8 o 
Journal of Agricultural Research 
Vol. XXVII, No. 2 
each variety is grown in ioo relatively long narrow plats arranged as 
shown below. The mean yields in each will be taken as 75 and 70 bushels 
per acre, respectively, with a probable error of ±0.707 bushel in each 
case. It is assumed that errors due to differences in stand or to competi¬ 
tion between varieties do not enter into the experiments. The planting 
arrangement in each case follows: 
Experiment 1. The ends of the plats of one variety abut upon the 
ends of the plats of the other. 
Experiment 2. The plats of the two varieties alternate. 
Experiment 3. The two varieties are included among 100 in a varietal 
comparison, all of the varieties being replicated 100 times, with the 
replications systematically distributed. 
The significance of the probabee error 
The significance of the data in relation to the probable error may be 
considered first. In each experiment the difference between the yields 
of the two varieties is 5 ± 1 bushels, and the odds are more than 1,300 
to 1 that this difference is not due to chance. The presumption as to 
causal relations, however, differs markedly in each case. Thus, in 
experiment 1, one would hardly care to attribute the difference in yield 
to a varietal difference, whereas in experiment 2, such an assumption 
is entirely warranted. It is clear that the probable error in either case 
measures the same thing. The difference in the presumption as to the 
causal relations rests, of course, upon a knowledge that the yields of 
both varieties, in so far as they are affected by soil productivity, represent 
random samples of essentially the same soil mass in Experiment 2, but 
not in Experiment i. 3 
The conditions in Experiment 3 do not permit such definite conclu¬ 
sions as to causal relations. The probable error again measures the 
portion of the difference that reasonably may be assigned to variations 
in the random sampling of the varieties and the soils in which they 
grew. Here, however, the yields as influenced by soil productivity do not 
sample entirely different soil masses, as in Experiment 1, nor do they 
sample what is essentially the same soil mass as was the case in Experi¬ 
ment 2. In so far as it is probable that 100 plats of one variety dis¬ 
tributed over a 30-acre field 4 would not encounter soil conditions 
materially different, as an average, from those encountered by 100 plats 
of another variety distributed over the same field, it is logical to 
assume that the difference in this experiment was due to a difference 
in the varieties. Such an assumption is based, however, upon the judg¬ 
ment as to equal chances, and not upon the probable error per se. 
The above consideration has been made somewhat detailed, not 
because it presents a new concept, but to emphasize clearly and dis¬ 
tinctly that interpretation as to causal relations in field experiments 
expressed in terms of the probable error really involves two elements of 
judgment. These are (1) the probable reliability of the two means from 
the standpoint of the random sampling of the varieties and the soil in 
which each grew and (2) the conclusion that there was no systematic 
3 It is conceivable that a difference obtained as in Experiment 2 might be due to something other than 
an inherent varietal difference, such as some previous fertilizer or cultural treatment that was similarly 
alternated and the alternations of which chanced to coincide with those of Experiment 2. The possibility 
of such an occurrence without the knowledge of the investigator, however, scarcely needs to be considered. 
A more probable cause of error in the assignment of causal relations would be a difference in seed value 
not inherent in the varieties. The consideration of this kind of error is entirely beyond the scope of the 
present paper. 
4 Something over 30 acres would be required for 100 replications of 100 varieties where each plat consisted 
of 10 hills 3.67 feet apart. 
