400 On the Frequency Distributions of Phafiocytic Counts 
p. 388 discussion of N.S.A.). Any test therefore must be based on the full accept- 
ance of the skeAvness of phagocytic distributions. 
Of the consequences of this admission we shall not here speak at length : we 
are at least justified in pointing out the danger of attaching weight to the evidence 
of small samples. 
There is no ground for the expectation that random deviations in excess or 
defect of a mean value will occur with equal frequency. 
Again, distributions with high and low mean and modal values not being 
always even of the same type, in forming a ratio we may be treating as comparable 
quantities which are, in some respects, incommensurable. While this latter 
consideration may be less weighty the former is of great importance. 
Having definitely, we think, established our contention as to the skewness of 
the phagocytic populations, we ask — what will be the distribution of means of 
samples taken from such a population ? 
To answer this we should require perhaps 300 samples of 50 or a total count of 
15,000 cells; we have not the hardihood to ask Dr Fleming or Dr Strangeways to 
undertake so heroic a count. 
One of Dr Strangeways' counts, however, extended to 2000 cells, and he grouped 
his results in 80 batches of 25. - 
Adopting a somewhat coarse unit of grouping — 0'12 bacilli — and using Shep- 
pard's corrections, we obtained the following constants : 
Mean* 1-691, Mode* 1-540, ^^, = 7-40104, /3, = '475566, ^S,- 3-31849. 
K,^- -50733, Range* 1-0366 to 4-15397. 
Equation : ^^ 12-03429 (l + -^^j x (l - gyy^J • 
P = -92. Skewness = -4597. See Graph 16. 
Now a sample of 80 means is too small to use as a conclusive argument, and 
besides, few or no pathologists would confine themselves to a phagocytic count of 
25. Nevertheless, regarding the curve as an illustration, it suggests some interest- 
ing reflections. 
The skewness is of course reduced, as we should expect on theoretical grounds, 
but still quite sensible and of the same order as in the case of the F. distributions. 
Supposing for a moment that the curve represents truly the distribution of 
the whole " population " of means, we see clearly how inappropriate would be 
the ordinary nomenclature for probable errors. 
Thus the chance against a positive deviation as great as or greater than -1691 is 
3-6 to 1, while the chance against a negative deviation of '0691 is 1-88 to 1, 
These values are reduced to unit of observation, the equation is in terms of the statistical unit of 
grouping. 
