1922] DENNY—FRUITS 51 
have a true random sample, or that there is a correlation between 
size and composition. The correlation coefficient between size and 
the soluble-solids-acid ratio, however, was calculated by the method 
recommended by ToLtey (9), and was found to be 0.158, with a 
probable error of 0.092, which does not indicate any significant 
correlation. 
_In order to partially eliminate the size of the fruit as a factor, 
the order in table I was rearranged by lot. With the new order, 
TABLE IV 
RESULTS OF CALCULATIONS OF PROBABLE ERROR BASED ON 
ANALYSIS OF GROUPS OF TEN FRUITS EACH 
SOLIDS-ACID RATIO 
GROUPS OF Io FRUITS EACH No. required 
P.E. sing. for —— 
assuran 
Me oa, oe ee I.0 18 
eae ey ree ve 0.9 15 
Saal ies a5 Gots 1.3 31 
Ree he Sea 2.0 18 
Se ks ee 1.6 47 
Oe ae es ia I.4 36 
Pea eke ewan ae ‘4 31 
Boe ae ees 43 31 
Ore a os ee 1.3 a1 
10.8 ee 0.5 5 
be Caen renin acta 1.8 590 
2 a eee ee 1.3 31 
Ee. ees 7.2 22 
BO er a naa Gen ie 0.90 15 
tf ER als eae a Sioa beree as 1.2 26 
the values of P.E. sing. and N were calculated after ten fruits 
were analyzed, after fifteen, etc. The results are shown in 
table III. P.E. sing. was found to vary from 1.3 to 1.4, causing 
N to vary from 31 to 36. Another rearrangement by lot is shown in 
the last two columns of table III. Values of P-E. sing. vary from 
1.0 to 1.4, causing N to change from 18 to 36. In both these cases, 
values by formula 2 would also have been variable, but of course 
would have been just half as large numerically. 
Use of small numbers to calculate probable error of 
single fruit 
It may be inquired what the P.E. sing. would have been for 
different lots of ten fruits each. Groups of ten each were selected 
