# Meta-analysis: effect sizes, heterogeneity, models, and forest plots

> Chapter 7 of 8 of The Systematic Review E-book by AIPRA. Meta-analysis pools results across studies once a quantitative summary is justified. It requires putting studies on a common scale (standardized mean difference or Hedges' g for continuous outcomes with differing instruments; odds ratios or relative risks for binary outcomes), assessing heterogeneity with Cochran's Q and the I-squared statistic, choosing a pooling model, and presenting results in a forest plot. Random-effects models are the default for most reviews because they assume true effects differ across studies; fixed-effect models assume a single shared true effect and are uncommon in contemporary reviews.

- Source: https://aipra.co/systematic-review-ebook/meta-analysis
- Topics: meta analysis; I2 heterogeneity; forest plot; random effects vs fixed effect; standardized mean difference; funnel plot publication bias; Egger's test
- Last updated: 2026-09-05
- Licence: free to read; cite as shown at the end of this file.

## Key points

- Studies must be converted to a common effect metric before pooling; use SMD or Hedges' g for continuous outcomes on differing scales, and OR or RR for binary outcomes.
- Always extract sample size and a measure of precision such as the standard error — meta-analysis weights studies through those variances, so pooling is not defensible without them.
- I-squared describes the fraction of total variation attributable to heterogeneity rather than within-study error. It is not a measure of how far effects differ on the outcome scale.
- As a rule of thumb, I-squared of roughly 0–40% is often treated as low and above about 75% as considerable, but these are guidance rather than hard rules.
- Random-effects models are the default for most reviews; fixed-effect models are appropriate only when studies are nearly identical in design, population, and conduct.
- If heterogeneity is high, explore it with prespecified subgroup analyses or meta-regression rather than reporting a single pooled effect alone.
- Funnel plot asymmetry can suggest small-study effects or publication bias, but many non-bias mechanisms distort funnels; interpret cautiously, especially with few studies.

## Chapter outline

1. Phase 1 — Building blocks: effect sizes
2. Phase 2 — Signal vs. noise: heterogeneity
3. Phase 3 — Choosing your model
4. Phase 4 — Forest plot and bias detection

## Questions this chapter answers

### What does I-squared mean in meta-analysis?

I-squared estimates the percentage of total variation across studies that is due to genuine heterogeneity rather than within-study sampling error. It is calculated as ((Q − df) / Q) × 100%. It does not indicate how large the differences in effect are on the outcome scale.

### What is a high I-squared value?

Commonly cited rules of thumb treat roughly 0–40% as low heterogeneity and above about 75% as considerable. These thresholds are guidance only; clinical and methodological differences between studies matter as much as the number, and heterogeneity should be interpreted in context.

### Should I use a fixed-effect or random-effects model?

Random-effects is the default for most systematic reviews because it assumes true effects vary across studies and estimates both within-study and between-study variance. Fixed-effect assumes one shared true effect with differences due only to sampling error, which is rarely plausible outside highly standardized settings.

### How do you read a forest plot?

Each study appears as its effect estimate with a confidence interval on a common axis, and a diamond summarizes the pooled estimate. The null line is at 1.0 for ratio measures such as odds ratios and relative risks, and at 0 for mean differences and standardized mean differences. If the pooled diamond does not cross the null line, the summary is conventionally statistically significant, but the visual should always be paired with the numeric estimate, interval width, and heterogeneity statistics.

### What is a funnel plot used for?

A funnel plot graphs effect size against precision to look for asymmetry that may indicate missing small or negative studies. Asymmetry is suggestive of publication bias or small-study effects but has other possible causes, so it is often complemented by formal tests such as Egger's regression and interpreted with caution when few studies are available.

### Which effect size should I use for continuous outcomes?

Use a standardized mean difference or Hedges' g when studies measure the same construct with different instruments or scales, such as different depression questionnaires. A raw mean difference is appropriate only when all studies report the same units.

## References cited

- Higgins JPT, Thompson SG, Deeks JJ, Altman DG. Measuring inconsistency in meta-analyses. BMJ. 2003;327(7414):557-560. doi:10.1136/bmj.327.7414.557
- DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials. 1986;7(3):177-188. doi:10.1016/0197-2456(86)90046-2

## How to cite this chapter

AIPRA. Meta-analysis: effect sizes, heterogeneity, models, and forest plots. In: The Systematic Review E-book. Updated 2026-09-05. Available from: https://aipra.co/systematic-review-ebook/meta-analysis