Experimental Error in Crop Tests 
67 
PROBABLF, ERROR FOR FIFTY GROUPS OF FOUR ADJACENT 
THIRTIETH-ACRE PUATS OF IvHERSOX OATS 
That the probable error cannot apply to the mean yields 
of adjacent duplicate plats in a variety test is brought out 
by the following data : 
In Table 32 are given the mean yields for 50 groups of 
four adjacent plats, together with the average deviation, 
standard deviation, and probable error for each group. The 
average deviation of each group from the mean yield for the 
entire 200 plats is also indicated and in the last column of 
the table is given the ratio of this deviation to the probable 
error. 
If it is permissible to assume that one group of four dupli- 
cate plats is comparable with another group of four plats in 
the same field, then it would also seem permissible to assume 
that in the present instances, the mean yield for the entire 
200 similarly treated oats plats should represent the correct 
yield or true value of any or all of the individual groups 
within the field. If this assumption be made with the adja- 
cent duplicate plats (Table 32), the actual error of these 
group means exceeded their probable error approximately 0, 
1, 2, 3, 4, 5, 6, 7, 8, 10, 11, and 15 times respectivelv in 9, 5, 
7, 7, 8, 4, 4, 1, 2, 1, 1, and 1 groups. (See Col. 11, fable 32). 
This is YQYy inconsistent with the table of probabilities quoted 
from Davenport on page 66, and shows that a uniform ap- 
pearing field may be so heterogeneous in soil conditions that 
its mean yield cannot be regarded as correctly representing 
the true value of its various parts. 
Since all the plats were treated and planted alike any dif- 
ference in the yields of the groups represents experimental 
error, either in mechanical operations or in soil variation. 
Among the 50 groups of adjacent plats, one group yielded 
14.2 bushels less and another group 7.3 bushels more per acre 
than the 200-plat mean. These extremes represent an experi- 
mental error of 21.5 bushels since both should have yielded 
alike if the method of comparison were reliable. 
Should we presume that groups No. 30 and No. 50 (Table 
32) are distinct varieties in a comparative variety test, we 
would have a difference in yield of 21.5 bushels per acre. 
After multiplying the probable error of each mean by three, 
there remains a net difference of 11.63 bushels between the 
probable error ranges. Placing confidence in the probable 
error calculation, we would believe that there is a difference 
