The effect of range restriction on one variable in a
bivariate normal distribution on the X-Y correlation
and the problem of estimating unrestricted from restricted
correlations has been widely studied for more
than half a century. The behavior of correction formulas
under truncation of both X and Y, however, remains
largely unresearched. The performance of the
correction formula for unidimensional truncation
(Thorndike, 1947, Case 2) and an approximation procedure
for correcting for bidimensional truncation proposed
by Wells and Fruchter (1970) were investigated.
The Thorndike correction formula undercorrects in
most circumstances. The Wells and Fruchter procedure
performs quite well under most conditions but often
results in a slight overcorrection. The performance of
the Wells and Fruchter and Thorndike formulas are
also compared under truncation on X or Y alone. In
these circumstances the Wells and Fruchter correction
is either equal or markedly superior to the traditional
correction. Based on overall performance in recapturing
the unbiased population values under both unidimensional
and bidimensional truncation, the Wells and
Fruchter correction is recommended as the preferred
procedure in many practical settings.
Alexander, Ralph A, Carson, Kenneth P, Alliger, George M & Barrett, Gerald V. (1984). Correction for restriction of range when both X and Y are truncated. Applied Psychological Measurement, 8, 231-241. doi:10.1177/014662168400800212
Alexander, Ralph A.; Carson, Kenneth P.; Alliger, George M.; Barrett, Gerald V..
Correction for restriction of range when both X and Y are truncated.
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