Standard errors of estimators that are functions
of correlation coefficients are shown to be quite different
in magnitude than standard errors of the initial
correlations. A general large-sample methodology,
based upon Taylor series expansions and
asymptotic correlational results, is developed for the
computation of such standard errors. Three exemplary
analyses are conducted on a correction for
attenuation, a correction for range restriction, and
an indirect effect in path analysis. Derived formulae
are consistent with several previously proposed
estimators and provide excellent approximations
to the standard errors obtained in computer
simulations, even for moderate sample size (n =
100). It is shown that functions of correlations can
be considerably more variable than product-moment
correlations. Additionally, appropriate hypothesis
tests are derived for these corrected coefficients
and the indirect effect. It is shown that in the
range restriction situation, the appropriate hypothesis
test based on the corrected coefficient is asymptotically
more powerful than the test utilizing the
uncorrected coefficient. Bias is also discussed as a
by-product of the methodology.
Bobko, Philip & Rieck, Angela. (1980). Large sample estimators for standard errors of functions of correlation coefficients. Applied Psychological Measurement, 4, 385-398. doi:10.1177/014662168000400309
Bobko, Philip; Rieck, Angela.
Large sample estimators for standard errors of functions of correlation coefficients.
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