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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

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Published on: February 12, 2014

About the z-multiplier in total error calculations.

Dietmar Stöckl¹, Linda M Thienpont

¹Laboratory for Analytical Chemistry, Faculty of Pharmaceutical Sciences, Gent University, Gent, Belgium.

Clinical Chemistry and Laboratory Medicine

|December 31, 2008

Summary

This study introduces new z-values for calculating total error (TE) in analytical measurements, considering the ratio of systematic error (SE) to random error (RE). These values refine TE calculations by accounting for varying SE/RE ratios, improving accuracy in scientific measurements.

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Area of Science:

Analytical Chemistry
Measurement Science
Statistical Analysis

Background:

Total error (TE) in analytical measurements combines systematic error (SE) and random error (RE).
Current methods typically use a fixed z-multiplier (1.96) for TE calculation, assuming minimal SE.
The impact of varying SE/RE ratios on TE calculations has not been previously addressed.

Purpose of the Study:

To determine SE/RE ratio-dependent z-values for TE calculations.
To provide a more refined method for assessing analytical measurement uncertainty.
To explore the relationship between SE/RE ratios and probability levels in TE.

Main Methods:

Empirical determination of z-multipliers using the NORMDIST function in Microsoft Excel.
Calculation of five probability distributions for SE/RE ratios ranging from 0 to 1.
Ensuring total probability outside TE boundaries remained within approximately 5%.

Main Results:

Z-multipliers decrease as the SE/RE ratio increases, ranging from 1.96 (SE/RE=0) to 1.645 (SE/RE=1).
Specific z-values were found: 1.769 (0.25), 1.68 (0.5), and 1.651 (0.75).
The one-sided 95% probability level is approached at SE/RE ratios greater than 0.75.

Conclusions:

The study provides refined z-values for TE calculations based on SE/RE ratios.
These findings enhance the understanding of probability levels in analytical measurements.
The results support a more accurate assessment of measurement uncertainty across different error profiles.