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Confidence intervals for the log-normal mean

X H Zhou1, S Gao

  • 1Department of Medicine, Indiana University School of Medicine, Indianapolis 46202-5200, USA.

Statistics in Medicine
|April 15, 1997
PubMed
Summary
This summary is machine-generated.

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For log-normal means, the naive confidence interval method is unreliable. Cox's method offers the best balance of accuracy and precision for larger samples, while bootstrap methods excel with smaller datasets.

Area of Science:

  • Statistics
  • Biostatistics
  • Quantitative Analysis

Background:

  • Accurate confidence intervals are crucial for statistical inference.
  • Log-normal distribution is common in various scientific fields.
  • Evaluating different methods for constructing confidence intervals is essential for reliable data analysis.

Purpose of the Study:

  • To compare the performance of four confidence interval construction methods for log-normal means.
  • To evaluate coverage error, interval width, and relative bias.
  • To identify the most appropriate method based on sample size.

Main Methods:

  • A simulation study was conducted.
  • Four methods were evaluated: naive, Cox's, conservative, and parametric bootstrap.

Related Experiment Videos

  • Methods were assessed for coverage error, interval width, and relative bias.

    • Main Results:

    • The naive method demonstrated inappropriate performance.
    • Cox's method exhibited the smallest coverage error for moderate to large sample sizes.
    • The bootstrap method showed the smallest coverage error for small sample sizes.
    • Cox's method yielded the narrowest interval width among appropriate methods.

    Conclusions:

    • The naive method for log-normal mean confidence intervals should be avoided.
    • Cox's method is recommended for moderate to large sample sizes due to its accuracy and precision.
    • Parametric bootstrap methods are suitable for small sample sizes.
    • Method selection depends on sample size and desired statistical properties.