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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...

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...

The Availability Heuristic

The Availability Heuristic

A heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. Different types of heuristics are used in different types of situations, and the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

Expected Frequencies in Goodness-of-Fit Tests

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).

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Related Experiment Video

Updated: Apr 5, 2026

Dissociation of the Confounding Influences of Expectancy and Integrative Difficulty Residing in Anomalous Sentences in Event-related Potential Studies

Dissociation of the Confounding Influences of Expectancy and Integrative Difficulty Residing in Anomalous Sentences in Event-related Potential Studies

Published on: May 9, 2019

Uncertainty and Expectation in Sentence Processing: Evidence From Subcategorization Distributions.

Tal Linzen¹, T Florian Jaeger²

¹Department of Linguistics, New York University.

Cognitive Science

|August 20, 2015

Summary

Human sentence processing relies on expectations. This study found that uncertainty about the full sentence structure, not just the next word, significantly impacts reading difficulty and processing times.

Keywords:

Competition Entropy reduction Prediction Sentence processing Surprisal Uncertainty

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Published on: April 19, 2017

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

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Last Updated: Apr 5, 2026

Dissociation of the Confounding Influences of Expectancy and Integrative Difficulty Residing in Anomalous Sentences in Event-related Potential Studies

Dissociation of the Confounding Influences of Expectancy and Integrative Difficulty Residing in Anomalous Sentences in Event-related Potential Studies

Published on: May 9, 2019

Experience is Instrumental in Tuning a Link Between Language and Cognition: Evidence from 6- to 7- Month-Old Infants' Object Categorization

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Published on: April 19, 2017

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Creating Objects and Object Categories for Studying Perception and Perceptual Learning

Published on: November 2, 2012

Area of Science:

Psycholinguistics
Cognitive Science
Computational Linguistics

Background:

Human sentence processing is largely expectation-driven, relying on statistical language experience to predict upcoming syntactic structures.
Readers' uncertainty about these predictions may influence processing difficulty, but the precise role of different types of uncertainty is not fully understood.

Purpose of the Study:

To investigate how uncertainty in sentence processing affects reading times.
To differentiate the impact of uncertainty about the immediate next word versus uncertainty about the entire sentence structure on processing difficulty.

Main Methods:

A self-paced reading study was employed.
Lexical subcategorization distributions were used to manipulate expectation strength and uncertainty.
Two types of uncertainty were compared: uncertainty about the verb's complement (next step) and uncertainty about the full sentence structure.

Main Results:

Uncertainty about the full sentence structure significantly predicted processing difficulty, with greater uncertainty reduction correlating with increased reading times (RTs).
Uncertainty about the next prediction step (verb's complement) did not significantly predict processing difficulty.
Previously observed effects of expectation violation (surprisal) were replicated, independent of uncertainty effects.

Conclusions:

Both surprisal and uncertainty play roles in human sentence comprehension.
Uncertainty regarding the overall sentence structure is a key factor influencing processing difficulty, more so than immediate lexical uncertainty.