Meta-Regression (moderators)

Verified

Meta (legacy hub)

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

Loading teaching datasets…

Or use your own dataset

Loading your datasets…

Explores whether study-level characteristics explain the variation in effect sizes across studies.

Meta-regression relates each study's effect size to moderators (dose, year, quality…) to explain heterogeneity — the continuous analogue of subgroup analysis.

Worked example

Does treatment dose explain why effects vary across trials?

30 trials' effect sizes were regressed on mean dose in a random-effects meta-regression.

Result

Higher dose predicted larger effects (β = 0.015 per mg, p < .001), explaining ~75% of the heterogeneity.

How you'd report it (APA)

Meta-regression showed dose predicted effect size (β = 0.015, p < .001), explaining ~75% of heterogeneity.

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

When to use it

  • A continuous study-level moderator
    You suspect a graded relationship. e.g. does mean dose, publication year, or study quality predict the effect?
  • Explaining heterogeneity
    Heterogeneity is substantial and you have a covariate that might account for it — the continuous analogue of subgroup analysis.
  • Enough studies for the covariates
    Rule of thumb: roughly ≥ 10 studies per moderator, or the regression overfits.

When NOT to — use instead

  • The moderator is categorical with few levels
    A 2–3 level grouping is cleaner as a subgroup analysis. → Subgroup analysis
  • Too few studies
    With few studies relative to moderators, meta-regression fits noise and the coefficient is unreliable.

Hypotheses

H₀: the moderator's regression coefficient β is zero — the study-level covariate does not explain variation in effect sizes.
Hₐ: β ≠ 0 — effect size changes with the moderator. Fitted as a (usually random-effects) regression of study effects on the moderator, weighting by precision and allowing residual heterogeneity τ².

Parameter tested: β — the change in pooled effect per unit of the moderator; plus residual τ² and the share of heterogeneity explained (R²-analogue)

Assumptions (and what to do if they fail)

Moderators pre-specified, few in numberhigh

Check: Covariates chosen a priori; roughly ≥ 10 studies per moderator.

If violated: Testing many moderators in a small set guarantees a spurious 'significant' one (data dredging).

Study-level, not participant-level, relationshiphigh

Check: The covariate is an aggregate per study (mean dose, % female), so the association is ecological.

If violated: Reading a study-level slope as an individual-level effect is the ecological fallacy — a within-study dose response can differ in sign from the between-study one.

Residual heterogeneity modelledmedium

Check: Use a mixed-effects (random-effects) meta-regression so leftover between-study variance is carried as residual τ².

If violated: A fixed-effect meta-regression understates the SE of β and overstates significance.

Linear, on the right effect scalemedium

Check: The effect–moderator relationship is assumed linear on the analysis scale (e.g. log-OR).

If violated: A curved relationship is missed or mis-summarised; inspect a bubble plot before trusting β.

Ready to run a Meta-Regression (moderators) on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

Run this test →