370 



THE AGRICLTLTUEAL NEWS. 



November 27, 1909. 



rect, on both sides of the true value, is given when we 

 take the total range (1S4-0 — 183-3 = 1'3) and divide it 

 by the number of observations (5): it is 0'26, so that 

 the probable error of the average result is a quarter of 

 a square yard, either way. In other words, for ordinary 

 purposes, the piece of land measures 184 square yards, 

 though it may be anything down to ISS-f, or up to 

 184^^, squ.are yards in area, as a matter of fact: and we 

 must not use this result (184) in conne-xion with any 

 observations that are of such a delicMcy that they 

 would be affected by a difference of a (|uarter of 

 a square yard in the area. 



The author of the paper which forms the basis of 

 this discussion also gives an illustration from a series 

 of agricultural experiments which were carried out at 

 Rothamsted. In this, the results given, in two simi- 

 larly treated plots, over a period of fifty years, are con- 

 sidered. Theoretically, these should have given exactly 

 similar yields, but it is demonstrated that, at the end 

 of the time mentioned, one showed an increased super- 

 iority over the other of 10 per cent. A calculation of 

 the probable error gives this as 2 per cent., so that, 

 from the fifty years' results, it may be concluded that 

 this superiority is certainly more than 8, but less 

 than 12 per cent. In a similar way, the mean 

 error of a single year's result is 10 per cent. The 

 author states that, as the general result of the 

 examination of many series of experiments, it has been 

 found that the mean error attached to the yield of 

 a single plot is about 10 per cent, above or below. 

 This is, of course, a figure obtained from a consideration 

 of the Itothamsted results only, and docs not necessarily 

 apply to other soils under different conditions. The 

 important fact to remember is that differences of treat- 

 ment which can only cause v.ariations ofyield within the 

 limits of the mean error are worthless in the matter of 

 making deductions from the results. 



As to the question of the size of experimental 

 plots, increased accuracy is not obtained by making 

 this large. It is very likely thai the effect would 

 be, on the contrary, to increase the magnitude of 

 such errors as exist already, and to introduce others. 

 No minimizing of this inaccuracy of the large plot can 

 be obtained, either, by selecting and weighing the 

 produce from small areas within it, for this, in the 

 words of the author, ' introduces the most fatal error of 

 all, a selection by the preconceived opinion of the 

 experimenter'. Another mistake that is likely to be 

 made when large plots are employed is to count the 

 number of holes and to calculate what the yield ought 

 to have been, had a plant been obtained in every 



one of them. ■ Most manures affect the texture of the 

 soil, and therefore the number of plants which establish 

 themselves is one of the factors in the result that is 

 directly affected by the manure.' 



These and other considerations, such as those of 

 variations in its properties in different parts of a given 

 area of soil, convenience in working, similar treatment 

 ot the plants at simultaneous periods in their develop- 

 ment, all point, then, to the superiority of the small 

 plot iur jigricultnral experiments. It is best that this 

 should beat least ,V-acre in area. By the utilization 

 of such plots, the only certain guide to accuracy, 

 namely the iu\iltiplicaiion of the number of experi- 

 ments by their repetition in space or time, or in both, 

 can be most conveniently employed. It is, in fact, 

 a matter of necessity if accurate results arc to be 

 obtained in places where only small areas of land are 

 available for experimental purposes. Reference to 

 publications of the Department, such as the Report on 

 Sai/ar-rii lie Experiments in the Leeirnr.l Islands 

 190.5-ti, Part II, p. 1: 1906-7, Part II, pp. 1 and 2; 

 Iteport on Agricaitural Eirperiments in Barbados, 

 1898-1900, p. 137, will make it clear that this policy 

 has been adopted by it for exactly the same reasons as 

 are enunciated above. 



In expressing the results from small plots in terms 

 of a yield per acre, care must be taken to avoid an 

 error, or better, a pretended accuracy, by including 

 fractional parts of the expressions obtained as a result 

 of the necessary multiplication, which are onlv the 

 product of experimental error and the factor which is 

 employed to get the return per acre. An appreciation 

 of the importance of this will lead to the emplovment 

 of the expression, 14 8 tons, instead of the false state- 

 ment, say, 14 tons Ki cwt. 48 lb. The latter wouKl be 

 recorded by the experimenter, of course, but the former 

 would apjiear in his report. 



In any set of experiments, then, the investigator 

 must know the extent of the probable error involved. 

 Without this knowledge, he cannot rightly interpret his 

 results, and he will probably waste time in attempting to 

 explain apparent discrepancies which reall}- arise from 

 the attribution of results to differences of treatment, 

 while they are actually caused by unavoidable errors 

 in experiment. With this knowledge, and the avoidance 

 of a factitious accuracy, he will present results that have 

 the self-recommendation of concordance; and, what is 

 almost as important, a knowledge on the part of his 

 readers, of the facts that have just been dealt with, 

 will enable them to profit by the power of discrimina- 

 into which it gives them, 



