Feb. 4, 191 8 Variability of Yields of Fruit Trees and Field Trials 267 



only once out of 11 times; yet this grove was chosen because of its ap- 

 parent regularity, for it has been judged sufficiently uniform for plot trials. 



The point might be justly raised that the small number of plots in- 

 volved in the above calculations are not sufficient to give the laws of 

 chance a fair opportunity of asserting themselves. On laying the area out 

 in plots of adjacent trees there were 30 plots, while made up of scattered 

 units there were 31 plots. Figure 9 shows the distribution of these plots, 

 together with the theoretical cur\^e, which was caclulated for the scat- 

 tered-unit curve. The scattered-unit curve closely approaches the theo- 

 retical normal curve 

 of errors, and there- I ' ■" 



fore reliance can be 

 placed upon its 

 probable error. 



In the case of the 

 plots of adjacent 

 trees, however, the 

 30 units are not suf- 

 ficient to give the 

 laws of chance fair 

 play. Table VII 

 sums up the results 

 of the foregoing cal- 

 culations, adding ex- 

 treme and mean 

 yields of the two dif- 

 ferent types of plots 

 and the theoretical 

 probable error. The theoretical probable error based on the theory of 

 random sampling for a hypothetical 32-tree plot is the probable error of 



one tree 26.67-^ -^32 =4-71 P^'^ cent. This is readily calculated from 

 the distribution of the yields on a one-tree unit, the curve of which is 

 shown by figure 10. The large number of trees involved, even though 

 the distribution is not normal, justifies the use of the probable error as a 

 minimum probable error. Based upon the theory of random sampling, 

 two hypothetical 32-tree plots with a probable error of 4.71 per cent 

 should show a minimum difference of (4.71 X V 2 X 3.53) = 23.51 per cent 

 to give an assurance of a lo-to-i chance that such a difference is real 

 and not due to casual variation. Therefore, if the calculations in Table 

 VII based on adjacent trees can not be fully relied upon because of the 

 small number (30) in the population and because their distribution is not 

 normal, we may at least reasonably expect that the necessary difference 

 between two such plots will fall between the theoretical 23.51 per cent 

 and 81.97 with a practical certainty that it will be greater than 50.02 per 

 cent of the mean. 



2 ^ -F ^ e 7- e 



Fig. 9. — Graphs of production, 32-tree plot, navel oranges (Arlington). 



Scattered in four 8-tree units. 



Adjacent»32-tree units. 



