Samples (x, y), taken from a bivariate normal distribution with correlation, p, can be allocated to one of the cells of a 2 X 2 contingency table according to whether x t xo or x > xO and whether y yo, where xo and yo are cut-off values. Such a contingency table is shown in Table 1, where a is the number of samples for which x > xo and y > yO, and Si is the proportion of samples for which x > xo. The tetrachoric correlation coefficient, r, is obtained from a 2 x 2 contingency table and provides an estimate of the underlying correlation, p. Everitt (1910) tabulated the parameters of a kth-order polynomial in r for k 6 and gave details of the parameters for 7 24; to obviate this, additional tables for use when r 2 0.8 were given by Everitt (1912). These tables are also given in the compilation by Pearson (1914), where they cover 16 pages. Clearly, this method of calculating r is cumbersome, and Brown (1977) has given an algorithm for finding the tetrachoric correlation; thus the original laborious method is replaced by a computer program.
[1]
R. Curnow,et al.
Multifactorial Models for Familial Diseases in Man
,
1975
.
[2]
G. Yule.
On the Methods of Measuring Association between Two Attributes
,
1912
.
[3]
Morton B. Brown.
Algorithm AS 116: The Tetrachoric Correlation and its Asymptotic Standard Error
,
1977
.
[4]
Stephen E. Fienberg,et al.
Discrete Multivariate Analysis: Theory and Practice
,
1976
.
[5]
John P. Rice,et al.
An Approximation to the Multivariate Normal Integral: Its Application to Multifactorial Qualitative Traits
,
1979
.
[6]
P. F. Everitt,et al.
TABLES OF THE TETRACHORIC FUNCTIONS FOR FOURFOLD CORRELATION TABLES
,
1910
.