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         The discussion of the biserial and multiserial correlation
coefficient  was engendered by a question whose solution seems more
amenable to canonical discriminant analysis (4 groups and multivariate
normal variables) or possibly multinomial logistic regression if
the indenpendent variables (dependent in the discriminat formulation)
have arbitrary distributions.  However, the purpose of this note is
to point to where, for those interested in biserial correlation (usually
those interested in classical item analysis), one might find a useful
mathematical discussion of this historical statistic.  This is, of
course, the now classical text:

           Lord, Frederick & David Novick. Statistical Theories of
Mental Test Scores (with contributions by Allen Birnbaum).
Reading, Mass.: Addison-Wesley Publishing Co., 1968.

            The discussion may be found beginning on page 337 and
continuing to page 344. It is followed by a discussion of the
tetrachoric correlation coefficient.  The assumptions and the mathe-
matical derivation of both these statistics as well as their usefulness
is provided.

            For those who prefer a much simpler and more practical
story, then that other classical work (now little used in the age
of computers) gives a useful discussion of the 4 correlation
statistics beloved of test item developers: biserial r, point biserial r,
tetrachoric r, and the phi-coefficient.  The book, of course, is
J.P. Guilford. Psychometric Methods, New York: McGraw-Hill, 1954
(2nd Edition).  The pages of interest begin on page 427, although
the entire Chapter 13 on Test Development still has much of interest
even for those who live in the hypothetical (imaginary) world
of latent structure analysis.  Finally, if one looks at the formula
(including the suggested adjustments which appear in early issues
of Psychometrica) then it is an easy matter to determine how large
a value greater than one might be estimated.  However, such
arithmetical exercises have little to do with the usefulness in
this late stage of test theory development of the biserial r.
                                              Allen Herzog
                                              UIC - Chicago