Meta-Analysis: Fixed-Effect (IV)

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Pools study effects assuming ONE common true effect — a narrow interval, for homogeneous studies only.

A fixed-effect (common-effect) meta-analysis weights studies by precision and assumes they all estimate the same effect; only appropriate when heterogeneity is negligible.

Worked example

What is the common effect across near-identical trials?

8 tightly-similar trials (I² = 6%) were pooled with a fixed-effect model.

Result

The common effect was SMD = 0.29 (95% CI [0.21, 0.36]), with negligible heterogeneity.

How you'd report it (APA)

A fixed-effect meta-analysis gave a common SMD = 0.29, 95% CI [0.21, 0.36] (I² = 0%).

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Studies estimate the same thing
    Near-identical designs, populations and outcomes, so one true effect is plausible. e.g. 8 replications of one protocol (I² ≈ 0).
  • Heterogeneity is genuinely negligible
    Q is non-significant and I² is low, checked before choosing this model rather than assumed.
  • You want the most precise pooled estimate
    When homogeneity holds, the fixed-effect interval is the narrowest defensible one.

When NOT to — use instead

  • Studies are heterogeneous
    Different populations or methods mean the true effect varies — a common-effect model understates the uncertainty. → Random-effects meta-analysis
  • You plan to generalise beyond these exact studies
    Inference to a wider universe of studies needs a between-study variance term. → Random-effects meta-analysis

Hypotheses

H₀: the single common effect θ is zero — pooling by inverse-variance weights, the studies' shared true effect equals the no-effect value.
Hₐ: θ ≠ 0. A separate homogeneity test (Cochran's Q, H₀: every study shares the same θ) must pass first, because the whole model assumes it.

Parameter tested: θ — one common effect estimated as the inverse-variance-weighted mean of the study effects; heterogeneity is reported (Q, I², τ²) but assumed negligible

Assumptions (and what to do if they fail)

One common true effect (homogeneity)high

Check: Cochran's Q non-significant and I² low (roughly < 25–40%) before adopting this model.

If violated: The pooled CI is falsely narrow and the estimate can be biased. Switch to random-effects rather than forcing homogeneity.

Each study's variance is the input, not its SEhigh

Check: The variance column must hold vᵢ = SEᵢ², not the standard error.

If violated: Passing SEs inflates the weights and shrinks the CI dramatically — a silent, large error.

Effects are on one consistent scalemedium

Check: All studies contribute the same metric (all log-OR, or all SMD), transformed the same way.

If violated: Pooling mixed metrics is meaningless; convert to a common effect size first.

Studies are independentmedium

Check: No study contributes two correlated estimates, and samples do not overlap.

If violated: Correlated estimates are double-counted, over-weighting shared data.

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