66 Nebraska Agricultural Exp. Station, Research Bui. 13 
± E the chances are even 
±2 E the chances are 4.5 to 1 
±3 E the chances are 21 to 1 
±4 E the chances are 142 to 1 
±5 E the chances are 1310 to 1 
±6 E the chances are 19,200 to 1 
±7 E the chances are 420,000 to 1 
±8 E the chances are 17,000,000 to 1 
±9 E the chances are about 1,000,000,000 to 1 
'*It is extremely improbable, therefore, that an error will 
be many times as large as the probable error. For instance, 
it is practically certain that the error is not as large as 9 E, 
since the table shows, that the chances are about a billion to 
one in favor of its being smaller than 9 E. 
'Thus by giving, along with any result, the calculated 
probable error, the reader may know what degree of con- 
fidence is to be placed in the results." 
In common usage, it is stated that the actual difference 
in the yield of two plats must be three times the probable 
error before the difference in yield is significant. 
It should be agreed at the outset that the probable error 
of a mean yield has significance only when the variations 
entering into the mean are purely accidental rather than sys- 
tematic. This distinction is understood by biometricians 
who universally attach importance to the probable error cal- 
culation when used in a legitimate manner. There appear to 
be strong possibilities of misusing the probable error and 
overestimating its value in agronomic studies. This need not 
be regarded as any defect in the probable error formula, but 
rather as a misapplication thereof to experimental results 
possessing either visible or invisible systematic errors. 
Field crop investigators consider it good technique to repli- 
cate test plats. It has been proposed that, in such tests, small 
probable errors for the mean yields of the various varieties 
or treatments would indicate reliability and justify con- 
fidence in the comparative yields. 
For the purpose of studying the significance of the prob- 
able error in field crop tests, the first 200 consecutive thir- 
tieth-acre Kherson oats plats described on pp. 52 to 64 have 
been grouped in 50 sets of four adjacent plats and also 50 
sets of four systematically distributed plats, and the prob- 
able error calculated for the mean yield of each group of 
four plats. 
