266 



Journal of Agricultural Research 



Vol. XII, No. s 



Tabi<E VI. — Table of odds for differences which may occur in one direction only 



On assuming that a lo-to-i chance is a reasonable assurance, the ques- 

 tion logically arises, "What difference between any two plots must be 

 manifested for this degree of confidence that the difference is due to 

 treatments applied?" By referring to columns 2 and 3, Table V, one 

 may find the difference in terms of the probable error which is necessary 

 between two results to obtain this degree of reliability. Here it can 

 be seen in column 2 that there must be a difference 3.53 times the prob- 

 able error to give the odds of 10 to i in column 3 against such a difference 

 occurring under uniform conditions. Thus we find in this example that 

 the difference between two 32 -tree plots in four scattered units must be 

 at least 14.17 per cent X 3.53 = 50.02 per cent of the mean production, 

 to give the assurance of a lo-to-i chance that the difference is due to 

 fertilizer, irrigation, or whatever factors are under consideration.^ 

 Even with this difference, conclusions based on such results obtained in 

 this navel orange (Arlington) grove may be correct 10 times out of 11 

 and wrong once out of 11 times. 



On turning now to the 32-tree plot of adjacent trees with navel oranges 

 (Arlington), it is seen the probable error is 16.42 per cent. To pro- 

 ceed as before, 16.42 per cent, the probable error of one plot, X V^ = 

 23.22 per cent, the probable error of the difference; 23.22X3.53 = 81.97 

 per cent. Therefore a difference between two such plots of 81 .97 per cent 

 of the mean of the total area would be necessary to give the assurance 

 that such differences are real 10 times out of 11 and due to pure chance 



1 If comparisons were being made between two radically different treatments which were known to pro- 

 duce different effects in fruit production, such as irrigation compared with dry farming, or the use of large 

 quantities of stable manure on light soils, compared with no manuring, then reference should have been 

 made to columns 2 and 3 in Table VI, which are based on the differences occurring in one direction only., 



