Meta-Analysis: Random-Effects (DL)

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…

Pools study effects assuming the true effect varies across studies — giving a wider, more honest confidence interval.

A random-effects meta-analysis models both within- and between-study variation — appropriate when studies differ in populations or methods (the usual case).

Worked example

What is the overall effect across heterogeneous trials?

25 trials with varied populations were pooled with a random-effects model.

Result

The pooled effect was log-OR = −0.27 (95% CI [−0.38, −0.17]) — i.e. OR = 0.76 — with moderate heterogeneity (I² = 37%).

How you'd report it (APA)

A random-effects meta-analysis gave a pooled log-OR = −0.27 (OR = 0.76), 95% CI on the log scale [−0.38, −0.17] (I² = 37%).

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

When to use it

  • Studies differ in population or method
    The usual real-world case: trials vary in dose, setting, or measure, so one common effect is implausible.
  • Heterogeneity is present
    Q is significant or I² is moderate-to-high, so the between-study variance should be modelled rather than ignored.
  • You want to generalise beyond the included studies
    Inference to the broader population of studies — reported honestly with a prediction interval, not just the CI of the mean.

When NOT to — use instead

  • Studies are truly homogeneous
    With I² ≈ 0 the random-effects and fixed-effect results coincide, and fixed-effect is the simpler statement. → Fixed-effect meta-analysis
  • Very few studies
    With only a handful of studies τ² is estimated poorly and the pooled CI is unreliable — interpret with great caution.

Hypotheses

H₀: the mean of the distribution of true effects, μ, is zero — averaging over study-to-study variation, the central effect equals no effect.
Hₐ: μ ≠ 0. Unlike the fixed-effect model this does not assume one common effect; it estimates a between-study variance τ² and widens the interval accordingly.

Parameter tested: μ — the mean true effect, with between-study variance τ² (DerSimonian-Laird); a prediction interval describes where a new study's true effect would likely fall

Assumptions (and what to do if they fail)

True effects follow a (normal) distributionhigh

Check: The random-effects model assumes study effects are drawn from a normal distribution with mean μ and variance τ².

If violated: With outlying studies or a skewed effect distribution, μ is not a good summary — inspect the forest plot and consider why studies differ.

τ² is estimablehigh

Check: DerSimonian-Laird τ² needs enough studies; with < ~5 it is very imprecise and can collapse to 0.

If violated: A τ² near 0 from too-few studies mimics fixed-effect and understates uncertainty. Report the small-k caveat.

Variance column is vᵢ, not SEᵢhigh

Check: Each study's within-study variance = SEᵢ², not the standard error.

If violated: Weights and τ² are both wrong; the pooled interval is badly miscalibrated.

Distinguish the CI from the prediction intervalmedium

Check: The CI is for the mean μ; the prediction interval is where a future study's effect would land and is much wider.

If violated: Reporting only the CI overstates how consistent the evidence is across settings.

Ready to run a Meta-Analysis: Random-Effects (DL) on your own data?

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

Run this test →