ON ERRORS OF RANDOM SAMPLING IN CERTAIN 
OASES NOT SUITABLE FOR THE APPLICATION OF 
A "NORMAL" CURVE OF FREQUENCY. 
By M. GREENWOOD, Junr. 
{From the Statistical Laboratory of the Lister Institute of Preventive Medicine.) 
I. 
Introduction. 
Those who believe that the more closely a branch of knowledge adapts itself 
to the principles of quantitative reasoning, the more justly it merits to be ranked 
as a science, have been gratified by the improved standard adopted in the treat- 
ment of medico-statistical results. It is true that even now medico-statistical 
writers fall short of the attainments regarded as essential in some other depart- 
ments of natural knowledge, and that a few prominent investigators vaguely 
denounce " mathematicians " — by which term is to be understood any one trained 
to employ modern biometric methods — as presumptuous intruders within the 
sphere of experimental medicine. Despite these obstacles, progress has been 
marked within recent years and we may have considerable confidence that future 
discussions as to the value of such procedures as vaccination or the determination 
of an opsonic index will be conducted with due regard to the claims of exact 
science. 
It is, however, in the nature of tilings that a reform of this magnitude should 
be accompanied by certain disadvantages which tend to impede the march of 
ideas. For instance, reformers may urge that the employment of certain argu- 
ments requires for logical validity the application of some specific test. After 
much discussion, the point is conceded and then the test is in danger of being 
applied in other and unsuitable instances. 
The particular illustration which has prompted these remarks is the employ- 
ment of some consequences of the current theory of errors of random sampling in 
certain cases which frequently arise in medical and pathological work. At one 
time it was customary to base conclusions as to the efficacy of some method of 
treatment upon short series of cases without any statistical test being employed. 
A practitioner might find, for example, that of 100 cases of typhoid fever treated 
without any special precautions as to diet, six had died. Of a subsequent 100, 
dieted in a particular way, but two succumbed and a conclusion very favourable 
to the new method of treatment might be ventured. Owing to the partial 
