Poisson-based detection limit and signal confidence intervals for few total counts

Area of Science:

• Analytical Chemistry
• Metrology
• Statistical Methods

Background:

• Traditional detection limit calculations often struggle with low count data.
• Existing methods may not fully integrate Poisson statistics, leading to inaccuracies.
• High uncertainty and false positives are common issues with few total counts.

Purpose of the Study:

• To present an alternative method for calculating detection limits.
• To address the limitations of accepted methods when dealing with low count data.
• To improve the reliability of detection limits in scientific measurements.

Main Methods:

• Developed an alternative detection limit calculation incorporating Poisson statistics.
• Defined detection based on consistent relative uncertainty across all count magnitudes.
• Included signal count uncertainty in the detection limit calculation.
• Proposed a method for determining confidence intervals for signals with background noise.

Main Results:

• The alternative method prevents excessive false positives.
• It reduces large relative uncertainty in signal determination, especially with few counts.
• The proposed confidence interval method aids in determining the most probable signal value.
• Negative signal results are avoided at low total counts.

Conclusions:

• The new method offers a more robust approach to detection limits, particularly for low count scenarios.
• It enhances the precision and reliability of quantitative analysis in various scientific fields.
• The method provides a statistically sound alternative to conventional detection limit calculations.