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The Reliability of a Difference between Two Averages 1
Author(s) -
Kemp W. B.
Publication year - 1924
Publication title -
agronomy journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.752
H-Index - 131
eISSN - 1435-0645
pISSN - 0002-1962
DOI - 10.2134/agronj1924.00021962001600060003x
Subject(s) - citation , reliability (semiconductor) , computer science , mathematics , library science , power (physics) , physics , quantum mechanics
Those who have occasion to interpret the results of crop investigations are very much indebted to Love and his coworkers for keeping constantly before them the necessity for applying some measure of reliability to the results of such studies. Anthony and Waring, together with these men, have brought to general attention the method of "Student," for measuring the reliability of a d~fference between two averages when this d~fference is determined under the peculiar conditions that exist in plot tests. Articles on this subject have compared the method of "Student" with an application of the ordinary formula or modifications of the ordinary formula as suggested by Bessel and by Peter. The "Student" method has given a measure of reliability that seems more reasonable than that obtained by these formulas. On account o’f this showing its use is recommended. In nearly all cases where such comparisons are made, the significance of results as measured by the two methods vary so widely that the casual reader is apt to doubt the reliability of .either method. It is in an effort to overome such doubts that this article is written. One very important consideration seems not to have been sufficiently stressed in these discussiqns. This consideration is the fact that superiority of "Student’s" method to the applications of the other formulas is not primarily because of the paucity of data, even though this does have some effect, nor because of a too closely drawn "Analogy between determinations made in the exact sciences and the measurement of field plot trials." It is because Bessel’s formula was never designed for use under such conditions and is, therefore, inadequate for this use. One of the specific limitations accompanying the use of Bessel’s formula is that there shall be ~o correlation between the deviations in the sets of data from which the diffe~:ence in a~erage is determined. But correlation is almost sure to be present whenever any such deviations as those induced by season or soil car~ modify the data. If such correlation does exist, its effect must bel removed either before or after the formula is applied. After thi~ removal it may be of value to compare the merits of the different methods, but before its removal no comparison can logically be made, for the formulas referred to are patently inapplicable.