No. 548] CONDENSED CORRELATION TABLES 479 



is to write the values of the first character under consid- 

 eration — designated for convenience as the subject — 

 down the side of a separate sheet for each class. Oppo- 

 site each entry is then written n, %{of) and 2(:r' 2 ), p, 

 and 2(i/' 2 ), q, %{z f ) and 2(s' 2 ) and so on, according to the 

 relationships desired. Thus, the measure used as the 

 subject and the number and summed first and second 

 powers of deviation of the individuals of the relative 

 array may be for the same or different characters or 

 classes, depending on whether direct or cross, intra-class 

 or inter-class correlation is to be computed. In any case, 

 the number and moments are only once determined for 

 each class — their repeated entry on the sheet is merely 

 rapid clerical work. 



This done, the sheets are clipped into strips by subject 

 entries, the strips seriated according to the subject, and 

 the class numbers and moments summed for each grade 

 on the machine. 



For inter-class correlations, the resulting table is cor- 

 rect, embracing as it does, say, S(pq) entries. For intra- 

 class relationships, say for x, the entries are too high by 

 S(n), Six') and S{x' 2 ) since it comprises S(n 2 ) entries 

 when only Sn(n-l) are desired. Hence, the actual fre- 

 quency for each subject grade must be subtracted from 

 the weighted frequency, and the products of the actual 

 frequency by the grade and by the square of the grade 

 must be deducted from the first and second summed 

 moment column, respectively. 



When the number of individuals per class, w, p, q, is 

 large (e. g., 25 or over) another procedure is desirable. 

 The classes of the subject character are seriated (in 

 transverse rows) in a table of vertical columns captioned 

 by the grades. Opposite each row is entered n,2(af) and 

 and and 5(3"), ■ for all 



characters to be correlated. The associated (weighted) 

 values for each subject grade are quickly gathered by 

 multiplying up and summing simultaneously the fre- 



