Miscellanea 
217 
In fact I believe tliat in the ease of integral variates the calculation with formula (i) will 
be considerably more rapid than the conventional product moment method. 
A further saving of time can be effected by doing away with the necessity for copying 
the entries from the correlation table into difference colunnis. This can be made clear by 
an illustration. 
Illitstration II. Calculation of correlation from non-symmetrical tables. Pearl's table for 
his Series V of Ceratophyllum*, showing correlation between the position on the branch and 
the number of leaves per whorl, is given below with the differences between the two variates 
indicated above each entry as small indices. These can be entered on a table— preferably in red 
TABLE II. 
Whorl's of Leaves in Oeratopliyllum. 
Position of Whorl on Branch. 
1 
3 
4 
5 
6' 
8 
9 
10 
Totals 
2^ 
_-i 
4 
11* 
1- 
21 
1-1 
I--' 
27 
0 
16'' 
6^ 
103 
11 
1" 
36 
40'i 
29s 
18^ 
143 
9'^ 
11 
2" 
4-1 
1-^ 
118 
8 
19" 
28'' 
2.5« 
17^ 
8-' 
3' 
3-1 
1-2 
111 
9 
58 
207 
19« 
22* 
173 
132 
61 
4" 
5-1 
137 
10 
7'-' 
58 
6-^ 
10* 
83 
142 
41 
3" 
67 
11 
110 
s 
7 
0 
6 
4 
3 
1 
1 
Totals 
107 
95 
79 
64 
46 
37 
27 
25 
12 
501 
ink or pencil to avoid confusion — much more quickly than the products of the deviations of the 
two variables from their assumed origins, and with much less chance of error, especially in the 
case of large tables. The work can be most rapidly done by taking first the diagonal cell 
and then the diagonal rows lying on either side of it. All the entries of any diagonal row 
will have the same index, but it should be put down in every case to avoid confusion. All 
that now remains to be done is to sum these diagonal colunnis and calculate the second moment. 
For this r can be at once calculated from formula (i) above. 
From our illustrative table wo have for the sums of the diagonal rows : — 
-i 
0 
1 
2 
3 
4 
8 
9 
10 
Total 
Frequency ... 
4 
13 
10 
17 
47 
64 
90 
102 
91 
45 
10 
7 
1 
501 
Note that a check for the accuracy of the work is furnished by the identity of the total with 
the N of the population. In the product moment method there is no convenient check for the 
accuracy of the multiplications leading to the S (.ly). In the present case we find 
S. D. Position =2-3733, 
S. D. Leaves =1-4003, 
S. D.2 Difference = 4-4380, 
r = -475, 
agreeing with the value given liy Pearl. 
* Pub. 58, Carner/ie Iimtitutioii of Washington, p. 0(1, Table 31, 1907. 
Bionietrika vii 28 
