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Fig. 3. | BMC Biology

Fig. 3.

From: Meta-evaluation of meta-analysis: ten appraisal questions for biologists

Fig. 3.

Common sources of non-independence in biological meta-analyses. ad Hypothetical examples of the four most common scenarios of non-independence (a-d). Orange lines and arrows indicate correlations between effect sizes. Effect size estimate (gray boxes, ‘ES’) is the ratio of (or difference between) the means of two groups (control versus treatment). Scenarios a, b, and d may apply to other types of effect sizes (e.g., correlation), while scenario c is unique to situations where two or more groups are compared to one control group. a Multiple effect sizes can be calculated from a single study. Effect sizes in study 3 are not independent of each other because effects (ES3 and ES4) are derived from two experiments using samples from the same population. For example, a study exposed females and males to increased temperatures, and the results are reported separately for the two sexes. b Effect sizes taken from the same study (study 3) are derived from different traits measured from the same subjects, resulting in correlations among these effect sizes. For example, body mass and body length are both indicators of body size, with studies 1 and 2 reporting just one of these measurements and study 3 reporting both for the same group of individuals. c Effect sizes can be correlated via contrast with a common ‘control’ group of individuals; for example, both effect sizes from study 3 share a common control treatment. A study may, for example, compare a balanced diet (control) with two levels of a protein-enriched diet. d In a multi-species study effect sizes can be correlated when they are based on data from organisms from the same taxonomic unit, due to evolutionary history. Effect sizes taken from studies 3 and 4 are not independent, because these studies were performed on the same species (Sp.3). Additionally, all species share a phylogenetic history, and thus all effect sizes can be correlated with one another in accordance with time since evolutionary divergence between species

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