178 



THE AGRICULTURAL NEWS. 



June 8, 1912. 



a means ijf estimating the value ot the methods em- 

 ployed, and of gaining information as to the amount of 

 dependence that may be placed upon the numerical 

 results. 



These means of obtaining checks on the results of 

 observations and experiments made in the course of 

 agricultural and other scientific investigation do not 

 €xhaust all the methods that have been devised for the 

 purpose. They are, however, sufficient in scope for 

 adoption in all ordinary cases. In practice, as a matter 

 of fact, it is often found that the needs of investigations 

 of the usual kind are supplied adequately by the 

 employment of two of the methods of obtaining assist- 

 ance in finding the true significance of sets of experi- 

 mental results. These are the determination of the 

 probable error, of the average and, less frequently, of 

 the probable error of any one result. It is to these, 

 therefore, that attention will be given shortly for the 

 purposes of illustration from actual investigations that 

 are being undertaken in the West Indies. 



It is instructive to compare the significance of the 

 general results for the Leeward Islands (actually for 

 Antigua and St. Kitts) with that of the results for one 

 estate, for a period of years; this has been done in the 

 third and last parts of the table, presenting figures 

 obtained at Buckleys, St. Kitts, for plant canes iluring 

 lllOO-.), and for ratoons during 1902-7. Here, with 

 plant canes, the probable error of the average is very 

 much the same in amount as the dirt'ereiices that are 

 made to be apparently due to the diti'erent methods of 

 manuring, and it is evident without further considera- 

 tion that there is nothing to be gained from the appli- 

 cation of artificial manures to plant canes, under the 

 conditions of the experiment. In view of what has been 

 said, the figures showing the probable error of one 

 experiment require no comment. The case of the trials 

 with ratoons presents, however, very different features; 

 here, basing the judgment on the figures for the diff- 

 erences for the manures and for the probable errors of 

 the averages, alone, significant gains are indicated 

 where artificial manures have been employed. 



The particulars of the means of illustration that 

 ■have been chosen for the special purpose are presented 

 in the table printed after the conclusion of this article. 

 In the first part of the table there are included, among 

 -others, the results of calculating the probable error of 

 "the average, and that of one experiment, in some of the 

 sugar-cane investigations that have been conducted 

 continuously at Dodds, Barbados, for the seventeen 

 years 1894 to 1910. It is seen here that the differences 

 obtained when nitrogen and when nitrogen and potash 

 are supplied to plant canes in addition to pen manure 

 are significant (that is outside of the limits of experi- 

 mental error) particularly in the case of the latter 

 method of manuring; while in the case of any one 

 experiment, in regard to the addition of nitrogen alone, 

 dependence cannot be placed on the numerical result, 

 as this may be entirely due to the error of experiment. 

 A similar conclusion is to be drawn from the figures 

 given for the Leeward Islands, 1901-6 in the second 

 part of the table, referring to the result of the em- 

 ployment of nitrogen (in artificial manure), potash 

 and phosphorus, in addition to pen manure; the average 

 of the results shows a gain of 3 tons of cane from the 

 last-named method of manuring, whereas the probable 

 error of the average in each case, is only OH and 0'63. 

 Further, the result of any one experiment is here again 

 -without significance; actuallj', in such a case, it is 

 possible for the difference arising from the errors of 

 experiment to be greater than that which may be 

 -expected from the addition of the manures. 



It may be well to explain that these conclusions 

 have been stated solely for the purpose of illustration 

 connected purely and simply with the determination of 

 the experimental error of field trials. It is especially 

 important that this fact should be realized a.^ 

 regards the results that are considered for plant 

 canes, particularly with respect to the results in 

 the first and second parts of the table. Here, the 

 average differences are shown to be sufficiently 

 large, as compared with the probable error of the 

 averages, to be significant, when they are considered 

 alone; but it is easy to understand that the matter is 

 not complete until the value of the increase of cane 

 indicated from the special method of manuring (with 

 the probable error subtracted) is compared with the 

 cost of the manures that uiay be regarded as the cause 

 of the inciease. 



The assistance given by the mathematician 

 to the experimenter, whether the work of the 

 latter is coi|nected with agriculture or not, has 

 enabled him to gauge with accuracy the value of the 

 results obtained by him and to test exhaustively their 

 dependence. Practical agriculturists have not been 

 slow to recognize this fact: and the determination of 

 the experimental error is gradually becoming a matter 

 of ordinary routine, in trials conducted both in the 

 field and in the laboratory. 



