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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.

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 particular...

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: 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 't,' or...

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: May 19, 2026

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

Recognition criteria vary with fluctuating uncertainty.

Joshua A Solomon¹, Patrick Cavanagh, Andrei Gorea

¹Optometry Division, Applied Vision Research Centre, City University London, UK.

Journal of Vision

|August 8, 2012

Summary

Human memory for visual orientation and size is more nuanced than previously thought. Recognition performance can exceed reproduction accuracy, suggesting confidence in memory plays a key role.

Area of Science:

Cognitive Psychology
Visual Perception

Background:

Human memory is often studied through reproduction tasks, where individuals attempt to recreate a stimulus.
Recognition tasks assess memory by presenting a probe and asking if it matches a previously seen standard.

Purpose of the Study:

To investigate whether human observers utilize information beyond explicit memory during recognition tasks.
To determine if confidence in memory reproduction influences recognition performance.

Main Methods:

Participants reproduced visual stimuli (orientation, size) from memory.
A recognition probe was presented, and participants performed a same/different task.
Simulations were used to compare human performance with an ideal observer model.

Related Experiment Videos

Last Updated: May 19, 2026

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

Main Results:

Recognition performance sometimes exceeded that of a simulated ideal observer.
Observers' ability to classify probes suggested they used information not available during reproduction.
Confidence in reproduction accuracy appears to enhance recognition.

Conclusions:

Human visual memory recognition is not solely based on explicit recall of stimulus features.
Confidence in memory reproduction acts as a valuable signal for recognition decisions.
Trial-by-trial adjustments of decision criteria based on confidence can improve recognition accuracy.