No. 595] 



LINKAGE INTENSITIES 



417 



eral classes are determined and S[(o — c) 2 /c] = x 2 calcu- 

 lated, S indicating summation. 



With n, the number of classes, here equaling four, and 

 x 2 , the probability, P, that departures from the calculated 

 series as great as those observed might occur through 

 the errors of random sampling, is obtained by reference 

 to Elderton's (1901) table (see also Pearson, 1914). 

 Wherever appreciably different gametic ratios have been 

 obtained by the two methods, P has been found to be 

 greater for the association-coefficient method than for the 

 method based on formulae II. The former method has, 

 therefore, given the closer fit. Since, in most of the oases 

 to which the test has been applied, x 2 is less than one and 

 since such values are not listed in Elderton's table, x 2 has 

 been used directly for the comparison of the two methods. 

 Where n is constant, the larger x 2 the less the probability. 



While this test for goodness of fit has shown the asso- 

 ciation-coefficient method to be the better of the two, the 

 fact that in most cases x 2 was less than one for both meth- 

 ods indicates that the approximate method suggested here 

 ordinarily gives results such that the departures of ob- 

 served from calculated frequencies might well be due to 

 errors of random sampling. The method has been found 

 convenient and usually sufficiently accurate where only an 

 approximate determination of the gametic ratio is de- 

 sired. Where the observed frequencies depart widely 

 from the form given by formula I, this method should not 

 be used. It should be noted, however, that in such cases 

 no calculated series fits the observed results well. This 

 limitation to the use of the new method does not lessen 

 materially the convenience of using it where it is appli- 

 cable. By a mere inspection of the observed frequencies, 

 it can usually be told whether they conform fairly closely 

 to formula I, that is, whether the first term is approxi- 

 mately equal to the sum of the second and third plus three 

 times the fourth. 



A few examples will illustrate the use of the approxi- 

 mate method of calculating gametic ratios from observed 



