XVIL—SIMPLER CASES OF SAMPLING FOR VARIABLES. 345 
the two standard errors, viz. 126, assumes almost exactly the theo- 
retical magnitude. In the case of the asymmetrical distribution of 
rates of pauperism, also used as an illustration in § 6, the standard 
error of the median was found to be 00655 per cent. The 
standard error of the mean is only 0:0493 per cent., which bears 
to the standard error of the median a ratio of 1 to 1°33. As 
such cases as these seem on the whole to be the more common 
and typical, we stated in Chap. VII. § 18 that the mean is in 
general less affected than the median by errors of sampling. At 
the same time we also indicated the exceptional cases in which 
the median might be the more stable—cases in which the mean 
might, for example, be affected considerably by small groups of 
widely outlying observations, or in which the frequency-distri- 
bution assumed a form resembling fig. 53, but even more 
exaggerated as regards the height of the central “peak ” and the 
relative length of the “tails.” Such distributions are not un- 
common in some economic statistics, and they might be expected 
to characterise some forms of experimental error. If, in these 
cases, the greater stability of the median is sufficiently marked 
to outweigh its disadvantages in other respects, the median 
may be the better form of average to use. Fig. 53 represents 
a distribution in which the standard errors of the mean and of the 
median are the same. Further, in some experimental cases it is 
conceivable that the median may be less affected by definite 
experimental errors, the average of which does not tend to be 
zero, than is the mean, —this is, of course, a point quite distinct 
from that of errors of sampling. 
12. If two quite independent samples of n, and n, observations 
respectively be drawn from a record, evidently €,5 the standard 
error of the difference of their means is given by 
Lio) 
€la = s + 2) (5) 
If an observed difference exceed three times the value of €19 
given by this formula it can hardly be ascribed to fluctuations 
of sampling. If, in a practical case, the value of o is not known 
a priory, we must substitute an observed value, and it would seem 
natural to take as this value the standard-deviation in the two 
samples thrown together. If, however, the standard-deviations 
of the two samples themselves differ more than can be accounted 
for on the basis of fluctuations of sampling alone (see below, § 15), 
we evidently cannot assume that both samples have been drawn 
from the same record: the one sample must have been drawn 
from a record or a universe exhibiting a greater standard-deviation 
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