72 Nebraska Agricultural Exp. Station, Research Bui. 13 
of 11.63 bushels in the true value of the two varieties. How- 
ever, we know in this case that both groups should have 
yielded alike since they were planted to the same crop. The 
probable error would give us confidence in very inaccurate 
results. 
Slightly different results are obtained when the above ex- 
ample is calculated by the following prescribed formula : "The 
probable error of the difference of two means each affected 
with a probable error, is equal to the square root of the sum 
of the squares of the probable errors." By this formula the 
difference in mean yield of groups Nos. 30 and 50 equals 
21.5 ±2.55 bushels. Three times the probable error is 7.65 
bushels which leaves a net difference of 13.85 bushels. 
PROBABI.K ERROR OF FIFTY GROUPS OF FOUR SYSTEMATICALLY 
DISTRIBUTED THIRTIETH-ACRE PLATS OF KHERSOX OATS 
Table 33 contains results with the same 200 Kherson Oats 
plats as compiled in Table 32, except that systematically dis- 
tributed plats rather than adjacent plats are averaged in 
groups of four each. If the mean yield of the entire 200 plats 
is here regarded as the true value of the various group means, 
the actual error of these group means exceeded their prob- 
able error 0, 1, 2, 3, and 4 times in 10, 25, 10, 1, and 4 groups 
(See Col 11). This is a marked reduction in actual error 
as compared with similar data for adjacent plats and indi- 
cates a great advantage for systematic distribution. An ap- 
plication of the probable error to these systematically distrib- 
uted plats would seem fairly reasonable altho it cannot be 
applied absolutely. 
Because of chance groupings of either large or small varia- 
tions where relatively small numbers are used, the actual 
error of a mean may be greater than three times its probable 
error, or it may be smaller than the probable error. Data may 
be either more or less accurate than an application of the 
probable error would indicate. 
EXAMPLES OF LIMITATION OF THE PROBABLE ERROR 
Small Grain Roiv Tests — In Tables 1 to 7 were given the 
relative small grain yields of rate-of-planting or variety tests 
in alternating nursery rows. The plats were replicated 50 
times and the probable error of the mean yields is indicated. 
The yields in these plats were subject to two sources of error, 
namely soil variation and plat competition. Corresponding 
