CHAPTER II. 
THE STATISTICAL METHODS EMPLOYED. 
All measurements are accompanied by unavoidable errors. 
Thus the attempt to measure the height of a man is influenced 
by the accuracy with which the measuring apparatus is con- 
structed, the care with which it is used, the position of the 
man’s head on the vertebral column, the thickness of the 
interveitebral disks and a multitude of other factors. Some 
of these influences would make the observed height greater 
than the true height, others would make it less. The one 
group tends to counteract or compensate the other, and the 
result of their conflict is the measurement actually observed. 
The observed height therefore is never, except by chance, the 
real height, but deviates from it in one or the other direction — 
is now above and now below the truth —as one or the other 
group of influences gets the upper hand. The greater the 
number of influences, the more perfectly does compensation 
take place and the more nearly does the observed result 
approach the truth. But the truth itself can never be known, 
for only when the number of influences is infinite, can the 
probability of perfect compensation between them rise to a 
certainty. That which we call true is merely the probable 
truth and is worthy of confidence in exact proportion to its 
numerical probability. 
The influences which affect a measurement are of two sorts, 
the one accidental and varying, such as, taking the measure- 
ment of height for an example, the degree of inclination of 
the head tothe axis of the body, the placing of the measuring- 
rod and the like, the other constant and unvarying, such as an 
inaccuracy in the construction of the measuring-rod or a per- 
sistent bias in the mind of the observer. In both classes, the 
degree of compensation varies with the number of influences, 
for even a constant cause, although not accidental in its nature 
and found always on one side of the mean, may be compen- 
sated by another constant cause on the opposite side of the 
5) 
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