Overview
Meta-analysis statistically combines results from studies identified in a systematic review. It can estimate an average effect, the range of effects across settings, and whether study characteristics explain differences. Its credibility depends on the review that feeds it and on analytic choices that are often under-reported.
We help you plan the analysis before extraction, choose the right effect size metric (standardized mean differences, odds or risk ratios, correlations and others), convert results reported in different formats, and handle dependent effect sizes from studies with multiple outcomes or groups. We then fit models in R (metafor, meta) or Comprehensive Meta-Analysis (CMA), explore heterogeneity and assess publication bias with appropriate caution.
You receive reproducible code or project files, forest and funnel plots, tables and a clear explanation of each result so you can write your results and discussion and respond to reviewers.
Who it’s for and the problems it solves
This is for you if you are…
- Doctoral and master's students whose systematic review includes a quantitative synthesis
- Clinicians and health researchers preparing a meta-analysis for publication
- Psychology, education and management researchers pooling correlations or standardized mean differences
- Authors responding to reviewer comments about heterogeneity, model choice or publication bias
Common problems we help with
- Studies report means, medians, t-values or odds ratios and you need one common effect size
- Several studies contribute multiple effect sizes and you are unsure how to handle dependence
- Your I² is high and you do not know whether pooling is still meaningful
- You ran Egger's test with only a few studies and a reviewer questioned it
- You are unsure whether to use fixed-effect or random-effects models
What’s included — and what isn’t
Included
- Analysis plan aligned with your protocol (for example, PROSPERO registration) and PRISMA 2020 reporting
- Data extraction template design for effect size data and moderators
- Effect size calculation and conversion: Hedges' g, Cohen's d, odds ratio, risk ratio, hazard ratio, Fisher's z-transformed correlations
- Fixed-effect and random-effects models with REML or other τ² estimators, and Hartung–Knapp adjustments where appropriate
- Heterogeneity: Q, I², τ² and prediction intervals
- Subgroup analysis and meta-regression for pre-specified moderators
- Dependent effects: multilevel (three-level) models and robust variance estimation
- Sensitivity analyses: leave-one-out, influence diagnostics, risk-of-bias subgroups
- Small-study effects and publication bias: funnel plots, Egger's regression test, trim-and-fill, and selection models where suitable
- Forest plots, funnel plots and summary tables, plus support for GRADE certainty assessment inputs
Not included
- Running the literature search or screening for you in this service (see our systematic review support)
- Adding, dropping or recoding studies after seeing results without reporting it as a deviation
- Writing the discussion section of your paper or thesis
- Promising statistical significance or publication
What you receive
- Analysis plan
- Effect size metric, model, heterogeneity strategy, moderators, sensitivity analyses and bias assessment, aligned with your protocol.
- Effect size dataset
- A spreadsheet of extracted and converted effect sizes with variances and notes on each conversion.
- Results and plots
- Pooled estimates with confidence and prediction intervals, forest and funnel plots, subgroup and meta-regression tables.
- Reproducible files
- Annotated R scripts (metafor or meta) or CMA project files, with package versions.
- Interpretation walkthrough
- A session explaining each result and how to report it in line with PRISMA 2020.
How it works
Plan
We review your protocol and included studies, and agree metrics, models and pre-specified analyses.
Extract and convert
We design or check the extraction sheet and compute effect sizes, flagging studies that need author contact or assumptions.
Model
We fit the main model, then heterogeneity, moderator, sensitivity and bias analyses.
Report
We deliver plots, tables and files with a walkthrough and answer follow-up questions.
Models, statistics and software
- Random-effects models
- Assume true effects vary between studies; τ² estimated by REML or alternatives, with Hartung–Knapp–Sidik–Jonkman confidence intervals where suitable.
- Heterogeneity statistics
- Cochran's Q tests heterogeneity; I² describes the proportion of variability due to heterogeneity; τ² and prediction intervals describe its size in effect-size units.
- Meta-regression and subgroups
- Test whether moderators explain heterogeneity; limited by number of studies and at risk of spurious findings if not pre-specified.
- Multilevel meta-analysis
- Three-level models and robust variance estimation for multiple effect sizes per study.
- Publication bias
- Funnel plots, Egger's regression test, trim-and-fill, PET-PEESE and selection models, interpreted as evidence of small-study effects rather than proof of bias.
- Software
- R metafor and meta, Comprehensive Meta-Analysis (CMA), Stata meta commands and RevMan for Cochrane reviews.
Reading heterogeneity correctly
I² is widely reported and widely misread. It tells you what proportion of observed variation reflects real differences between studies, not how large those differences are. A high I² with small, consistent effects may matter less than a moderate I² with effects ranging from harm to benefit. We report τ² and a prediction interval, which shows the range in which the effect in a new setting is likely to fall, so readers can judge heterogeneity in practical terms.
The Cochrane Handbook's rough bands for I² overlap deliberately and are meant as a guide, not cut-offs. We help you interpret heterogeneity in the context of your effect sizes and number of studies.
Publication bias tests and their limits
Funnel plot asymmetry can reflect publication bias, but also genuine differences between small and large studies, or chance. Egger's test and similar methods have low power with few studies; a common guideline is not to use them with fewer than ten. Trim-and-fill gives an adjusted estimate under strong assumptions. We use these methods as sensitivity analyses and help you describe them cautiously.
- Check the number of studies before testing for asymmetry
- Use a contour-enhanced funnel plot to see where missing studies would fall
- Report adjusted estimates as sensitivity analyses, not replacements
- Consider selection models where there are enough studies
When not to pool
Sometimes studies are too different in population, intervention, outcome or design for an average to be meaningful. We help you decide when a narrative or structured synthesis (for example, following SWiM guidance) is more honest than a pooled estimate, and how to explain that choice.
What the work can look like
Illustrative example — fictional data
Illustrative meta-analysis summary
A fictional review pooled 18 randomized trials of a school-based mindfulness program on anxiety. The numbers are invented to show how results are reported.
Pooled effect
A random-effects model (REML, Hartung–Knapp adjustment) gave Hedges' g = −0.28, 95% CI [−0.41, −0.15]. Heterogeneity was substantial (I² = 64%, τ² = 0.05), and the 95% prediction interval [−0.76, 0.20] suggests effects in a new school could range from moderate benefit to none.
Moderators and bias
Meta-regression suggested smaller effects in trials with active control groups. The funnel plot was mildly asymmetric and Egger's test p = 0.07; trim-and-fill imputed three studies, reducing g to −0.21 as a sensitivity estimate.
Illustrative only: the review, trials and statistics are invented and are not a real client's findings.
What you’ll need to provide
- Your review protocol or registration and research question (PICO or equivalent)
- The list of included studies and full texts or extracted data
- Risk-of-bias assessments, if completed
- Target journal or program requirements
- Software preference: R, CMA, Stata or RevMan
You don’t need everything ready to ask for a quote — tell us what you have and we’ll say what’s missing.
What affects price and turnaround
Price depends on
- Number of included studies and effect sizes
- Complexity of effect size conversions and missing data
- Dependent effect sizes requiring multilevel or robust variance models
- Number of outcomes, subgroups and moderators
- Whether extraction support is needed in addition to analysis
Turnaround depends on
- Completeness of the extraction sheet at the start
- Need to contact study authors for missing data
- Number of revision rounds after supervisor or reviewer feedback
Every project is quoted individually. How we price our work.
Questions people ask before starting
How many studies do I need for a meta-analysis?
Technically two, but results from very few studies are imprecise, heterogeneity is hard to estimate and publication bias cannot be tested well. We help you decide whether pooling is informative for your set of studies.
Fixed-effect or random-effects?
Fixed-effect assumes one true effect shared by all studies; random-effects assumes true effects vary. In most social and health research the random-effects assumption is more realistic, but we explain the choice in relation to your question.
Should I use R or CMA?
R metafor is free, flexible and reproducible, and handles multilevel models well. CMA offers a point-and-click interface that some supervisors prefer. We work in either and can provide equivalent outputs.
Can you do the systematic search as well?
Yes, through our systematic review service, which covers protocols, search strategies and screening. This page focuses on the statistical synthesis.
Will you write my results section?
We provide tables, plots and a detailed explanation. You write the results and discussion; we can review your draft for statistical accuracy.