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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 't,' or...

Modified Boxplots

Modified Boxplots

A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...

Boxplot

Boxplot

Box plots (also called box-and-whisker plots or box-whisker plots) give an excellent graphical image of the concentration of the data. They also show how far the extreme values are from most data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. To construct a box plot, use a horizontal or vertical number line and a rectangular box. The...

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.

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...

Confidence Intervals

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...

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Related Experiment Video

Updated: May 7, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Contour boxplots: a method for characterizing uncertainty in feature sets from simulation ensembles.

Ross T Whitaker¹, Mahsa Mirzargar, Robert M Kirby

¹SCI Institute, University of Utah.

IEEE Transactions on Visualization and Computer Graphics

|September 21, 2013

Summary

This study introduces contour boxplots, a novel visualization method for exploring simulation ensembles. Contour boxplots effectively display variability in contour data, enhancing uncertainty quantification in scientific modeling.

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Last Updated: May 7, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

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Published on: September 7, 2019

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

Published on: October 11, 2018

Area of Science:

Computational science and engineering
Data visualization
Scientific computing

Background:

Ensembles of numerical simulations are crucial for quantifying uncertainty in fields like meteorology and solid mechanics.
Visualizing ensemble variability is challenging, often relying on direct member visualization or aggregate statistics.
Key simulation insights are frequently derived from contour or level set features, not just dense fields.

Purpose of the Study:

To introduce a novel visualization technique, contour boxplots, for exploring ensembles of contours or level sets.
To generalize the concept of data depth to contours for robust statistical analysis.
To demonstrate the application of contour boxplots for visualizing simulation data variability.

Main Methods:

Generalization of functional data depth to contours.
Development of contour boxplots based on data depth for ordering and statistical representation.
Demonstration of visualization methods for two-dimensional simulation data.

Main Results:

Successful generalization of data depth to contour data.
Introduction of contour boxplots as an effective tool for visualizing ensemble variability.
Demonstrated utility in weather forecasting and computational fluid dynamics simulations.

Conclusions:

Contour boxplots offer a powerful new method for exploring and communicating uncertainty in simulation ensembles.
This approach enhances the analysis of feature-based data derived from numerical simulations.
The technique provides a robust alternative to traditional visualization and aggregation methods for contour data.