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<p>Numerous variance estimators exist for the normal distribution, yet the unbiased estimator–commonly known as Bessel’s correction–remains the most widely used in practice. This article reviews various alternative estimators, that result from using different standardization factors for the sum of squares. It is demonstrated that there is no compelling reason to favor the unbiased variance estimator over other estimators and that better alternatives are available. Implications of these findings for applications involvings small sample size are discussed.</p>

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The Optimal Standardization Factor for the Variance of the Normal Distribution: A Historical Perspective and Recommendations for Practice

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月23日

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  • Dominic Edelmann

摘要

Numerous variance estimators exist for the normal distribution, yet the unbiased estimator–commonly known as Bessel’s correction–remains the most widely used in practice. This article reviews various alternative estimators, that result from using different standardization factors for the sum of squares. It is demonstrated that there is no compelling reason to favor the unbiased variance estimator over other estimators and that better alternatives are available. Implications of these findings for applications involvings small sample size are discussed.