CHAPTER III 
THE STATISTICAL STUDY OF VARIATION 
In the present chapter we shall consider the application of purely 
statistical methods in the analysis of biological phenomena especially the 
phenomena of variation. The treatment given here does not pretend to 
be exhaustive or rigorous, but it presents the commonly used method 
of recognized biometricians, from several of whom valuable suggestions 
have been received. We shall have occasion to refer to the utilization 
of statistics in the study of heredity by the “biometrical school,” but 
the application of statistical methods in the analysis of specific genetic 
problems will be deferred until later chapters. 
Causes of Fluctuations.—Continuous variations, or the slight differ- 
ences normally found in organisms, are generally referred to as fluctuating 
variations or fluctuations. It is frequently assumed that “fluctuating 
variability’ is due entirely to differences in environment. But, as was 
stated in the preceding chapter, either the modifications in development 
due to environment, or individual differences which are caused by seg- 
regation and recombination of genetic factors, may display the normal 
curve of variation when examined statistically. Hence fluctuations 
may be due to either of two causes and before conclusions may be drawn 
from the study of frequency distributions and statistical constants, the 
causes of the variations studied must be clearly differentiated. The only 
way to accomplish this is to make one set of conditions or the other as 
uniform as possible. If the object be to examine modifications, only 
pedigree material should be used and, on the other hand, if variations due 
to recombinations are to be considered, the environmental conditions 
must be as uniform as possible or else due account must be taken of exist- 
ing irregularities. Certain technical requisites to the biometrical method 
will be mentioned later. This difference in the nature of fluctuating 
variations according to their cause is of such fundamental importance 
that it should be clearly understood at the outset. 
Law of Statistical Regularity—This fundamental principle, which 
is also known as the law of probability or law of chance, may be most 
simply introduced by means of an illustration. Suppose two persons, 
blindfolded, were each to pick about 500 beans from a bag containing a 
million beans of any standard variety. The average weights of the beans 
picked out by the two persons would be almost identical even though the 
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