So far this meta-analysis technique has corrected for one source of error,
sampling error. There are two other forms of error. The other two are measurement
error, and range restriction.
Measurement Error or Test reliability is
assessed by using the two reliabilities which apply to the study: rxx and ryy.
While you can correct the individual study statistics for range
variation, all too often this information is not available at the study
level. Hunter and Schmidt (Hunter et. al, 1982 and Hunter and Schmidt, 1990)
present a method of correcting the sample weighted mean effect size using
a distribution of reliability estimates. A distinct advantage to this method
is that it does not depend on using jus the studies directly involved in
the meta-analysis. Any study that assesses the pertinant reliability estimates
can be used to construct the reliability distribution.