M. Greenwood and J. D. C. White 
401 
Translating these results into terms of opsonic indices, an index of '9 is more likely 
to occur in random sampling than one of I'l, or positive and negative deviations 
from uuity do not occur with equal frequency (see Table VIII.). 
TABLE VIII. 
Some Ordinates and Areas from the Curve of Means. 
Ordinate 
Fraction of Total Area 
[Total Area = l] bounded 
by this ordinate 
Odds against such 
a deviation or 
a greater 
Opsonic Index 
in terms of 
Mean 
1-353 - 
•14971 
5-68 to 1 
-8 
1-5219 - 
-34773 
1-88 to 1 
-9 
1-8601 + 
-73464 
3-60 to 1 
1-1 
2-195 + 
-92572 
12-46 to 1 
1-3 
Concluding, we have shown : (1) that phagocytic counts have pronouncedly 
skew distributions ; (2) that the means of small samples have likewise a skew 
distribution ; (3) that although there is a sensible reduction in skewness when 
the modal value is raised by the employment of thick bacillary emulsions, there 
is no ground for thinking that the skewness can, under possible experimental 
conditions, be so reduced as to render testing on the basis of the Gaussian curve 
allowable ; (4) the F. counts also differ from those of Dr Strangeways in the 
following respects : (a) they exhibit greater absolute but less relative variation, 
{h) the negative portion of the curve is increased, (c) they exhibit less uniformity 
in the value of P; (5) that the doubts expressed by Pearson as to the validity of 
employing " normal " tests for samples of skew material are experimentally proved 
to be well-founded. 
A further examination of these phenomena and an attempt to solve approxi- 
mately some of the problems arising therefrom will form the subject of a second 
memoir*. 
* We desire to express our sense of obligation to Professor Pearson, who has kindly allowed some of 
the more important calculations to be verified in his laboratory and has constantly helped us with 
advice and criticism. 
Biometrika vi 
51 
