SHORTER ARTICLES AND DISCUSSION 



COMPUTING CORRELATION IN CASES WHERE SYM- 

 METRICAL TABLES ARE COMMONLY USED 



In studying the assortative mating of Paramecium I have 

 found occasion to compute the correlation in many cases for 

 which double or symmetrical tables lire commonly employed. 

 I have found thai in such cases the use of symmetrical tables 

 is quite unnecessary and the computations can be performed 

 with much less labor without them. It will, therefore, be worth 

 while to show how the use of symmetrical tables can be avoided. 



When the two objects to be compared are alike, as when the 

 two members, .1 and B, of conjugating pairs are examined, 

 evidently either .1 or B might be entered in either the horizontal 

 rows or the vertical columns of the correlation table. In such 

 cases, the mean computed from the rows, and that computed 

 from the columns are likely to differ, depending on which indi- 

 viduals were entered in the rows, which in the columns. If, for 

 example, the larger individual is always entered in the vertical 

 columns, the smaller in the horizontal rows, as in Table II, then 

 the means and standard deviations of the two sets will differ 

 much. As a result the coefficient of correlation computed in 

 the usual way will show varying values, depending on how the 

 pairs are entered in the table. From the collection shown in 

 Table II we can by varying the method of entering the pairs 

 get coefficients of correlation varying from 0.132 to 0.523. 



Under such conditions Pearson (1901), Pearl (1907) and 

 others enter each pair twice, once in the rows, once in the col- 

 umns. This gives a "symmetrical" table, in which the sums 

 of either the rows or the columns include all the individuals. 

 This method is theoretically correct, since each individual func- 

 tions both as "principal" and as "mate"; the coefficient of 

 correlation computed from such symmetrical tables is the cor- 

 rect one. But such symmetrical tables are cumbersome and 

 involve much labor. Pearl (1907) gives a formula by which the 

 same coefficient can be obtained without making symmetrical 

 tables, by computations involving the two means and standard 



