344 



Trials of New Varieties of Cereals . 



[July, 



way of discounting them, viz., to arrange and multiply the plots 

 of each race at each station in such a manner as to give an 

 approximately even chance of getting the same proportion of 

 good and bad patches, and at the same time to keep the laces 

 to be compared as close together as possible in order to secure 

 general similarity of soil conditions. 



On account of these unavoidable casual errors the yields of 

 cereals cannot at present be compared with the accuracy obtain- 

 able in physical experiments in the laboratory. With the help 

 of the statistician, however, we may make steady approaches 

 in this direction. The value of reliable results when they can be 

 obtained is sufficiently great to justify the attempt. 



Probable Error of Yield Trials. — Every farmer knows that he 

 cannot obtain a fair sample of the grain threshed from a stack 

 by taking a handful out of one bag. Neither is it possible to 

 find the yielding capacity of a parcel of seed by sowing it on 

 any one patch of ground, large or small. Still less is it possible 

 to estimate the difference in the yielding capacity of two parcels 

 of seed by sowing each of them on a single plot, even if the plots 

 are side by side. To obtain sound comparisons, at any one 

 station, it is necessary to average the results of a number of plots 

 of each race. Having done this, if we have excluded systematic 

 errors, we can calculate, by an arithmetical device based on the 

 laws of probability applicable to chance events, the probable 

 error* of the average result. Obviously the probable error of an 

 average is likely to be less than that of any one plot, and the 

 greater the number of plots the smaller is likely to be the 

 probable error of the average. 



Briefly stated, probable error is an average error computed in 

 a particular manner in order to afford a measure of the un- 

 reliability attaching to any average of results by reason of the 

 operation of chance conditions. 



The degree of unreliability indicated by any probable error 

 depends on the size of the probable error in proportion to the 

 quantity to which it refers. For instance : — Tf the probable 

 error of a difference between two averages of say 5 per cent, is 

 as much as 3 per cent, it is an indication that the difference of 

 5 per cent, is one that might easily be due to chance conditions. 

 If, however, the probable error of the same difference is only 

 1 per cent, it would be extremely improbable that such a difference 

 (5 per cent.) arose entirely from chance conditions. If in com- 



* For a full discussion of the theory involved see " An Introduction to the 

 Theory of Statistics " by C. Udny Yule. 5th Edition. 



