Statistical inference for a linear function of medians: confidence intervals, hypothesis testing, and sample size...

Area of Science:

• Statistics
• Biostatistics
• Quantitative Methods

Background:

• The population mean is a common measure of centrality, but can be misleading with skewed or heavy-tailed response variable distributions.
• The population median offers a more robust measure of centrality in such cases.
• Sample medians can be more efficient estimators than sample means for heavy-tailed distributions.

Purpose of the Study:

• To propose a confidence interval for a general linear function of population medians.
• To provide a method for robust statistical inference when data distributions are non-normal.
• To extend hypothesis testing capabilities to functions of population medians.

Main Methods:

• Development of a confidence interval for general linear functions of population medians.
• Application of the interval for testing directional and finite interval hypotheses.
• Derivation of sample size formulas for interval estimation and hypothesis testing.

Main Results:

• A novel confidence interval for linear functions of population medians is presented.
• The proposed interval accommodates various statistical contrasts, including pairwise comparisons, main effects, and interactions.
• The method is applicable for both hypothesis testing and interval estimation.

Conclusions:

• The proposed confidence interval provides a valuable tool for statistical analysis, particularly when dealing with non-normally distributed data.
• This approach offers a robust alternative to traditional methods relying on the population mean.
• The developed methods support precise statistical inference and sample size determination for median-based analyses.