This project provides a neural network–based tool for estimating the sample mean and standard deviation from summary statistics, including the median, range, and/or quartiles. The method is designed for situations where individual-level data are unavailable and only limited summary statistics can be accessed, especially when the data is skewed or does not meet the normality assumption.
The tool is deployed as a lightweight web application and can be accessed directly at:
👉 https://amss-stat.github.io/estimating-sample-mean-standard-deviation/
All computations are performed locally in the browser, without requiring data upload or server-side processing.
Typical application scenarios include:
- Meta-analysis
- Systematic reviews
- Evidence synthesis across multiple studies
The estimation procedure is based on neural network models trained on large-scale diverse synthetic data, covering a wide range of common distributional families and sample sizes.
Given a set of summary statistics (e.g., sample size, median, minimum/maximum, and/or quartiles), the tool:
- Infers sample mean and standard deviation using pretrained neural networks
- Reconstruct the latent distribution
- Selects the best-fitting distribution by comparing theoretical and observed quantiles
This framework enables accurate estimation even under skewed or non-normal distributions, where traditional methods often perform poorly.
Extensive simulation studies show that:
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The proposed method outperforms classical estimators (e.g., Luo, Wan et al.) in most settings
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The improvement is particularly pronounced for:
- Skewed data
- Situations where the normality assumption is violated
If you use this tool or method in your research, please cite:
Zhang, Qinyuan; Li, Qizhai. Neural network-based estimation of sample mean and standard deviation from some quartiles. J Syst Sci Complex (2026).
📄 Paper link: 👉 https://doi.org/10.1007/s11424-026-5481-4
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This method is data-driven and highly extensible, and performs well across a broad range of common distributions and practical scenarios.
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As with any model-based approach, estimation accuracy may degrade under:
- Unusual data-generating mechanisms
- Extremely irregular summary statistics
If you encounter such cases, we strongly encourage you to contact us.
✉️ Contact: zhangqinyuan19@mails.ucas.ac.cn
We actively expand the model library by training additional neural networks to improve performance in newly identified scenarios.
We welcome all forms of feedback, including:
- Unexpected estimation behavior
- Potential bugs or numerical issues
- Suggestions for new distributional settings
Please contact the authors at: ✉️ Contact: zhangqinyuan19@mails.ucas.ac.cn
Your feedback will directly help improve the robustness and applicability of this tool.