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THE AMERICAN NATURALIST [Vol. XL V 



deviations and the coefficient of correlation found in the usual 

 way. 



But it is possible to find the correct coefficient of correlation 

 from ordinary tables, and with much less labor than by either 

 the use of symmetrical tables or by the method given by Pearl. 

 To see how this ran be dune, it is well to examine a symmetrical 

 table prepared for computation of the coefficient of correlation, 

 such as is given in Table I. Here the large figures give the 

 frequencies, while the subscripts in smaller type give the prod- 

 ucts of the deviations from the approximate mean 057). There 

 are two main points to be considered: (1) How the quantity 



S(xy) is to be correctly obtained; (2) how the mean and stan- 

 dard deviation are to be correctly obtained. 



1. With regard to the first point, it will be observed that such 

 a table is divisible by a diagonal passing from the upper left- 

 hand corner to the lower right-hand corner into two halves which 

 are in all respects duplicates as regards both frequencies and 

 deviation products. (The frequencies through which the diag- 

 onal line passes are to be divided evenly between the two halves.) 

 It is evident, therefore, that if we use only one of these halves 



