The standard error of correlations that have been
adjusted for selection with commonly used formulas
developed by Pearson (1903) was investigated. The
major purposes of the study were (1) to provide large-sample
approximations of the standard error of a correlation
adjusted using the Pearson-Lawley three-variable
correction formula; (2) to examine the standard errors
of adjusted correlations under specific conditions;
and (3) to compare various estimates of the standard
errors under direct and indirect selection. Two theory-based
large-sample estimates of the standard error of a
correlation adjusted for indirect selection were developed
using the delta method. These two estimates
were compared to one another, to a bootstrap estimate,
and to an empirical standard deviation of a series
of adjusted correlations generated in a simulation
study. The simulation study manipulated factors defined
by sample size, selection ratio, underlying population
distribution, and population correlations in situations
that satisfied the basic assumptions of the
Pearson-Lawley procedures. The results indicated that
the large-sample and bootstrap estimates were very
similar when the sample size was 500 and, in most
cases, the simpler of the two large-sample approximations
appears to offer a reasonable estimate of the
standard error of an adjusted correlation without resorting
to complex, computer-intensive approaches.
Index terms: correlation coefficients, missing data,
Pearson-Lawley corrections, selection, standard errors
of correlations, validity studies.
Allen, Nancy L & Dunbar, Stephen B. (1990). Standard errors of correlations adjusted for incidental selection. Applied Psychological Measurement, 14, 83-94. doi:10.1177/014662169001400109
Allen, Nancy L.; Dunbar, Stephen B..
Standard errors of correlations adjusted for incidental selection.
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