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Sample size determination when the underlying distribution is highly right-skewed
Basanese, Michael Daniels, William Hammerling, Dorit
Basanese, Michael
Daniels, William
Hammerling, Dorit
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2026-04
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Abstract
Sampling from right-skewed distributions can result in inaccuracy in the sample mean. For these distributions, the presence (or absence) of rare but extremely large values in a sample can cause the sample mean to overestimate (or underestimate) the true mean. This issue is particularly relevant for methane emissions from the oil and gas sector, where emissions distributions are highly right-skewed and sample means are often necessary for regulatory reporting. One way to alleviate this issue is to collect large enough samples for the sample mean to closely approximate the true mean, but obtaining large samples is often costly or logistically challenging. Also, the sample size required to accurately estimate the true mean varies based on the underlying distribution, necessitating tailored sampling guidance. To address this, we developed a web tool that analyzes how sample mean accuracy varies with sample size for a variety of right-skewed distributions. Currently, the tool focuses on an application for methane emissions, but the underlying methodology can be applied to right-skewed distributions in any field. The tool includes methane emissions distributions from six US oil and gas basins and right-skewed parametric distributions and can also be applied to any user-uploaded distribution. For a selected distribution, the tool simulates sampling across a sequence of sample sizes and provides error metrics and interactive visualizations of sample mean behavior. These outputs help users determine the sample size required to achieve acceptable accuracy in the sample mean, supporting the future collection of representative samples from right-skewed distributions and improving the robustness and reliability of subsequent analyses.
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