Nov. 15,1925 Limitation of Student's Method in Fertilizer Experiments 951 
Table II.— Student’s method applied to wheat yields obtained in potato-wheat-clover 
rotation at Wooster, Ohio 
Actual yields 
Differ¬ 
ence in 
Devi¬ 
ation 
from 
5 68 
(D) 
Gains effected 
Differ¬ 
ence in 
Devi¬ 
ation 
from 
1.88 
(D) 
Year 
Plot 
No. 
11“ 
Plot 
No. 
30*- 
yields, 
No. 11 
over 
No. 30 
D 2 
Plot 
No. 
11 
Plot 
No. 
30 
gains, 
No. 11 
over 
No. 30 
D 2 
1895_ 
Bush . 
16. 25 
Bush. 
9.92 
Bush. 
6.33 
0.65 
0.42 
Bush. 
8.03 
Bush. 
3.64 
Bush. 
4.39 
2.51 
6.30 
1896....__ 
15.20 
5. 66 
9. 54 
3.86 
14.90 
8.14 
-. 42 
8. 56 
6.68 
44.62 
1897_ 
45.00 
34.67 
10. 33 
4.65 
21. 62 
8.44 
.72 
7.72 
5.84 
34.11 
1898_ 
33. 25 
35.08 
-1.83 
7.51 
56.40 
9.36 
10.39 
-1.03 
2.91 
8.47 
1899_ 
39.00 
30.50 
8.50 
2.82 
7.95 
9.75 
6.67 
3.08 
1.20 
1.44 
1900—__ 
46.91 
38.83 
8.08 
2.40 
5. 76 
2. 33 
5.83 
-3.50 
5.38 
28.94 
1901___ 
29.17 
29.00 
.17 
5.51 
30.36 
3.56 
6.59 
-3.03 
4.91 
24.11 
1902___ 
55.00 
41. 52 
13.48 
7.80 
60.84 
16.47 
10.99 
5.48 
3.60 
12.96 
1903.._ 
42.33 
34.17 
8.16 
2.48 
6.15 
11.08 
11.25 
-.17 
2.05 
4.20 
1904_ 
35.96 
31.54 
4.42 
1.26 
1.59 
14.89 
9.79 
5.10 
3.22 
10.37 
1905_ 
37.00 
29. 71 
7.29 
1.61 
2.59 
12.83 
10.79 
2.04 
.16 
.03 
1906__ 
52.33 
43.50 
8.83 
3.15 
9.92 
6.02 
5. 92 
.10 
1.78 
3.17 
1907__ 
42. 75 
37.42 
5.33 
.35 
.12 
8.03 
2.70 
5.33 
3.45 
11.90 
1908_ 
50.42 
44. 37 
6.05 
.37 
.14 
11.15 
13.29 
-2.14 
4.02 
16.16 
1909_ 
43. 54 
42.12 
1.42 
4.26 
18.15 
2.40 
7.80 
-5.40 
7.28 
53.00 
1910. ___ 
34.12 
34.00 
.12 
5.56 
30.91 
11.44 
8.30 
3.14 
1.26 
1. 59 
1911_ 
25.83 
30.83 
-5.00 
10.68 
114.06 
12.24 
13. 61 
-1.37 
3.25 
10.56 
1912__ 
18.04 
6.92 
11.12 
5.44 
29.59 
6.52 
.91 
5.61 
3.73 
13.91 
Mean_ 
36.80 
31.10 
5.68 
22.86 
<7=4.80 
9.04 
7.15 
1.88 
15.88 
<r=3.98 
Z= 1.18 (5, p. 416). £=0.471. 
P=±0.9999+. P= ±0.9635. 
Odds=Over 10,000 to 1. Odds=26 to 1. 
« Fertilizer treatment consists of 120 pounds of nitrate of soda, 50 pounds of dried blood, 160 pounds of 
acid phosphate, 100 pounds of muriate of potash, applied to wheat; and 80 pounds of nitrate of soda, 160 
pounds of acid phosphate, and 100 pounds of muriate of potash, applied for potatoes. 
b Fertilizer treatment consists of 8 tons of manure applied for potatoes. 
Here it is shown that, because of the striking parallelism of the 
paired yields, the fertilizer treatment given to plot No. 11 is much 
superior to that given plot No. 30, this certainty being expressed by 
odds far exceeding 10,000 to 1. However, when the actual gains 
effected are paired, the parallelism is broken at seven different 
points, thus presenting in graphic form a more or less crisscross 
effect. Consequently, the odds are not sufficientlv high to establish 
the fact that there is any important difference in the two treatments, 
odds 30 to 1 being accepted as the mathematical expression for 
establishing statistical significance^ 
In some cases when paired yields are subjected to Student’s 
method for interpretation, odds indicate no degree of certainty that 
one fertilizer is better than another; but when the paired gains are 
subjected to the same test, odds are sufficiently high to enable one 
to come to quite a different conclusion. To illustrate this point, the 
published results obtained with corn for 20 years on plots Nos. 
17 and 26 in the five-year rotation at Wooster have been selected, as 
follows ( 1 , 3 , 4j and Table III): 
