J. A. Harris 
449 
II. Statement and Illustration of Problems. 
Problem I. To form Direct or Cross Intra-class or Inter-class Correlation or 
Contingency Tables when the Number of Possible Combinations is Large. 
A method for the rapid formation of the complete direct intra-class table 
has been described and illustrated elsewhere*. The method of dealing with 
both direct and cross intra-class correlations by means of condensed tables has 
also been indicated^. Both direct and cross inter-class correlation tables (full 
or condensed) are formed by the same method, but more simply since the 
entries are 8 (pq), not S [n .(n — 1)], and the tables as first formed can be used 
without reduction. The method of dealing with fractional inter-class correlation 
tables will be illustrated as a check under Problem V. 
Problem II. To Determine the Correlation between a Character and an 
Array of Associated Characters. 
This serves chiefly as a simple introduction to the more complex cases to be 
described presently. One wishes often to correlate between a first measure and 
an arra}' of associated measures}. Tables may be difficult to form or cumber- 
some, while moments of the arrays of measurements around 0 as origin, 2 (y) 
and 2 (y'-), may be wanted for other purposes, or, if not, are at least quickly 
calculated. Then, by the use of a machine for simultaneous multiplication and 
addition, we get for the rough moment coefficients 
8 (nx')IS (») = vx = m x , S (nx'*)/S (») = p m " (ii), 
8 (y')/8 (to) = V - m y , S$ (y'*)/8 (») = v y " (iii), 
and for the rough product moment coefficients 
S{x'[t(y')]}/S(n) (iv), 
where n is the number of y measurements associated with any x, N = S(n) is 
the number of measurements in all arrays or classes, S denotes a summation 
within the class, and S a summation of classes for the whole population. From 
this point the work is straightforward by (i), i.e. 
r j[4S(/)PH M)> [ 
The particular advantages of this method of calculating correlation are seen in 
cases where : («) the class moments have already been calculated for other 
* Harris, J. Arthur, " On the Formation of Correlation and Contingency Tables when the Number 
of Combinations is large," American Naturalist, Vol. xlv. pp. 566 — 571, 1911. 
t Harris, J. Arthur, "The Formation of Condensed Correlation Tables when the Number of 
Combinations is large," American Naturalist, Vol. xlvi. pp. 477 — 486, 19T2. 
J A single parent may produce a score or a hundred offspring. Or, one may desire to know the 
relationship between the weight of the seed planted and the weight of the seeds produced, or between 
the number of pods per plant aud the number of ovules and seeds produced per pod. 
