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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...

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: 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: 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.

Interpretation of Confidence Intervals

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...

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Related Experiment Video

Updated: Dec 21, 2025

A Tactile Automated Passive-Finger Stimulator TAPS

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Published on: June 3, 2009

Bayesian regression explains how human participants handle parameter uncertainty.

Jannes Jegminat^1,2, Maya A Jastrzębowska^3,4, Matthew V Pachai^3,5

¹Department of Physiology, University of Bern, Bern, Switzerland.

Plos Computational Biology

|May 19, 2020

Summary

This summary is machine-generated.

Humans predict outcomes using Bayesian regression when task parameters are uncertain. This study shows people effectively integrate prior knowledge and observed data, aligning with optimal Bayesian predictions.

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Last Updated: Dec 21, 2025

A Tactile Automated Passive-Finger Stimulator TAPS

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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

Area of Science:

Cognitive neuroscience
Computational neuroscience
Human decision-making

Background:

The human brain processes sensory uncertainty using Bayes' rule.
How humans predict outcomes with uncertain generative model parameters remains unclear.

Purpose of the Study:

To investigate if and how humans incorporate parameter uncertainty in a regression task.
To compare human performance against Bayesian regression and sub-optimal models.

Main Methods:

Participants extrapolated parabolas from noisy data points.
The quadratic parameter was sampled from a bimodal prior distribution.
Human performance was evaluated against Bayesian regression and simpler computational models.

Main Results:

Human performance aligned with Bayesian regression predictions under tested conditions.
Evidence supports probability matching over Bayesian decision theory for human response generation.

Conclusions:

Humans can effectively account for parameter uncertainty in predictive tasks.
Human prediction strategies may favor probability matching when dealing with uncertainty.