FURTHER SUPPLEMENTARY TABLES FOR DE- 
TERMINING HIGH CORRELATIONS FROM 
TETRACHORIC GROUPINGS. 
By ALICE LEE, D.Sc. 
The difficulty of determining correlations between -80 and 1-00 by the tetra- 
choric method, owing to the slow convergency of the terms of the fundamental 
equation for 'tetrachoric /•' has long been recognised. In 1912 Everitt* pubhshed 
" Supplementary Tables for Determining High Correlations from Tetrachoric 
Groupings." These tables much simplified the work within the field in which it is 
really possible to determine accurately a high correlation — beyond certain values 
of 'h and k' such determination is impossible owing to the influence of random 
sampling on a quadrant category which in most practical cases will only contain 
an isolated unit or two. Everitt's tables covered the values of /• from + -80 to 
+ 1-00 for values of the dichotomic planes given by h and k varying from + -0 
to + 2-6. They admitted at once of our dealing with those cases of negative values 
of r, for which either h or k was negative, but not with cases in which r was 
negative and both h and k remained of the same sign. The present tables provide 
for this omitted portion of the possible field and thus complete Everitt's work. 
I have followed his method of quadrature in evaluating my integrals. But 
I have preserved more decimal places than he has done, partly because my 
significant figures are thrown into higher decimal places than his by the nature 
of the case, and partly because recent experience in other fields has shown workers 
in the Biometric Laboratory, that tables are often of service for purposes other 
than those for which they were originally calculated, and that it is worth while 
preserving every reliable figure. I think my results are always correct to six 
figures and generally to the actual number tabulated. While many of the entries 
would only be of service in the case of total populations approaching the magnitude 
of census populations, their indication of the high decimal place in which the 
first significant figure can occur in the 'd' quadrant, Avill help to dispel the illusion 
that absence of frequency in a quadrant is necessarily indicative of absolute 
association, when the table is based on a limited sample. A further reason for 
the number of figures I have preserved may be found in what I believe to be one 
of the principal uses of tables of this type. They are not only valuable for the 
calculation of the correlation in the case of given data, but also in many theoretical 
investigations where the correlation is supposed known a priori and we require 
* Biomelriku, Vol. viii. p. 385. 
