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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 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...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

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...

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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Related Experiment Video

Updated: Aug 27, 2025

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Experimental Research Examining How People Can Cope with Uncertainty Through Soft Haptic Sensations

Published on: September 16, 2015

Mental control of uncertainty.

Samuel J Gershman¹, Taylor Burke²

¹Department of Psychology and Center for Brain Science, Harvard University, MA, Cambridge, USA. gershman@fas.harvard.edu.

Cognitive, Affective & Behavioral Neuroscience

|September 28, 2022

Summary

This summary is machine-generated.

Thinking can reduce uncertainty by improving attention and sensory data reliability. This study explores rational inattention models and confirms that incentives enhance performance by increasing data reliability.

Keywords:

Bayesian inference Information theory Numerosity Perception Rational inattention

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Area of Science:

Cognitive Science
Neuroscience
Economics

Background:

Intuition suggests attention reduces uncertainty by increasing sensory data reliability.
Rational inattention models formalize this via a cost-benefit trade-off for attention.
These models link economics to rate-distortion theory.

Purpose of the Study:

To survey the origins and applications of rational inattention models.
To investigate the role of incentives in attention and sensory data reliability.
To test rational inattention predictions with new experimental data.

Main Methods:

Literature review of rational inattention models.
Experimental study using a numerosity judgment task.
Manipulation of performance incentives to measure effects on attention and reliability.

Main Results:

People improve task performance when incentivized.
Incentives lead to increased reliability of sensory data.
Findings align with predictions from rational inattention theory.

Conclusions:

Rational inattention provides a framework for understanding how cognitive effort impacts perception.
Incentives can effectively modulate attention and improve information processing.
This research bridges economic theory with psychological and neuroscientific findings.