This is a nice picture. I upload it from Cathera Hall 305.

Elliptical distribution and the dependent effect sizes

Synthesis of dependent effect sizes (such as the correlations) can conducted throgh a few methods (Gleser and Olkin, 1994; Raudenbush, Becker and Kalaian, 1988; Rosenthal and Rubin, 1986). And the corresponding variance-covariance between the dependent effect sizes can be computed by the formula developed by Steiger and the colleagues (1980; 1984). Asymptotically, the dependent effect sizes such as correlations is normally distributed. According Steiger etc.(1984) It is clear that the forth moments of multivariate distribution such as the dependent effect sizes (correlated random variables) will determine the asymptotic variance-covariance of correlations between the random variables. In our case the forth moments of the distribution of the multi-dependent-effect-size (correlations) will determine the asymptotic variance-covariance of the correlations between those dependent effect sizes which are correlations computed from previous studies. The components the are functionally related to the correlation matrix of the multivariate distribution and the kurtosis parameter defined as following.

Understanding the functional relationship between the forth moment and the correlation matrix of the multivariate distribution. And the relationship was defined as above. So far I think we need to understand the definition of elliptical distribution. The followings are some links about its definition and applications. http://www.quantlet.com/mdstat/scripts/mva/htmlbook/mvahtmlnode42.html http://www.math.ethz.ch/~mcneil/ftp/KendallsTau.pdf http://kups.ub.uni-koeln.de/volltexte/2004/1319/pdf/frahm.pdf