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One of the difficulties encountered by the newcomer to statistics is the use of
a wide variety of terms for correlation coefficients. There are many
measures of association between variables; here we confine ourselves to the
parametric statistics computed by normal theory. These statistics correspond most
naturally to our genetic theory, in which we assume that a large
number of independent genetic and environmental factors give rise to
variation  ``multifactorial inheritance"^{}.
Table 2.2 shows the name given to the correlation
coefficient calculated under normal distribution theory, according to
whether each variable has:
two categories (dichotomous);
several categories (polychotomous);
or an infinite number of categories (continuous).
If both variables are dichotomous, then the correlation
is called a tetrachoric correlation
as long as it is
calculated using the bivariate normal integration approach described
in Section 2.3 above. If we simply use the Pearson product
moment
formula
(described in Section 2.2.1 above) then we have
computed a phicoefficient which will probably underestimate the
population correlation in liability. Because the tetrachoric and polychoric
are
calculated with the same method, some authors refer to the tetrachoric as a
polychoric, and the same is true of the use of
polyserial
instead
of biserial.
As we shall see,
the theory behind all these statistics is essentially the same.
Table 2.2:
Classification of correlations according to their observed
distribution.

Two 
Three or more 

Measurement 
Categories 
Categories 
Continuous 
Two 
Tetrachoric 
Polychoric 
Biserial 
Three or more 
Polychoric 
Polychoric 
Polyserial 
Continuous 
Biserial 
Polyserial 
Product Moment 
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Jeff Lessem
20020321