One study is an anecdote with error bars. Pool many and the noise averages down — but not equally: a precise study should count for more than a sloppy one. Slide (or tap) to pour the studies into one inverse-variance-weighted estimate and watch the confidence interval tighten.
Fixed-effect meta-analysis, computed live: each study i has an effect yᵢ and standard error SEᵢ; its weight is wᵢ = 1/SEᵢ². The pooled estimate is the inverse-variance weighted mean μ = Σwᵢyᵢ / Σwᵢ, with SE(μ) = 1/√Σwᵢ and 95% CI = μ ± 1.96·SE(μ). The precise (small-SE) study genuinely dominates the pool — a fail-loud self-check throws unless the pooled estimate sits nearer the lowest-SE study than the plain average does.
The 7 studies are a fixed synthetic set (seeded yᵢ, SEᵢ); real meta-analysis adds heterogeneity (random-effects τ², I²) and worries about which studies are comparable at all. The inverse-variance pooling arithmetic shown is exact.