1909.] The Experimental Error in Field Trials. 365 



THE EXPERIMENTAL ERROR IN FIELD TRIALS. 

 A. D. Hall, M.A., F.R.S., 



Director of the Rothamsted Experimental Station. 



In all experimental work some error is inevitable; it is only 

 on paper that results come out exactly, but when dealing with 

 things, even the simplest measurements involve an error, the 

 magnitude of which depends on the methods employed. A 

 carpenter measuring a table with a foot-rule can with care be 

 exact to within an eighth of an inch; the maker of fine 

 machinery will only allow himself a margin of about a 

 thousandth of an inch; while it is possible with the utmost 

 refinement to make sure of the length of a small piece of 

 polished metal to within about a millionth of an inch. Grant- 

 ing, then, that it is impossible to eliminate error and that 

 absolute correctness is unattainable, the scientific method 

 is to ascertain how large the error is likely to be and decide 

 whether it is such as will vitiate the conclusions drawn from 

 the experiment. 



As a rule, we can do this most readily by repeating the 

 measurement, changing, if possible, the process and the 

 instruments used; a consideration of the differences in the 

 results obtained will then show us what is the most probable 

 result and within what limits it is likely to be correct. If, for 

 example, successive measurements of a piece of land bring 

 out the area as 184, 184*3, 183*5, 184*6, and 183*3 square 

 yards, we may accept 184 square yards, the mean of the 

 results, as the most probable area, and we may further con- 

 clude that we are then not likely to be more than a quarter 

 of a square yard wrong on one side or the other. The more 

 measurements we make the nearer the mean will be to the 

 truth, always provided that there is not some definite source 

 of error which is repeated in all the experiments, such as 

 would be caused by want of truth in the measuring tape in the 

 example we have been using. 



Field trials, whether they are to test the effects of different 

 manures, or different varieties of the same crop, or variations 

 in the cultivation, are generally recognised as being subject 

 to a large number of sources of error, so that it becomes of 

 considerable importance in drawing conclusions from such 

 experiments to know what degree of accuracy in the results we 



