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Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range.

Xiang Wan1, Wenqian Wang2, Jiming Liu3

  • 1Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong. xwan@comp.hkbu.edu.hk.

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Researchers often need to estimate sample mean and standard deviation for meta-analysis when only medians or quartiles are reported. This study introduces improved estimation methods, enhancing accuracy for pooled results in systematic reviews.

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Area of Science:

  • Biostatistics
  • Medical Research Methodology

Background:

  • Systematic reviews and meta-analyses frequently require pooling sample mean and standard deviation from clinical trials.
  • Many trials report data using median, min/max, or quartiles, necessitating estimation of mean and standard deviation.
  • Existing methods for estimating these parameters have limitations.

Purpose of the Study:

  • To propose novel methods for estimating sample mean and standard deviation.
  • To address limitations in existing estimation techniques, particularly Hozo et al.'s method.
  • To explore estimation strategies when interquartile range is available.

Main Methods:

  • Developed a new estimation method for sample standard deviation incorporating sample size.
  • Investigated sample mean and standard deviation estimation in scenarios with available interquartile range.
  • Conducted simulation studies to evaluate proposed methods.

Main Results:

  • Proposed methods significantly improve existing techniques for estimating sample standard deviation.
  • Estimates are nearly unbiased for normal data and slightly biased for skewed data.
  • Performance remains strong for both normal and skewed data across different scenarios.

Conclusions:

  • New approximation methods enhance the estimation of sample mean and standard deviation.
  • The study provides guidance for meta-analysis in various data reporting situations.
  • A summary table with formulas is offered for practical application in meta-analysis.