Experimental Error in Crop Tests 
65 
son of long narrow plats with short wide plats. The group- 
ings illustrated in the following diagrams were compared. 
(In the 1x9 grouping, three groups were necessarily irregu- 
lar in shape since 9 is not a multiple of 69.) 
The results are included in Table 31. Long, narrow plats 
are indicated to be more reliable than short wide plats of 
the same area. Increasing the size of the plat is less effec- 
tive in overcoming experimental error than the systematic 
distribution of plats equal in combined area. 
SIGNIFICANCE OF THE PROBABLE ERROR" 
The "probable error" calculation is being used somewhat 
by field crop experimenters. Its use is rather inviting since 
a small ''probable error" is customarily regarded as indicat- 
ing accuracy in the results. Davenport's interpretation is 
generally accepted, namely: ''It (the probable error) indi- 
cates the degree of confidence which we should place in results 
obtained by statistical methods." 
Where plats are replicated two or more times, the prob- 
able error of the mean is based upon the standard deviation, 
and is determined by the following formula : 
standard deviation 
Probable error of mean = ~z 0.6745 — , ^ . , = 
1 number of variates 
or 
which is also stated = - 0.6745—^= 
1 n 
The probable error is regarded as an upper and lower 
limit of divergence for which the chance is even that the 
true mean does not lie outside of these limits. Commenting 
upon the likelihood of the true mean lying outside of the 
limits set by the probable error, Davenport (1907) states: 
"Of course the error in a determination has also an even 
chance of lying outside the limits set by the probable error 
(E), but the following table will show that it is very unlikely 
that the error is many times as great as E. Thus the chances 
that the true value lies within the range set by it E, =t 2E, 
etc., are as follows : 
