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--- faq [2019/11/21 10:12] – external edit 127.0.0.1
+++ faq [2020/06/03 23:54] – Wolfgang Viechtbauer
@@ Line 33: / Line 33: @@
 Similar (and much more thorough/extensive) tests have been conducted for the more intricate methods in the package.
-It may also be useful to note that there is now an appreciable user base of the metafor package (the [[http://www.jstatsoft.org/v36/i03/|Viechtbauer (2010)]] article describing the package [[http://scholar.google.nl/scholar?oi=bibs&hl=en&cites=8753688964455559681|has been cited in over 5000 articles]], many of which are applied meta-analyses and/or methodological/statistical papers that have used the metafor package as part of the research). This increases the chances that any bugs would be detected, reported, and corrected.
+It may also be useful to note that there is now an appreciable user base of the metafor package (the [[https://www.jstatsoft.org/v36/i03/|Viechtbauer (2010)]] article describing the package [[http://scholar.google.nl/scholar?oi=bibs&hl=en&cites=8753688964455559681|has been cited in over 5000 articles]], many of which are applied meta-analyses and/or methodological/statistical papers that have used the metafor package as part of the research). This increases the chances that any bugs would be detected, reported, and corrected.
 Finally, I have become very proficient at hitting the [[https://xkcd.com/323/|Ballmer Peak]].
@@ Line 63: / Line 63: @@
 ??? How are $I^2$ and $H^2$ computed in the metafor package?
-!!! For random-effects models, the $I^2$ statistic is computed with $$I^2 = 100\% \times \frac{\hat{\tau}^2}{\hat{\tau}^2 + \tilde{v}},$$ where $\hat{\tau}^2$ is the estimated value of $\tau^2$ and $$\tilde{v} = \frac{(k-1) \sum w_i}{(\sum w_i)^2 - \sum w_i^2},$$ where $w_i$ is the inverse of the sampling variance of the $i$th study ($\tilde{v}$ is equation 9 in Higgins & Thompson, 2002, and can be regarded as the 'typical' within-study variance of the observed effect sizes or outcomes). The $H^2$ statistic is computed with $$H^2 = \frac{\hat{\tau}^2 + \tilde{v}}{\tilde{v}}.$$ Analogous equations are used for mixed-effects models.
+!!! For random-effects models, the $I^2$ statistic is computed with $$I^2 = 100\% \times \frac{\hat{\tau}^2}{\hat{\tau}^2 + \tilde{v}},$$ where $\hat{\tau}^2$ is the estimated value of $\tau^2$ and $$\tilde{v} = \frac{(k-1) \sum w_i}{(\sum w_i)^2 - \sum w_i^2},$$ where $w_i = 1 / v_i$ is the inverse of the sampling variance of the $i$th study ($\tilde{v}$ is equation 9 in Higgins & Thompson, 2002, and can be regarded as the 'typical' within-study variance of the observed effect sizes or outcomes). The $H^2$ statistic is computed with $$H^2 = \frac{\hat{\tau}^2 + \tilde{v}}{\tilde{v}}.$$ Analogous equations are used for mixed-effects models.
 Therefore, depending on the estimator of $\tau^2$ used, the values of $I^2$ and $H^2$ will change. For random-effects models, $I^2$ and $H^2$ are often computed in practice with $I^2 = 100\% \times (Q-(k-1))/Q$ and $H^2 = Q/(k-1)$, where $Q$ denotes the statistic for the test of heterogeneity and $k$ the number of studies (i.e., observed effects or outcomes) included in the meta-analysis. The equations used in the metafor package to compute these statistics are based on more general definitions and have the advantage that the values of $I^2$ and $H^2$ will be consistent with the estimated value of $\tau^2$ (i.e., if $\hat{\tau}^2 = 0$, then $I^2 = 0$ and $H^2 = 1$ and if $\hat{\tau}^2 > 0$, then $I^2 > 0$ and $H^2 > 1$).