1922] DENNY—FRUITS 47 
twenty-seven outside. Table II indicates further that the chances 
are 4.64 to 1 that no single sample would deviate from 10.89 by as 
much or more than 2.0 times 0.4: that is, of the fifty-one fruits in 
table I, about nine should be outside the limits 11.69 to 10.09, and 
forty-two should be within them. A count shows that in this case 
five are outside and forty-six within. 
In the second place, table II may be applied in an entirely 
different case, namely, when comparing the analytical results from 
two different lots of fruit in order to estimate the degree of assurance 
that the difference shown between them is significant. For 
example, in table VII it is shown that the refractive index of the 
juice of the Eureka strain of lemons was 44.60.2, while that of the 
Shade Tree strain was 45.7+0.3. The differenceis 1.1. What are 
the chances that this difference is significant and not due merely 
to a sampling error? This calculation is made from the following 
pe EE an he 
P.E. of difference  V(o.2)*-+(0.3)? 030 > 
figure 3.0 is here termed the coefficient of odds, and its value is 
sought in column r in table II, from which it appears that the odds 
are about 22 to 1 (judging from these data, at least) that the juice 
of lemons from the Shade Tree strain is higher with respect to 
refractive index. Table II applies only in those cases in which the 
difference between two results may be expected to occur in either 
direction. For a table showing odds when it is known that the 
difference between two results will be in one direction only, see 
Woop (11, p. 26). 
formula: 
Formulas for calculating number of fruits for sample 
Two general sets of conditions may be recognized under which 
samples are collected for analysis: (1) When samples are taken 
from each of two or more different lots of fruit, with the object of 
later comparing them, to determine whether the differences between 
them are significant, and what the odds are that this is so. 
(2) When a sample is taken from a single lot of fruit for the pur- 
pose of obtaining a figure that will represent the composition of 
that lot, and to attain a certain assurance that this figure is cor- 
rect within certain desired limits. 
