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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: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

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...

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...

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.

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...

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Related Experiment Video

Updated: Dec 29, 2025

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

Published on: September 7, 2019

Evaluating and presenting uncertainty in model-based unconstrained ordination.

Andrew Hoegh¹, David W Roberts²

¹Department of Mathematical Sciences Montana State University Bozeman MT USA.

Ecology and Evolution

|January 29, 2020

Summary

This summary is machine-generated.

Model-based ordination reveals significant uncertainty in ecological community composition gradients. Simulation studies and the UncertainOrd R package help visualize and understand this uncertainty for more transparent scientific reporting.

Keywords:

Bayesian estimation latent factor models multivariate species models ordination

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Last Updated: Dec 29, 2025

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Area of Science:

Ecology
Computational Biology
Statistics

Background:

Ecological community composition is analyzed using ordination techniques to visualize relationships between sample units based on taxa presence or abundance.
Traditional ordination methods often rely on distance-based approaches, but model-based methods are gaining traction.
Model-based approaches, particularly Bayesian latent factor models, offer a way to assess uncertainty in ordination results.

Purpose of the Study:

To demonstrate and quantify the uncertainty inherent in model-based unconstrained ordination.
To investigate factors influencing uncertainty in ordination, such as the number of sampling units and species.
To provide tools for transparently reporting ordination results by accounting for uncertainty.

Main Methods:

Analysis of established ecological datasets (spider and dune) using model-based unconstrained ordination.
Conducting simulation studies to assess the impact of sample size and species richness on ordination uncertainty.
Development of an R package (UncertainOrd) for visualizing ordination uncertainty.

Main Results:

Ordination projections for the spider and dune datasets exhibited substantial uncertainty.
Simulation studies indicated that increasing sampling units or species can influence the variability of latent factors.
The UncertainOrd package provides effective visualization tools for representing ordination uncertainty.

Conclusions:

Model-based ordination methods, while powerful, produce results with significant uncertainty that needs to be acknowledged.
Understanding the sources of uncertainty is crucial for designing future ecological studies and interpreting ordination results.
Accurate reporting of uncertainty, facilitated by tools like UncertainOrd, enhances the transparency and reliability of ecological research.