22 
The Prohahle Error of a Mean 
view of the well-known fact tliat the varieties which have a high yield tend to 
produce soft corn, it is interesting to see how much evidence the experiments 
afford as to the correlation between softness and fertility in the same variety. 
Further, Mr Hooker* has shown that the yield of wheat in one year is largely 
determined by the weather during the preceding harvest. Dr Voelcker's results 
may afford a clue as to the way in which the seed is affected, and would almost 
justify the selection of particular soils for growing seed wheatf. 
The figures are as follows, the yields being expressed in grammes per pot. 
Year 
1899 
1900 
1901 
Average 
Standard 
z 
Soil 
Light 
Heavy 
Light 
Heavy 
Light 
Heavy 
Deviation 
Yield f)f corn from soft seed 
hard „ 
7-85 
7-27 
8-89 
8-32 
14-81 
13-81 
13-55 
13-36 
7^48 
7-97 
15-39 
13-13 
11-328 
10-643 
Difleretice 
+ •58 
+ -57 
+ 1-00 
+ -19 
- -49 
+ 2-26 
+ -685 
-778 
•88 
Yield of straw from soft seed 
hard „ 
12-81 
10-71 
12-87 
12-48 
22-22 
21-64 
20-21 
20-26 
13-97 
11-71 
22-57 
18-96 
17-442 
15-927 
Difference 
+ 2-10 
+ -39 
+ -78 
-•05 
+ 2-66 
+3-61 
+ 1-515 
1-261 
1-20 
If we wish to find the odds that soft seed will give a better yield of corn on the 
average, we divide the average difference by the standard deviation, giving us 
Looking this up in the table for w = 6 we find p = -9465 or the odds are 
•9465 : 535, about 18: 1. 
Similarly for straw z = 1-20, = -9782, and the odds about 45 : 1. 
In order to see whether such odds are sufficient for a practical man to draw a 
definite conclusion, I take another set of experiments in which Dr Voelcker com- 
pares the effects of different artificial manures used with potatoes on the large 
scale. 
The figures represent the difference between the crops grown with the use of 
sulphate of potash and kainit respectively in both 1904 and 1905. 
cwt. qr. Ih. ton cwt. qr. Ih. 
1904 + 10 3 20 : + 1 10 1 26) 
1905 + 6 0 3 : + 13 2 8 
(two experiments in each year). 
* Journal of Roxjal Statistical Societij, 1907. 
t And perhaps a few experiments to see whether there is a correlation between yield and ' mellow- 
ness' in barley. 
