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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...

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:

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: Significant Figures

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a measured value; for example, if a scale that shows weight to the nearest pound reads “140,” then the 1 (hundreds), 4 (tens), and 0 (ones) are all significant (measured) values.

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: Sep 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

Communicating uncertainty using words and numbers.

Mandeep K Dhami¹, David R Mandel²

¹Middlesex University, London, NW4 4BT, UK.

Trends in Cognitive Sciences

|April 10, 2022

Summary

This summary is machine-generated.

Communicating uncertainty effectively is crucial. While senders prefer verbal probabilities, recipients in important decisions favor precise numeric probabilities due to potential miscommunication with words.

Keywords:

communication imprecise probabilities probability risk uncertainty verbal probabilities

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Last Updated: Sep 27, 2025

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

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Published on: September 16, 2015

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

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Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Using the Threat Probability Task to Assess Anxiety and Fear During Uncertain and Certain Threat

Published on: September 12, 2014

Area of Science:

Decision Science
Risk Communication
Cognitive Psychology

Background:

Effective communication of uncertainty is vital in our information-rich world.
Senders often opt for verbal probabilities (e.g., 'likely') over numeric ones (e.g., '75% chance'), even in critical fields like climate science.
Verbal probabilities can be ambiguous and potentially exploited, impacting sender credibility and leading to miscommunication.

Purpose of the Study:

To investigate the preference and effectiveness of different probability expressions in communicating uncertainty.
To analyze the potential for miscommunication associated with verbal versus numeric probabilities.
To understand recipient preferences for probability formats in consequential decision-making.

Main Methods:

Analysis of communication strategies in uncertain domains.
Examination of sender preferences for expressing probability.
Evaluation of recipient preferences for probability formats in decision-making contexts.

Main Results:

Senders favor verbal expressions of uncertainty for ease of use and credibility management.
Verbal probabilities can be easily misunderstood, and their imprecision is not fully mitigated by associated numeric ranges.
Recipients making consequential decisions show a clear preference for precise numeric probabilities.

Conclusions:

The ease of verbal probability expression for senders contrasts with the potential for significant miscommunication.
Recipient preference for precise numeric probabilities highlights a critical gap in current uncertainty communication practices.
Improving the clarity and effectiveness of uncertainty communication requires careful consideration of both sender and recipient perspectives, favoring numeric formats for high-stakes decisions.