10 BULLETIN 1321, U. S. DEPARTMENT OF AGRICULTURE 
individual ear rows due to conditions not related to differences in 
the seed value of the individual ears planted in them. It seems 
entirely conservative, however, to estimate that 90 per cent of the 
variation in the yield of the ear rows was due to causes affecting 
the yields of the check rows also and in no way related to the object 
of the present study. 
If yo, is the standard deviation of A for constant X, its value 
is given by the formula yoi=cij(1—rix). Then, 100 X rix, 
gives the percentage of the squared standard deviationof A 
that disappears when X is made constant or that is a function 
of the variability of XY. The value of (1—rix) gives the maximum 
limit for the squared correlation between A and any other variable, such. 
as B, that is independent of X. Finally, the ratio ri3,;+(1—r?x) 
measures the portion of all the variability in A not a fune- 
tion of X that is a function of B. If we let X represent vari- 
ability in experimental conditions in no way related to variation 
in the factors being studied, it is evident that a relatively low value 
for r.,, nevertheless, may indicate an important relation between 
A and B if the value of riz be large. 
On the assumption that 90 per cent of the variation was due to vari- 
ability in the experimental conditions, rix=0.90 and (1—rjx) =0.10. 
The latter, therefore, is the maximum limit for the squared 
correlation between yield and any ear character. The coefficients 
of correlation between yield and the ear characters have the same 
significance under these conditions as coefficients 3.16 times as 
large would have in data in which the yields had not been influenced 
by variation in experimental conditions. It should be kept in mind, 
however, that this interpretation applies only to the 10 per cent of 
the variation remaining after eliminating the effect of accidental 
variation. This remaining variation is so small that the coefficients 
must be interpreted as indicating very slight but very definite ten- 
dencies. 
CORRELATIONS AMONG THE EAR CHARACTERS 
The coefficients of total correlation among the eight ear characters 
are shown in Table 6, and the coefficients of partial correlation be- 
tween some of the characters are shown in Table 7. The correspond- 
ing coefficients are much alike for the four varieties, the differences 
being about what would be expected from a knowledge of the varietal 
characteristics. It should be borne in mind that these ears consti- 
tuted a carefully selected population. The seed ears in any season 
were from a comparatively few rows which had been selected because 
they produced the largest yields in the previous year. _A lack of 
environmental influence is indicated by the small correlations be- 
tween such characters as length and circumference of ear. 
