950 
Journal of Agricultural Research 
Vol. XXXI, No. 10 
When Student’s method is applied to the paired yields a conclusion 
is reached showing the odds to be 195 to 1 that the fertilizer applied 
to plot A is more effective than the fertilizer applied to plot B. This 
can be true only when the natural soil productivity is a constant. 
However, if soil heterogeneity prevails to the extent that plot A 
represents a higher natural productivity than that represented by 
plot B, and this establishing a high degree of parallelism between 
the paired yields owing to the fact that yield A is always higher than 
B, in all probability the odds of 195 to 1 carry but little or no signi¬ 
ficance as regards the fertilizer applied to plot A. 
Now let it be further assumed that the figures in the second column 
under A and B represent the actual increases effected in each case, 
these being entirely within the range of probability. In comparing 
the paired gains , either by a simple comparison of the data or by 
applying Student’s method, it becomes plainly evident that no 
significance can be attached to the higher yields obtainedr on plot A, 
which are higher because of the difference in inherent productivity. 
It seems an absolute certainty that fertilizer A is not the more effec¬ 
tive fertilizer, especially when cognizance is taken of the fact that 
the average gain effected by the one fertilizer is equal to the average 
gain effected by the other. 
The foregoing illustration, though hypothetical, raises the question 
as to how Student’s method should be applied to fertilizer results. 
Should the actual yields or the gains effected be paired? 
It is a fact generally known that the soil constituting the plots of 
a series of tests in an experiment, though it be of the same type, 
usually varies more or less in its producing power on a given area, 
thus introducing the factor of soil heterogeneity in the interpretation 
of results. This condition, together with the fact that in but a few 
of the long-time fertility experiments already established are any 
of the fertilizer treatments repeated, makes it highly probable that 
the pairing of actual yields by Student’s method may not establish 
certainty that one fertilizer treatment is more effective than another. 
This point is well illustrated by the published 18-year results ob¬ 
tained with wheat on plots Nos. 11 and 30 in the potato-wheat-clover 
rotation test at Wooster, Ohio, which follow (1 , 3 , 4, and Table II). 
