THEORY OF STATISTICS. 
the mingling of records, e.g. respecting the two sexes, which a 
careful worker would keep distinct. 
Take the following case, for example. Suppose there have been 
200 patients in a hospital, 100 males and 100 females, suffering 
from some disease. Suppose, further, that the death-rate for males 
(the case mortality) has been 30 per cent., for females 60 per cent. 
A new treatment is tried on 80 per cent. of the males and 40 per 
cent. of the females, and the results published without distinction 
of sex. The three attributes, with the relations of which we are 
here concerned, are death, treatment and male sex. The data show 
that more males were treated than females, and more females 
died than males ; therefore the first attribute is associated nega- 
tively, the second positively, with the third. It follows that there 
will be an illusory negative association between the first two— 
death and treatment. If the treatment were completely inefficient 
we would, in fact, have the following results :— 
Males. Females. Total. 
Treated and died . . . 4 24 48 
» and did not die . 6 16 72 
Not treated and died . : ; 36 42 
ry and did not die , i 4 38 
v.e. of the treated, only 48/120 =40 per cent. died, while of those 
not treated 42/80 =0525 per cent. died. If this result were stated 
without any reference to the fact of the mixture of the sexes, to 
the different proportions of the two that were treated and to the 
different déath-rates under normal treatment, then some value in 
the new treatment would appear to be suggested. To make 
a fair return, either the results for the two sexes should be 
stated separately, or the same proportion of the two sexes 
must receive the experimental treatment. Further, care would 
have to be taken in such a case to see that there was no 
selection (perhaps unconscious) of the less severe cases for treat- 
ment, thus introducing another source of fallacy (deat’ positively 
associated with severity, treatment negatively associated with 
severity, giving rise to illusory negative association between 
treatment and death). 
A misleading association between the characters of parent and 
offspring might similarly be created if the records for male-male 
and female-female lines of descent were mixed. Thus suppose 50 
per cent. of males and 10 per cent. of females exhibit some 
attribute for which there is no association in either line, then we 
would have for each line and for a mixed record of equal 
numbers— 
50