Unique unbiased median solution for even sample sizes

Area of Science:

• Statistical modeling
• Robust estimation in experimental biology

Background:

• Experimental biology data often contain outliers and asymmetric distributions.
• The median is a robust measure of central tendency, less affected by outliers than the mean.
• The conventional median calculation can introduce bias in datasets with an even number of observations, assuming data symmetry.

Purpose of the Study:

• To identify and derive an unbiased median estimator for ranked datasets.
• To address the bias introduced by the conventional median in asymmetric distributions with even sample sizes.

Main Methods:

• Derived an unbiased median estimator by minimizing the sum of residuals raised to a rational power approaching one.
• Compared the properties of the unbiased and conventional medians using Poisson-distributed datasets.
• Generated random samples using the Mersenne Twister algorithm in IgorPro software.

Main Results:

• For odd sample sizes, the unbiased median is identical to the conventional median.
• For even sample sizes, the unbiased median equalizes the product of distances to data points above and below it, differing from the conventional median in asymmetric distributions.
• Both estimators underestimated the mean of Poisson data, but the unbiased median was consistently closer to the expected value and exhibited lower variance.

Conclusions:

• The proposed unbiased median estimator is more accurate and has reduced variance compared to the conventional median for even sample sizes.
• This unbiased median provides a superior measure of central tendency for asymmetric biological data.
• The findings offer a more robust statistical tool for analyzing biological datasets prone to outliers and asymmetry.