How to cite the Studio
For methods sections or software lists, cite the version used and the access date when relevant. The recommended APA-style software reference is:
ERN Institute. (2026). ERN Meta-Analysis Studio (Version 1.0) [Computer software]. https://erninstitute.com/tools/meta-analysis-studio/
The Studio is independent software. Its citation does not replace citations to the underlying meta-analysis methods or original dataset sources.
Current statistical workflow
- Effect sizes: Hedges g from eligible independent-group means, Student t, or two-group F tests; Fisher z from correlations; log odds ratios from binary event counts; and generic inverse-variance inputs.
- Models: common-effect inverse-variance pooling and random-effects pooling. Between-study variance can be estimated using restricted maximum likelihood (REML), Paule–Mandel, or DerSimonian–Laird.
- Inference: Wald or Knapp–Hartung confidence intervals, with the automated selection rule documented in the Studio. The inference setting is exported with the fitted model.
- Heterogeneity: Cochran's Q, between-study variance (τ²), and estimator-consistent I² and H² for random-effects models. Prediction intervals are available when the selected model supports them.
- Reproducibility: exported files retain the submitted rows, effect-size calculations, validation notices, model settings, results, and plots.
REML and Knapp–Hartung are established methods, also implemented in the R metafor package (Viechtbauer, 2010). We do not imply that identical output is guaranteed across packages when defaults, small-sample corrections, variance conventions or prediction-interval formulas differ.
Validation status
The repository tests now cover 10 curated datasets containing 256 effect-size records and 11 metric-specific model regressions. A separate Python/NumPy/SciPy implementation recalculated 28 common- and random-effects configurations from the same effect estimates and sampling variances. These comparisons covered pooled estimates, standard errors, confidence intervals, Q, I², REML, Paule–Mandel, DerSimonian–Laird, inference selection, and eligible prediction intervals. The largest absolute numerical discrepancy was below 0.000001.
We also compare restricted maximum likelihood (REML) models with published R/metafor results for brain-image persuasiveness, writing-to-learn interventions, and handedness and eye dominance. The Bourassa single-level fit is checked solely as a numerical regression test; it is not an appropriate substitute for the dependency-aware multilevel analysis reported in that source. These tests compare against published output, not a fresh execution of R.
What this establishes: pooling calculations agree closely with an independent numerical implementation on the tested cases and with selected published metafor examples. What it does not establish: complete validation of every raw-data conversion, every possible input or output file, or direct agreement across a comprehensive R/metafor test battery. A separate R interoperability audit remains to be completed.
The tests are available in the public website source repository. Run node tests/meta-analysis-engine.test.js, node tests/effect-size-converter.test.js, node tests/repository-datasets.test.js, node tests/metafor-published-example.test.js, and node tests/export-integrity.test.js. Run python tests/statistical-crosscheck.py for the independent SciPy comparison when NumPy and SciPy are installed.
Worked example: brain images and scientific persuasiveness
Source: Michael and colleagues (2013), distributed as dat.michael2013. ERN's curated CSV includes 12 independent-study effect sizes on the raw mean-difference scale. This example reproduces the original documentation's intercept-only REML model; it is a software demonstration, not a new scientific finding.
- Open the preselected dataset in the Studio (or choose “Brain images and scientific persuasiveness” in Step 1). Review the 12 raw mean-difference estimates in Step 2.
- In Step 3, select Mean difference, Random effects, REML, Wald (normal) inference, and a 95% confidence level. Choosing Wald is important for comparing with the source's printed interval; the Studio's automatic inference choice may differ.
- Run the analysis. Expect a pooled mean difference of approximately 0.067, standard error 0.035, 95% confidence interval −0.001 to 0.135, and Cochran's Q of 15.73. The published R example reports the same quantities rounded to two decimals: 0.07, 0.03, 0.00 to 0.14, and 15.73 for Q. A slight apparent discrepancy at the lower confidence limit reflects rounding.
- Review the forest plot and download the workbook in Step 2 or the model CSV and forest SVG under Step 4's additional downloads. The workbook includes the settings and row-level calculations.
Important design limits
The Studio assumes that pooled estimates can legitimately be treated as independent. Repeated study labels trigger a review step, but confirming independence does not correct dependent effects. The current models do not estimate multilevel structures, cluster-robust variance, paired-outcome covariance or other dependency structures. For this reason, the curated Bourassa dataset (54 effects from 47 studies) and writing-to-learn dataset (48 effects under 45 study labels) are available for calculation and export only; Step 3 pooling is disabled for those selections. Researchers can analyze the records using an appropriate dependency-aware model elsewhere. The single-level results for both files are retained as numerical regression fixtures, not recommended inferential analyses.
The raw-data converter is intentionally restricted to clearly defined designs. For adjusted, paired, repeated-measures, cluster-randomized or otherwise complex designs, calculate an appropriate estimate and sampling variance using a design-aware method before considering generic inverse-variance pooling. Ineligible statistics should not be forced into the supported conversion routes.
Different effect-size metrics are fitted separately. A mixed dataset does not cause the Studio to combine Hedges g, Fisher z, and log odds ratios into one pooled estimate.
Privacy and analytics
Your uploaded CSV or tab-separated file is read and processed by JavaScript in your browser. ERN Institute's Studio does not transmit the file, study identifiers, effect-size inputs or model results to its own server for calculation. When you choose a public example, your browser fetches that already-public CSV from ERN Institute before processing it locally.
The website uses Google Analytics 4 to measure visits and broad interactions such as loading an example, running a model or clicking a download. Our custom Studio analytics events do not include the contents of research files, filenames, study identifiers or model results. Google Analytics may still process ordinary web-visit data, including browser, device and page information, according to Google's data-use explanation. This privacy statement concerns the current Studio workflow, not other third-party tools or extensions in your browser.
Related methodological source
Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. https://doi.org/10.18637/jss.v036.i03
For the open-data examples, see the ERN repository and cite the corresponding original data publication and metadat package as indicated there.
Questions about calculations or reproducibility? Contact ERN Institute. Please describe the issue without sending confidential participant-level data.