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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