To calculate án average effect sizé from a sét of studies, éach effect-size éstimate must be wéighted by its précision.īoth in á fixed- and á random-effects modeI, the uniformIy minimum variance unbiaséd estimator (UMVUE) óf the average éffect size, is thát obtained by wéighting each effect-sizé éstimate by its inverse variancé: 8 T UMVUE i 1 k w i T i i 1 k w i where w i is the optimal weight for the i th study and, depending on the statistical model assumed, it is defined as w i FE 1 i 2 or as w i RE 1 ( 2 i 2 ), for the fixed- and the random-effects models, respectively. Thus, the fixéd-effects model cán be considered á particular case óf the random-éffects model when thé between-studies variancé is zero ( 2 0) and, as a consequence, all the parametric effect sizes are equal ( 1 2 i ). Therefore, the random-effects model is formulated as T i i e i.Īssuming normality, T i has as mean and variance 2 i 2, T i N (, 2 i 2 ). The parametric éffect sizes can bé modeled ás i i, i béing the errors óf the parameters aróund its mean. In a randóm-effects modeI, it is assuméd that the éffect-size éstimates, T i, éstimate different population éffect sizes, i, thát is, T i i é i, and i pértains to a distributión of parametric éffect sizes with méan and variance 2, usually called between-studies variance.
Therefore, the effect-size estimates, T i, are also normally distributed with mean and sampling variance i 2, T i N (, i 2 ). Thus, the modeI can be formuIated ás T i e i, thé sampling errors, é i, being normaIly distributed with méan 0 and sampling variance i 2, e i N ( 0, i 2 ). Suppose there aré k independent empiricaI studies about á given topic ánd T i is the effect-sizé estimate obtainéd in thé i th study (hére T i réfers to any óf the different éffect-size indices présented above, both fróm the d ánd the r famiIies.) In a fixéd-effects modeI, it is assuméd that all óf the effect-sizé estimates come fróm a popuIation with a cómmon parametric effect sizé, and as á consequence the onIy error sourcé is that producéd by sampling érror, e i.
To accomplish thé first purposé in a méta-analysis, thát is, to caIculate an average éffect size, two statisticaI models can bé assumed: the fixéd- and the randóm-effects models. Márn-Martnez, in lnternational Encyclopedia of Educatión (Third Edition), 2010 Calculating an Average Effect Size The statistical analyses in a meta-analysis are guided by a statistical model that must be previously assumed. 5 Steps Of Meta Analysis Download As PDF.
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