Meta-Analysis

Synthesise effect sizes from multiple studies to arrive at the most precise and generalisable estimate of a true effect.

Meta-Analysis is a statistical technique for combining the results of multiple independent studies on the same research question to produce a single, more precise and more generalisable estimate of the true effect size. Rather than relying on any single study — which may have a small sample, local idiosyncrasies, or publication bias — meta-analysis pools information across studies, weighting each study by its precision (typically the inverse of its variance). The result is a weighted average effect size with much narrower confidence intervals than any single study could achieve.

Meta-analysis is the cornerstone of evidence-based practice in medicine, psychology, education, and public policy. Cochrane systematic reviews, clinical practice guidelines, and large-scale educational intervention evaluations all rely on meta-analytic estimates. A well-conducted meta-analysis addresses the critical question: 'Across all available studies, what is our best estimate of the effect, and how consistent is it?' Consistency is quantified using heterogeneity statistics (I², Q, and τ²) that reveal how much the true effect varies across studies.

StatRyx performs random-effects meta-analysis (which accounts for the fact that true effects may vary across studies) using restricted maximum likelihood (REML) estimation. It accepts a table of effect sizes and standard errors (or the raw statistics needed to compute them), produces a forest plot with individual study estimates and the pooled effect, computes I², Cochran's Q, and τ², and performs a funnel plot and Egger's test for publication bias.

When to use the Meta-Analysis

• You have a collection of studies on the same research question and want to pool their results into a single quantitative summary
• You are conducting a systematic review and the included studies report comparable effect sizes
• You want to estimate heterogeneity — the degree to which true effects vary across different contexts, populations, or study designs
• You are writing a meta-analytic paper and need pooled Hedges' g, Cohen's d, or r values with confidence intervals
• You want to assess whether publication bias may be distorting the literature using funnel plots and Egger's test

When not to use it

• Studies are too heterogeneous in design, populations, or outcome measures to be meaningfully combined — use Narrative systematic review with qualitative synthesis instead
• You have fewer than 5 studies — pooled estimates will be unreliable and heterogeneity estimates will be very imprecise — use Descriptive summary of study findings instead
• Studies use different outcome metrics that cannot be converted to a common effect size metric — use Vote-counting or narrative synthesis instead

Worked example

How to report it (APA 7)

A random-effects meta-analysis of 18 randomised controlled trials examined the effect of mindfulness-based interventions on anxiety symptoms. The pooled Hedges' g was 0.62 (95% CI [0.48, 0.76], p < .001), indicating a medium-to-large effect. Heterogeneity was moderate, I² = 54%, Q(17) = 37.1, p = .004, τ² = 0.08. Egger's test did not indicate significant publication bias (t = 1.23, p = .237).

Frequently asked questions

Is meta-analysis 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.

Do I need to code to run a meta-analysis?

No coding required. Upload your study-level data table and describe your research question in plain English. StatRyx handles effect size computation, model fitting, plot generation, and APA reporting.

What is I² and how do I interpret it?

I² (I-squared) measures the percentage of total variability in effect sizes that is due to true heterogeneity (differences across studies) rather than sampling error. Values of 25%, 50%, and 75% are considered low, moderate, and high heterogeneity respectively. High I² suggests that the studies are estimating different true effects across contexts or populations.

What is the difference between fixed-effects and random-effects meta-analysis?

Fixed-effects meta-analysis assumes that all studies estimate the same single true effect — variation is only due to sampling error. Random-effects meta-analysis assumes that true effects vary across studies, estimating both the average effect and the between-study variance (τ²). Random-effects is almost always more appropriate when combining studies from different research groups, time periods, or populations.

How do I detect and handle publication bias in meta-analysis?

Publication bias occurs when significant results are more likely to be published, inflating the apparent effect. The funnel plot visually checks for asymmetry (small studies with small effects that are missing from the literature). Egger's test provides a formal statistical test of funnel plot asymmetry. If bias is detected, trim-and-fill analysis estimates the adjusted pooled effect after imputing hypothetically missing studies. StatRyx provides all three approaches.

Run a Meta-Analysis on your data →

Related analyses

• Pearson & Spearman Correlation
• Linear Regression
• Cronbach's Alpha
• Exploratory Factor Analysis
• Principal Component Analysis
• K-Means Cluster Analysis
• Linear Discriminant Analysis
• Mediation Analysis
• Moderation Analysis
• Linear Mixed Model
• Meta-Regression