CHAPTER 4 



THE BIOMETRICAL ANALYSIS 



AMit'we Scales Constitution of the Statistics The Test of Dominance and Linkable 

 Randomly Breeding Populations and Correlations between Relatives 

 Effective Factors or Units The Union of Genetics and Biometry 



The knowledge that the polygenes are borne on the chromo- 

 somes provides us with a base from which to explore the genetical 

 properties of continuous variation. We cannot follow these genes 

 in their individual segregations by the mendelian method; we can 

 nevertheless feel confident that they will segregate on mendelian 

 principles. That is to say, the various types of family, raised by 

 crossing and inbreeding, will contain the different homozygotes and 

 heterozygotes in the proportions which mendelian experiments and 

 a knowledge of chromosome numbers have led us to expect. 



Before we turn, however, to the interpretation of the biometrical 

 quantities, means, variances and covariances, in terms of mendelian 

 segregations, we must first consider one other problem. This is the 

 problem of the scale to be used in measuring or representing the 

 degree of expression of the character. This problem does not arise 

 with the mendelian method where we compare the frequencies of 

 distinct types, but it is basic to all biometrical analysis, where we 

 compare the magnitudes of individual expressions. An appropriate 

 scale will go far to ensure the success of an analysis: an inappropriate 

 scale may lead to serious misjudgment. 



The scales that we use in measuring character expression are the 

 ones which experience has shown to be most convenient. They do 

 not bear any necessary relation to the ways in which genes act or 

 supplement one another in action. They may be satisfactory for the 

 purpose of genetic analysis or they may not. We need, in fact, some 

 way of deciding whether a given scale, be it the one we customarily 

 use for measuring length, weight or any other property, or be it 

 some transformation of the customary scale, as for example into log 

 measure, is satisfactory for our purpose. 



Our task is that of interpreting tiie means, variances and 



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