後設分析 (Meta-Analysis) 後設分析
Released已發布Apply meta-analysis to synthesize effect sizes across multiple studies, assess heterogeneity, and evaluate publication bias. Use this skill when the user needs to combine findings from prior research, compare fixed-effect vs random-effects models, compute pooled effect sizes, or when they ask 'what does the overall evidence say', 'how do I combine results across studies', or 'is there publication bias'.
學術研究技能：後設分析 (Meta-Analysis) 分析與應用。
Overview概述
Meta-analysis statistically combines effect sizes from multiple independent studies to produce a pooled estimate with greater precision and generalizability. It quantifies between-study heterogeneity and tests for publication bias, providing a rigorous evidence synthesis that goes beyond narrative literature reviews.
When to Use使用時機
- Synthesizing quantitative findings from multiple studies on the same research question
- Resolving conflicting results across studies
- Estimating an overall effect size with tighter confidence intervals
- Identifying moderators that explain heterogeneity across studies
When NOT to Use不適用時機
- Studies are too heterogeneous in constructs, measures, or populations to combine meaningfully
- Fewer than 5 studies are available (pooled estimates become unreliable)
- Primary studies have fundamentally different research designs (mixing RCTs with observational)
- The research question is qualitative or conceptual rather than quantitative
Assumptions前提假設
IRON LAW: A meta-analysis is only as good as the studies it includes —
garbage in, garbage out. Publication bias inflates pooled effect sizes
because non-significant findings go unpublished.
Key assumptions:
- Studies estimate the same underlying construct (conceptual homogeneity)
- Effect sizes are statistically independent (one effect per study, or use multilevel models)
- Study-level moderators are coded reliably and without bias
- The search strategy captures the relevant population of studies (no systematic omission)
Framework 框架
Step 1 — Extract and Code Effect Sizes
Convert study findings to a common effect size metric (Cohen's d, Hedges' g, r, OR). Code study-level moderators (sample size, design, context). See references/ for conversion formulas.
Step 2 — Choose Fixed-Effect vs Random-Effects Model
Fixed-effect assumes one true effect; random-effects assumes effects vary across studies. If studies span different populations or contexts, random-effects is almost always appropriate.
Step 3 — Assess Heterogeneity
Compute Q statistic (test of homogeneity), I² (proportion of variance due to heterogeneity), and τ² (between-study variance). I² > 75% indicates substantial heterogeneity warranting moderator analysis.
Step 4 — Test for Publication Bias and Report
Use funnel plot, Egger's regression test, and trim-and-fill method. Report pooled effect, CI, prediction interval, and results of bias assessment.
Output Format輸出格式
Gotchas注意事項
- Combining apples and oranges: statistically possible but conceptually meaningless if constructs differ
- Random-effects models give more weight to small studies, which are often lower quality
- I² depends on precision of included studies; low I² with imprecise studies does not mean homogeneity
- Funnel plot asymmetry can be caused by factors other than publication bias (small-study effects)
- File-drawer problem: unpublished null results are systematically missing
- Moderator analyses with many subgroups and few studies per subgroup are underpowered and unreliable
References參考資料
- Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to Meta-Analysis. Wiley.
- Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539-1558.
- Rothstein, H. R., Sutton, A. J., & Borenstein, M. (2005). Publication Bias in Meta-Analysis. Wiley.