Different fields. Stronger evidence.
A meta-analysis workspace for health, education, psychology, ecology, engineering and beyond. Define your question, verify your data and explore the evidence.
Your evidence collection
Upload papers and supplements, then link each comparison to its source.
Define your comparison
Use the same group order and outcome direction in every study. A higher value may represent benefit or harm, depending on your question.
Categories might be teaching method, treatment class or material type. Populations might be age groups, species or experimental systems.
Search record
Record databases, exact search terms, search dates and citation searches. This log is manual, not an automatic literature search.
Add PDF papers to open them alongside your data review.
Extract, then verify
One row per independent comparison. Enter event counts or group means, SDs and sample sizes.
Changing format keeps your rows but clears their verification. Never mix unrelated response variables just because both have an effect size.
Rows are suggestions until you check “Verified”. Source references, outcome timing and measurement units require your review. Paired designs, clustering, shared controls and repeated measures are not modelled in this version.
Explore the pooled effect
Effects compare group 1 with group 2. Higher values may mean benefit or harm.
This check does not establish comparability. If studies address different questions, analyse them separately. The fields of research may differ; the pooled outcome must represent a defensible common construct.
Random effects allow between-study variation. The model alone does not establish generalisability. Subgroup estimates describe patterns and do not test a moderator effect.
Analysis methods
A structured workflow for planning, extracting and synthesising quantitative evidence.
- Literature search: document databases, dates, terms and citation searches in Papers.
- Inclusion criteria: define the comparison, response variable, eligible measurements and experimental designs before screening.
- Effect sizes: enter event counts for risk ratios or means, SDs and sample sizes for Hedges’ g. Use SD rather than SE.
- Basic meta-analysis: review source values, independence, effect direction and comparability. Choose a model and inspect the forest plot.
- Moderators: explore study-category or population subgroups. Use the R export for further analysis; sparse subgroups require caution.
- Publication bias: inspect the funnel plot when at least ten studies are available. Asymmetry can reflect heterogeneity, design differences or small-study effects as well as publication bias.
Supported designs & statistical details
This version supports independent two-group binary outcomes (risk ratios), continuous outcomes (Hedges’ g), and independent Pearson correlations. It does not implement hazard ratios, diagnostic accuracy, prevalence pooling, network meta-analysis, paired designs or multilevel models. PDFs are stored for manual review; they are not automatically extracted or screened.
Hedges’ g can combine different measurement scales when they measure the same construct with consistent direction. Record each scale and its units. Standardisation does not make unrelated outcomes comparable.
Studies receive inverse-variance weights, rather than weights based solely on sample size. Random-effects weights use within-study variance plus estimated between-study variance.
Hedges’ g = J × (mean group 1 − mean group 2) / pooled SD, with the exact gamma-function small-sample correction J. The sampling variance uses the large-sample approximation N/(n₁n₂) + g²/(2N). Normal 95% intervals are exploratory, especially with few studies.
Risk ratios use the log scale. If any cell is zero, add 0.5 to all four cells. Studies with zero events in both groups require separate handling and are blocked here.
One comparison per independent study. For clustered samples, paired designs, multiple effect sizes, shared controls or repeated measurements, use a statistical design that accounts for dependence. This workspace does not implement those models.
Effect-size documentation · R meta package documentation
Two-group analyses and correlations require different effect sizes and variance calculations. Choose the method that matches your question and study design.
Combine correlations
Pool independent Pearson correlations from any discipline using Fisher’s z transformation.
Enter correlations for the same pair of constructs, with consistent variable coding and direction. For example, study the relationship between practice time and performance, or material density and strength.
Optional worked example: published ecology benchmark
Rafaluk-Mohr (2019) benchmark
Approximate digitisation of published Figure 3A, checked against Table 1 and forest plots. Sample sizes were inferred from standard errors. These inputs are not the author’s original dataset.
The paper’s text says eight restricted datasets, while its table and figure identify nine. Reproducing the nine-row subset gives a close match. Several same-paper datasets may be dependent; this model does not account for that dependence.
Benchmark discrepancies and full audit
The full and restricted pooled r values match approximately, not exactly. The reported fungal sign in the restricted analysis disagrees with the plot. Some reported subgroup coefficients resemble common-effect rather than random-effects outputs. The virulence-measure moderator result was not reproduced. Original extracted data and historical R settings are still needed.
Read the complete auditFor original data, n is the number of independent paired observations underlying a Pearson correlation, not the number of extracted datasets. Do not enter Spearman correlations or values converted from other statistics without reviewing the appropriate variance/conversion method.
From study data to a pooled estimate
A practical guide: choose your question, enter compatible data, select a model and read the evidence.
Watch: your first meta-analysis
An illustrated walkthrough with English voice-over, including practice data, pooled results, correlations and exports. About 3 minutes, with matching captions and a transcript.
Illustrated interface examples; all practice values are synthetic.
Read the tutorial transcript
Welcome to How to Do Meta Analysis. Follow this illustrated guide to practise with synthetic data, then repeat the workflow with verified research data.
Open Papers. Define your research question, outcome, and comparison groups. Here, we compare structured feedback with usual teaching, using assessment pass rates.
Add your papers as PDFs and record your search. Read each eligible study and extract its data manually. Uploading a PDF does not automatically extract or screen it.
Choose the right format. Use events and totals for risk ratios, means and standard deviations for Hedges G, or Pearson R and sample size in Correlations.
To practise, choose Education example and load synthetic data. Export an existing project first, because loading an example replaces the current dataset.
Verify every row. Synthetic study one has twelve events out of thirty in group one, and four out of thirty in group two. Check the source, outcome, time, and group order.
Open Analyse. Review comparability and independence, choose your statistical model, and run the checked dataset. Choose the model for the question, not the smallest P value.
The practice result is a risk ratio of two point one four, with a confidence interval from one point three zero to three point five three. These results are synthetic.
In the forest plot, square areas show study weights. Lines show confidence intervals, and the diamond shows the pooled result. Review variation and study designs too.
For wing and tarsus length, open Correlations. Enter the reported Pearson R, sample size, and source for each independent dataset. Analyse raw paired measurements first.
Export your project JSON as a backup. You can also export data, calculation results, a forest plot, and an R script. PDFs and correlation projects need separate backups.
You are ready to practise. Define your question, verify compatible and independent data, then analyse and export. Find the full guide under Learn on the website.
1. Start with a question you can actually pool
Specify the population or system, comparison, outcome and assessment time. An effect size puts results on a common mathematical scale; it does not make different research questions equivalent.
For example: do independent studies of great tits find a relationship between wing length and tarsus length? That is a correlation question, rather than a comparison of two intervention groups.
2. Choose the right data format
| Your studies report | Enter | Method here |
|---|---|---|
| Events in two independent groups | Event counts and totals for each group | Risk ratio (RR) |
| Continuous measurements in two independent groups | Mean, SD and sample size for each group | Hedges’ g |
| A relationship between two variables | Pearson r and the number of independent pairs | Fisher-z correlation pooling |
Use SD, not SE. Check group order and variable coding. For raw paired measurements, first inspect a scatterplot and calculate the correlation outside this workspace. Avoid reusing participants across supposedly independent rows.
3. Practise before using your real data
Open Extract & review, choose an example discipline and load synthetic data. Select binary or continuous outcomes, inspect each row and check its verification box. These examples are invented for learning and cannot support scientific conclusions.
4. Choose the model for your question
| Common effect | Random effects |
|---|---|
| Assumes the included studies estimate one underlying effect. Differences in observed estimates reflect sampling error under the model. | Allows underlying effects to vary across studies and estimates their mean. Between-study variance influences the weights. |
| Weight is 1 / within-study variance. | Weight is 1 / (within-study variance + τ²). |
Choose based on the design and the scientific question before inspecting which result is statistically significant. Random effects cannot repair incompatible outcomes or dependent observations. With few studies, between-study variance and uncertainty are difficult to estimate.
5. Read the forest plot
Each square marks one study’s estimate; its area represents that study’s relative weight. The horizontal line is its 95% confidence interval. The diamond shows the pooled estimate and interval.
The reference line is 1 for a risk ratio and 0 for Hedges’ g or a correlation. An interval crossing this line is compatible with no effect under the model; it does not establish that the effect is absent. Check magnitude, precision and practical meaning together.
A positive effect is not automatically beneficial. For example, more failures and more successful assessments have opposite practical meanings.
6. Inspect variation and study weights
The results include a study-weight table and three heterogeneity summaries. I² describes the estimated proportion of observed variation attributable to heterogeneity, rather than sampling error. τ² estimates between-study variance on the analysis scale. Q summarises variation around the common-effect estimate.
Read these alongside the actual study estimates, confidence intervals and study designs. I² is not the percentage of studies that disagree, and no single numerical cutoff tells you whether pooling is appropriate.
7. Explore, document and export
Use descriptive subgroups to inspect study categories or populations. Their separate estimates do not test whether groups differ. Funnel plots are available for datasets with at least ten studies, but asymmetry alone does not establish publication bias.
Export your project, data and calculation results. The two-group analysis also exports a forest SVG and an R script to reproduce its stated formulas. Advanced models such as meta-regression or multilevel analysis require a separate, appropriate workflow; they are not implemented here.