LIMITATION OF STUDENT’S METHOD WHEN APPLIED 
TO FERTILIZER EXPERIMENTS 1 
By W. W. Weik 
Associate Soil Technologist, Bureau of Soils, United States Department of 
Agriculture 
The advantages of Student’s method for interpreting paired 
experiments are fully recognized by many agronomists largely 
because of the fact that this method brings within the range of 
statistical inquiry many crop and fertilizer tests the small-sample 
results of which furnish insufficient variability to enable one to judge 
of the significance or certainty of the results by the application of 
the usual probable-error formulas. . 
It has been pointed out by Love and Brunson 2 ( 8 ) that biometrical 
methods must be used with great care, that- experimental data must 
be wisely and judiciously interpreted if the conclusions reached are 
to be of permanent value, and that Student's method is no exception 
to this rule. These same writers have also suggested that this method 
can be successfully applied only when the paired observations are 
made under similar conditions, or when the members of each pair are 
exactly comparable. # . - 
This present paper is presented with a view to illustrating, briefly, 
some of the limitations of Student's method when used in the inter¬ 
pretation of fertilizer results, and to calling attention to some precau¬ 
tions that should be taken in arriving at any mathematical expression 
of the significance or nonsignificance of one fertilizer treatment as 
compared with another. 
Let the data in Table I be assumed for a pair of fertihzer tests on 
corn, obtained on two differently fertilized plots, A and B, belong¬ 
ing to the same series of tests: 
Table I .—Fertilizer tests on corn on differently fertilized plots 
Year 
Plot A 
Plot B 
Yield 
per acre 
Increase 
effected 
per acre 
Yield 
per acre 
Increase 
effected 
per acre 
Bushels 
77.20 
53.50 
66.10 
65.80 
52.40 
57.30 
Bushels 
14 
12 
14 
10 
9 
13 
Bushels 
75.60 
49.70 
56.50 
63.80 
42.40 
47.70 
Bushels 
14 
11 
14 
11 
8 
14 
Mean___ 
62.05 
12 
55.95. 
12 
1 Received for publication Feb. 20, 1925; issued January, 1926. 
2 Reference is made by number (italic) to “Literature cited/ p. 956. 
Journal of Agricultural Research, 
Washington, D. C. 
74780—26t-4 (949) 
Vol. XXXI, No. 10 
Nov. 15,1925 
Key No. H—10 
