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Several STAT-L'ers  asked for the reference on multiserial correlation. Here it
is with some additional information that may be helpful.



The point biserial correlation is a special case formula of the Pearson
correlation when one of the variables is a dichotomy.  This formula was
generalized to the point multiserial correlation, Das Gupta, S. "Point biserial
correlation coefficient and its generalization", Psychometrika, 1960, 25:393-
408.  The biserial correlation is likewise a correlation between a continuous
variable and a dichotomous variable, but the dichotomous variable is assumed
to have an underlying normal distribution.  This too has been generalized
to the multiserial correlation, Jasper, N. "Serial Correlation", Psychometrika,
1946, 11:23-30.  There is also a generalization of eta to this case, Wherby, R.
J. and Taylor, E.K. "The relation of multiserial eta to other measures of
correlation", Psychometrika, 1946:155-161.

Since there is no difference in end result between the biserial and the
Pearson correlation, it has always seemed strange to me that the point biserial
formula persists, but it does.  The biserial and its generalization are
another matter, definite differences exist.  For example it is possible that
the biserial correlation can be greater than 1.  A correlation of 5.6 gives
some a pause.

Biserial and point biserial correlations find one of their most common uses in
item analysis in classical test theory.  You can thus find more about them in
texts on statistics and measurement in education and psychology.  For example
see GLass, G.V. and Hopkins K.S. "Statistical Methods in Education and
Psychology" Prentice Hall, 1984.

I would appreciate knowing in what contexts some of you are using these.

john neel
Department of Educational Foundations
Georgia State University