Nov. 15,1925 Limitation of Student 1 s Method in Fertilizer Experiments 955 
applied directly for wheat, 0 n plot No. 32; and that when the par¬ 
allelism of the gains is subjected to the same method of interpreta¬ 
tion exactly the opposite conclusions are reached, namely, the odds 
are 34 to 1 that it is the manure and not the chemical-fertilizer 
treatment which is the more effective. 
It is not the aim here to discredit Student’s method. Its advan¬ 
tages are fully recognized. Nor is it the intention of the writer to 
raise at this time any question as to the certainty of significant 
differences in fertilizer effects, especially in those cases where, largely 
because of soil heterogeneity, the interpretation, when based on the 
parallelism of gains, leads to conclusions opposite to those arrived 
at when the interpretations are based on paired yields. (This 
latter point presents a distinct problem, since it is well known that 
the response made by a soil type to a given fertilizer treatment 
will vary more or less on local areas or spots, depending in a large 
measure upon the kind of fertilizer and the degree of difference m 
the natural producing power of the soil.) The writer wishes simply 
to call attention to the fact that this method of interpreting fertilizer 
results has its limitations. 
The facts are that natural soil productivity is not a constant on 
all the plots of a fertility experiment and that the application of 
Student’s method to paired yields may not lead to correct inter¬ 
pretations of fertilizer results. When Student’s method is applied 
to yields soil homogeneity is assumed, but when the method is 
applied to paired gains soil heterogeneity enters into consideration. 
Thu§ it seems more correct statistically and more logical (in order 
to meet the conditions under which many fertilizer experiments 
are conducted) to apply Student’s method, wherever possible, to 
parallel gains as a better test of the certainty of any significant 
difference in fertilizer effects, 
A study of the principles on which Student’s method is based 
and of the statistical formulas on which its proof rests can hardly 
lead one to restrict its application to paired yields. Furthermore, 
in experiments in which the effects of different fertilizer treatments 
are compared, the interest does not center so much on the yields as 
on the gains effected, particularly when such gains can be expressed 
as “deviation from normal,” or deviations from control-plot treat¬ 
ment, assuming progressive differences between control plots. Thus 
from both the practical and economic points of view it is the differ¬ 
ence between gains effected, or second differences, which finally 
determines which of two fertilizer treatments is the more effective 
and also perhaps the more profitable. 
It has long been the practice to measure the comparative values 
of different fertilizers in terms of margin of profit over the cost of 
the fertilizers as determined by the market value of the increases 
obtained. This is highly desirable from the economic or profit 
point of view. However, there remains to be given alongside these 
profits, which serve to measure the comparative economic values 
of any two fertilizers, some mathematical expression of the statistical 
significance of the effects of one fertilizer treatment when compared 
with the other. This can be done consistently, and probably with 
less error as affecting conclusions, when the interpretation of results 
is based on the parallelism of gains rather than of actual yields. 
