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There are two types of Quantitative Review procedures. One type involves the
combination of probability values or Z scores. The procedures for
this method was developed in parallel during the 30's by Cochran (1937),
Fisher (1932), Pearson (1933) and Tippett (1931). These procedures were
developed to address the need in agricultural research to combine the results
of a number of independent tests, all of which were planned to test a common
hypothesis. An alternative approach was also developed by Fisher in 1932,
the r to Z transformation.
The demands of World War II served to assist in the development of combinatorial
procedures. In their landmark study on the American soldier, Stouffer and
colleagues during the 1940's developed a probability combination method.
A more recent version of the combinatorial procedure is Winer's (1971) method
of combining independent t tests.The other type of meta-analysis
is the accumulation of effect sizes, correlation coefficients or to Cohen's d statistic.
Thorndike (1933) was among the earlier researchers to accumulate results
across studies using an average correlation. He also corrected the observed
variance of results across studies for sampling error (unreliability). The
intent of this procedure was to integrate differing research on intelligence.
While procedures for averaging correlations were available since the 1930's,
as noted above, and were discussed in various behavioral statistics texts
(cf. McNemar, 1969), these procedures generally involved the use of Fisher's
r to Z transformation, or were generally not used. Unfortunately no guidelines
existed that allowed for a "dimensionless" statistic which could be used
as a rubric or common statistic which would be independent of any specific
measurement unit. Cohen (1977) developed one such statistic now in common
use, the effect size statistic, or d. it was originally developed for use
in statistical power analysis and to estimate the optimal sample size for
a study.
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