STUDIES ON OAT BREEDING. 171 



ments involving a much larger number of plots for each variety 

 or else carried on for a number of years would be necessary to 

 settle such questions definitely. However these data together 

 with certain other observations to be discussed later enable us 

 to reach fairly definite conclusions regarding certain varieties. 



What we wish to know in this connection is the amount of 

 variation between the different plots of the same variety. Thus, 

 that variety in which all four plots yield at nearly the same rate 

 is, so far as we can judge from this experiment, less affected 

 by the environment than a variety in which there is a wide dif- 

 ference in the yield of different plots. In order to measure this 

 variation resort must be had to certain mathematical methods. 

 Two mathematical constants may be calculated, viz., the stand- 

 ard deviation which measures the variation in absolute units 

 and the coefficient of variation which measures the variability 

 as a percent of the mean." For comparative purposes it simply 

 needs to be remembered that a variety with the smaller constant 

 (standard deviation or coefficient of variation) is the less vari- 



"For any readers who are unacquainited with the use of biometrical 

 methods the following brief explanation may be of assistance. 



The standard deviation denoted by the Greek le'tter sigma (s) is ob- 

 tained by finding the difference between each observation and the mean 

 of all the observations. These dii^erences are then squared which makes 

 them all positive in sign. The sum of these squared deviations is next 

 divided by the number of observations (n) and the square root of this 

 result is then obtained. The result technically expressed as the square 

 root of the mean squared deviations is the standard deviation. 



The formula is ^ — y "" \ where S (D^) is the sum of the squared 



u 

 deviations. The standard deviation expresses the variation in terms of 

 unit value, for example as bushels per acre in Table 7, or as pounds per 

 bushel in Table 12. 



In order to reduce this concrete value to a relative basis so that bushels 

 may be compared with pounds resort may be had to the coefficient of 

 variation. The coefficient of variation is obtained by dividing the stand- 

 ard deviation by the mean and multiplying the results by 100. 



4,- x ICO 



Coeff. of variation =; 



mean. 



This expres'ses the variation as a percent of the mean. It is the best 

 method known of expressing the variation of a series of observations in 

 a single mathematical term. 



