58 



BREEDING CROP PLANTS 

 TABLE XI. THE PAIRING METHOD 



After the deviations have been converted into percentages of the 

 mean, their sum is divided by n where n is the number of pairs. 

 By multiplying the average yield of all plots by this percentage, a 

 probable error for yield of a single plot may be obtained. 



Wood and Stratton (1910) present the following probable 

 errors obtained by the pairing method, based on a large number of 

 replicated plots including the different crops wheat, barley, oats, 

 mangels, rutabagas, potatoes, and seed grasses. 



400 pairs of plots, different sizes ......... P.E. 4.2 per cent. 



45 pairs of plots, each 

 52 pairs of plots, each 

 29 pairs of plots, each 

 200 pairs of plots, each 

 75 pairs of plots, each 



acre .......... P.E. 3.5 per cent. 



acre .......... P.E. 3.5 per cent. 



o acre ......... P.E. 3.9 per cent. 



acre ....... . . P.E. 4.6 per cent. 



o acre ......... P.E. 3.1 per cent. 



In applying the method of Wood and Stratton at the Min- 

 nesota Experiment Station it was found that a slight modifica- 

 tion usually gave probable errors which more nearly approached 

 those obtained by the use of check plots. The modification 

 consisted of squaring the deviations before dividing by n and 

 extracting the square root of the quotient. This calculation 

 is given in the last column of the preceding table. 



Replication and Its Value. It has been found that systematic 

 repetition of the plots reduces the probable error and hence 

 increases the significance of the results. The number of replica- 

 tions necessary in order to make reliable comparisons is some- 

 what dependent on the kind of crop but to a greater extent on soil 

 heterogeneity. If it were desired to establish a significant dif- 

 ference of as little as 2 bu. between varieties, more replications 

 would be needed than if a significant difference of 4 bu. was 

 accepted as satisfactory. Several investigations have been re- 



