FIELD PLOT TECHNIC 53 



Where r PlP2 is the constant sought, S is indicative of summation, 

 C P the calculated values for the groups, p l9 p 2 , etc., the as- 

 signed values for the ultimate units, m the number of groups, n 

 the number of units in each group, p the average value of all 

 the ultimate units and <r p their standard deviation ; we may, by 

 substituting the given values, derive the coefficient of correlation. 



{[1,080 - 280] ^- 4[4(4 - 1)]} - 4 2 



L2247 2 



16.6667 - 16 0.6667 

 -T1999- = L4999 



. . 

 = 



The magnitude of the coefficient obtained may be influenced 

 by the size of the ultimate and group units, the nature of the 

 character measured, and the variety or strain grown. 



The above-outlined method is especially useful where it is 

 desirable to determine the relative heterogeneity of several 

 fields. The application of this test for uniformity to a field 

 that is being used for experimental work would, in many cases, 

 prevent the use of the field for breeding operations for at least 

 a year. 



Estimating Soil Heterogeneity by Means of Checks. Check 

 plots are often used in determining the comparative soil variability 

 of fields that are being used for plot studies. This is done by the 

 calculation of statistical constants. When used for this purpose 

 checks should be systematically placed over the entire experi- 

 mental area. The number should be large in order that an 

 approach to a normal frequency distribution may be obtained, 

 and systematic distribution should be followed in order to insure 

 a representative random sample. Comparison of soils should be 

 made in the same year and by the use of the same strain as the 

 check. In general, the greater the degree of soil heterogeneity 

 the greater will be the calculated standard deviation, coefficient 

 of variability, and probable error. 



Use of Checks in Correcting Yields. Aside from the use 

 to indicate soil variation, checks plots have often been used 

 to make direct corrections for yield. Table IX, taken from 

 Wood and Stratton (1910), illustrates a simple use of checks 



0.6745 (1 - r 2 ) 



1 P. E. coefficient of correlation = 



Vn 



0.6745 ( 1 - 0.444 2 ) 



Vie = ' 135 ' 



