Metamean

Metamean is a term used in statistics to denote the pooled mean across multiple studies in a meta-analysis, reflecting the central tendency of a measured outcome across the included research. While not universally standardized, metamean is often understood as the estimate obtained by combining study-level means with weights that reflect the precision or size of each study.

For a fixed-effect model, let mean_i be the observed mean in study i and SE_i its standard error. The metamean is computed as sum(w_i * mean_i) / sum(w_i), where w_i = 1 / SE_i^2. If SE_i is not directly reported, SE_i can be approximated as SD_i / sqrt(n_i). In a random-effects model, between-study heterogeneity tau^2 is added to the variance, and weights become w_i = 1 / (SE_i^2 + tau^2). Tau^2 can be estimated via methods such as DerSimonian-Laird or REML.

In settings with equal measurement scales and approximately equal variances, researchers may use simple inverse-variance weights or even sample-size weights w_i = n_i, which approximate the inverse-variance approach when SDs are similar.

Metamean is used to summarize outcomes across clinical trials, behavioral experiments, or other studies to support evidence-based conclusions about a treatment effect or intervention.

Interpretation depends on the comparability of studies; heterogeneity in populations, outcomes, or measurement tools can bias the metamean. Publication bias, selective reporting, and dependencies among studies can also distort estimates. Data harmonization and sensitivity analyses are important.

Related concepts include meta-analysis, fixed-effect models, and random-effects models.

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