M. Greenwood and J. D. 0. White 
527 
Let us suppose that the distribution of samples of 50 that we obtained is 
actually the distribution of samples of 50 in general, then the following experiment 
may be considered. The 400 cards were shuffled and drawn as before except that 
after each drawing the card was replaced, the process being carried on until 400 
numbers had been written down, a second series of 400 numbers was then obtained 
in the same way and the indices were computed. Tables XIII, XIV and Graph 7 
TABLE XIIL 
Constants of the Experimental Frequency Distribution Obtained by the Method of 
Replacement. {Mean, Mode and a, Expressed in Terms of the Opsonic Index.) 
Mean Mode 
1-0196 -9697 
6-7337 
/3i 
-207: 
37-9597 
3-2155 62-7551 44-6934 9-0844 51-6706 
Ko ft- 3 Skewness P 
--8536 -2155 -2428 -8988 
Equation : 
^ = 80-0808 h + — „ 
37-9597 
A change of '1 in the iudex is taken as the statistical unit of grouping and index -45 as zero. 
TABLE XIV. 
Chances of Obtaining Certain Deviations, on the Basis 
of an Experimental Curve from Samples of 50 
{Method of Replacement). 
Opsonic 
Index 
rraction of Total 
Area bounded by 
corresponding 
Ordinate 
Odds against 
such a Deviation 
or a Greater 
■6 
•0075 
132 to 1 
■7 
-0458 
20-8 to 1 
■8 
-1454 
5-88 to 1 
■9 
-3096 
2-23 to 1 
1-1 
-3165 
2-16 to 1 
1-2 
-1795 
4-57 to 1 
1-3 
-0910 
9-99 to 1 
1-Jt 
-0413 
23-2 to 1 
1-5 
-0167 
58-9 to 1 
1-6 
-0059 
168 to 1 
give the statistical constants and other information which resulted from an analysis 
of this experiment. It will be noticed that the table of chances does not differ 
appreciably from that due to the other experiment (XV). On this account, and 
because of the doubtfulness of the assumption in the case of lOO's and the smaller 
practical interest in the case of 25's, the experiment was not repeated in these 
67—2 
