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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

Propagation of Uncertainty from Systematic Error

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...

Significant Figures in Calculations

Significant Figures in Calculations

Uncertainty in measurements can be avoided by reporting the results of a calculation with the correct number of significant figures. This can be determined by the following rules for rounding numbers:

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Updated: May 2, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Alcohol calculations and their uncertainty.

¹Road Accident Analysis, United Kingdom johnsearle@meadh.freeserve.co.uk.

Medicine, Science, and the Law

|March 20, 2014

Summary

This study reveals discrepancies in Widmark Factor calculations for women, differing from previous research. It demonstrates that blood alcohol concentration error ranges are not fixed percentages but must be calculated individually.

Area of Science:

Forensic Science
Toxicology
Biostatistics

Background:

Blood alcohol concentration (BAC) is commonly estimated using dilution models.
Discrepancies exist between the total body water and Widmark Factor formulations.
Previous work by Forrest and Barbour showed variations, particularly for women, often used interchangeably.

Purpose of the Study:

To investigate the source of discrepancies in Widmark Factor values between Forrest and Barbour's work.
To derive and publish formulae for calculating the coefficient of variation in BAC estimations.
To re-evaluate Gullberg's conclusions on fixed coefficients of variation for BAC calculations.

Main Methods:

Analysis of Widmark Factor formulations and historical data.
Derivation of new formulae for calculating the coefficient of variation.

Keywords:

Widmark alcohol calculations error uncertainty

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Comparison of derived coefficients with Gullberg's fixed percentages.

Main Results:

Identified the source of significant differences in Widmark Factors for women between Forrest and Barbour.
Derived formulae demonstrate that the coefficient of variation is case-specific, not a fixed percentage.
Gullberg's conclusion that a fixed coefficient of variation (±21% for BAC, 12.5% for drink volume) is applicable was found to be mistaken.

Conclusions:

The Widmark Factor formulation requires careful application, especially concerning sex-based differences.
Accurate BAC estimation necessitates calculating a case-specific coefficient of variation.
Fixed coefficients of variation are inappropriate for reliable BAC calculations.