Growth and valuation in maize. ]27 



deviation of simple sampling for the five series of observation ma\' be 

 compared directly with the corresponding root -mean -square deviations, 

 and the significance of the latter estimated. 



This theoretical standard deviation may be derived from the 

 following relationship. If o is the standard deviation of a whole series 

 of observations, and 01, 02 0, are the standard deviations of the 



respective component series, whose means diverge from the mean of the 

 whole series by amounts di, d2 dr, then 



Nö^ = ^(i\„oV) + -S(N„d„2), 

 where 111 is any subscript and N = ^(Nm)^)- 



If the observed root -mean -square deviation (standard deviation) 

 exceeds the theoretical standard deviation calculated from the above 

 equation, it is certain that some influence other than chance determined 

 the distribution of the observations. Of course the gi-eater the excess 

 of the root-mean-square deviation the greater is the influence affecting 

 the observations. 



Returning now to a discussion of the results shown in Fig. 8. it 

 is noted that in every instance except one, the root-mean-square 

 delation is greater than the standard deviation of simple sampling. 

 The one exception is that for plants starting in quintile IV in series A. 

 In this instance the distribution of the plants does not diverge 

 farther from the theoretical mean than might be expected on the theory 

 of simple sampling. In the case of plants starting in quintües I and V 

 the values of the root -mean -square de\1ations are very large, ranging 

 from four to six times the theoretical standard deviations. It should 

 be remembered that here the comparison is betw^een two standard 

 deviations. The conditions are quite different from those in Fig. 6 where 

 a mean was compared with its standard deviation. If, as in the present 

 case, the observed standard de\iation exceeds the theoretical constant, 

 it means that the distribution of the observations was determined by 

 some factor other than chance. The greater the excess the gi-eater was 

 this extraneous influence. 



Considering now the changes in the root -mean -square deviations 

 for plants starting in the different quintiles it is seen from Fig. 8 that 



■) In calculating the standard deviations from the above equation the actual 

 standard deviation for each quintile is needed, but as was stated above, these constants 

 have not been tabled. Since they do not vary greatly in any case from the value 

 3'34 percent, no significant change would be made in the constants by using that value 

 throughout. However, in calculating the standard deviations given in the last columns 

 of tables 7 — 9, the actual values of the individual standard deviations were used. 



