Estimation of standard deviations and inverse-variance weights from an observed range

Area of Science:

• Statistics
• Biostatistics
• Clinical Research Methodology

Background:

• Estimating standard deviation from sample range is common in clinical studies, especially when data is incomplete.
• This estimation is vital for interpreting individual studies and conducting meta-analyses.
• Existing methods often fail to distinguish between estimating population standard deviation and sample standard deviation.

Purpose of the Study:

• To compare various estimators of standard deviation derived from sample range.
• To evaluate estimators based on bias and mean squared error for normally distributed data.
• To recommend preferred methods for estimating population and sample standard deviation.

Main Methods:

• Comparative analysis of different statistical estimators for standard deviation using sample range.
• Evaluation of bias and mean squared error for each estimator.
• Development and proposal of a Taylor series method for inverse-variance weighting when only sample range is available.

Main Results:

• Unbiased estimators exist for both population and sample standard deviation.
• The proposed Taylor series method shows minimal bias, even with small sample ranges.
• The commonly used naive method of inverse estimated variance is substantially biased and overweights small samples.

Conclusions:

• Accurate estimation of standard deviation from sample range is achievable with appropriate methods.
• The Taylor series method is recommended for inverse-variance weighting in meta-analyses with limited data.
• The naive method should be avoided due to significant bias and potential for misleading results in meta-analyses.