EXPERIMENTS IN FIELD PLOT TECHNIC 57 



variability of the mean of 16 replicate plots will be about half that of 

 the mean of 4 replicate plots. Now the maximum use of check plots, 

 that is, the practice of alternating check plots and test plots, requires 

 the same land and labor as would be required by doubling the num- 

 ber of replications, if no check plots were used. As doubling the 

 number of replications will in general give a standard deviation about 

 equal to the original standard deviation divided by the square root of 



2, it will reduce variability about 30 % (=. = .7071 \ . If alternat- 

 ing with check plots will consistently reduce variability more than 30 

 per cent it will be generally a more economical way to control error. 

 Similarly, the use of check plots in every third plot requires as much 

 land as would be required by increasing the number of replications by 

 50 per cent (using three replications instead of two, or fifteen instead 

 of ten). From this relation the reduction of variability necessary if 

 this practice is to equal replication in effectiveness can be easily com- 

 puted. Such determinations for check plots at various intervals are 

 shown in Table 30. 



TABLE; 30. REDUCTION OF VARIABILITY BY THE USE OF CHECK PLOTS EQUIVALENT 



TO THAT PROBABLY ATTAINABLE WITH THE SAME NUMBER 



OF PLOTS BY REPLICATION. 



Reduction in 

 standard deviation to 



If protected single-row or 3-row plots are used in preliminary 

 experiments a more reliable measure of soil productivity is available, 

 and consequently the adjustment of yields is more likely to be of value, 

 than when unprotected single-row plots are used. By the use of 

 planting plans of the sort employed in these experiments, it is pos- 



