Meta-Regression

Explain heterogeneity in meta-analytic effect sizes by modelling them as a function of study-level predictors.

Meta-Regression extends random-effects meta-analysis by regressing the study-level effect sizes on one or more study characteristics (moderators) to explain why effects vary across studies. Examples include testing whether effect sizes increase with sample size, decrease with publication year, or differ by geographic region or methodological quality.

StatRyx fits a mixed-effects meta-regression model (REML estimation), reports the moderator coefficient with its 95% CI and p-value, and computes the R²-analog (proportion of between-study variance explained by the moderator). Residual heterogeneity after the moderator is also reported.

Meta-regression extends a meta-analysis by asking why effect sizes differ across studies. Each study's effect size is regressed on study characteristics (moderators such as publication year, sample type or dosage), weighted by its precision. Under a random-effects model it reports how much of the between-study heterogeneity (τ²) each moderator explains, often as R². Because the unit of analysis is the study, power depends on the number of studies, not the number of participants.

When to use the Meta-Regression

You have a meta-analysis with significant heterogeneity (I² > 50%) and want to explain what drives the variation
You have a priori hypotheses about which study characteristics moderate the effect size
You want to test whether effects are stronger in, for example, clinical than in student samples
You want to check whether effect sizes have declined over publication years
You have continuous study-level moderators that cannot be split into subgroups cleanly

When not to use it

You have fewer than 10 studies (meta-regression is very underpowered) — use Subgroup analysis or narrative description of variation instead
You are data-dredging for significant moderators — use Report all tested moderators and correct for multiple comparisons instead
Your moderator is a participant-level variable (e.g., each person's age) — use Individual participant data meta-analysis — study averages can mislead (ecological fallacy) instead

Worked example

Moderator	B	SE	95% CI	p	R²-analog
Publication Year	−0.031	0.012	[−0.055, −0.007]	.012	.24

How to report it (APA 7)

Meta-regression indicated that publication year significantly moderated effect sizes, B = −0.031, SE = 0.012, p = .012, with effect sizes declining over time. The moderator explained 24% of between-study variance (R²-analog = .24). Residual heterogeneity remained significant, I² = 41%.

Frequently asked questions

Is meta-regression free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

How many moderators can I include?

Technically unlimited, but power drops rapidly. A rule of thumb is at least 10 studies per moderator in the model.

How do I report a meta-regression in APA 7?

Name the model (usually random-effects), then each moderator's coefficient with SE and p, plus the variance explained: "Publication year moderated the effect, B = −0.031, SE = 0.012, p = .012, explaining 18% of the between-study heterogeneity."

How many studies do I need for meta-regression?

A common rule of thumb is at least 10 studies per moderator (Cochrane Handbook). With fewer, the results are very unstable and should be described as exploratory.

Subgroup analysis or meta-regression?

A subgroup analysis compares the pooled effect between categories of a moderator; a meta-regression can do the same and also handle continuous and multiple moderators together. With one categorical moderator they give equivalent answers.

Run a Meta-Regression on your data →