — If an 

 observed difference between two averages, each of a considerable 

 number of cases, is more than four times the probable error of 

 the difference, the difference may be regarded as significant in 

 the sense that it is extremely unlikely to have arisen from the 

 operation of chance events. 



Since it is useless to expect a very rapid rate of advance in the 

 yield of cereals from the breeding of new races, and since it is 

 highly desirable that published conclusions should have a high 

 degree of reliability, a " fine sieve " is required through which 

 to sift results of yield trials. It is therefore suggested that a 

 probable error of 1 per cent, or less in weight of grain should be 

 aimed at in the difference between any two races at any station 

 in any one year. 



Before considering whether there is any practical arrangement 

 of plots which will give this degree of accuracy it will be as well 

 to see how this compares with the kind of results at present 

 obtained in field trials. Before doing so it will be instinctive 

 to refer briefly to the probable errors which occur in the plant 

 breeding stage. 



Thn plant breeder usually proceeds year by year somewhat as 

 follows : — 



1. Single, plants of (liferent races icith equal soil space per plant. The 

 writer finds that with 12 6q. in. soil space per plant, and with all tlie plants of 

 the same race and comparing adjoining plants the differences run from zero 

 up to a quite indefinite maximum ; the probable error of the percentage 

 difference is somewhere about 80 per cent, of the average weight of two 

 adjoining plants. A difference of 300 per cent, between two adjoining plants 

 is therefore not conclusive evidence of any racial difference, but may be due 

 to conditions external to the plant. The probable error is much greater even 

 than this for single plants under field conditions with necessarily wide 

 differences in soil space per plant. It follows, although the argument cannot 

 be developed here, that it is practically impossible to select single plants for 

 racial productivity. Incidentally also it shows the great difficulty, it* not 

 impossibility, of adapting pot-culture methods to estimates of productivity, 

 except in respect of very great differences. 



2. Bows of 12 plants with equal soil space per plant. The probable error 

 of the difference between two averages of say 12 row weights is likely to be 



