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Uncertainty: Confidence Intervals00:54

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...
Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...
Confidence Intervals01:21

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...
Response Surface Methodology01:16

Response Surface Methodology

Response Surface Methodology (RSM) is a collection of statistical and mathematical techniques used to develop, improve, and optimize processes. It is particularly valuable when many input variables or factors potentially influence a response variable.
The process of RSM involves several key steps:
Uncertainty: Overview00:59

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 Intervals01:19

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: May 30, 2026

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients
07:06

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients

Published on: March 29, 2022

The dynamic Allan variance III: confidence and detection surfaces.

Lorenzo Galleani1

  • 1Politecnico di Torino, Torino, Italy. galleani@polito.it

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|August 24, 2011
PubMed
Summary

We developed confidence and detection surfaces to distinguish random clock stability fluctuations from genuine clock anomalies. This enhances the statistical significance of dynamic Allan variance (DAVAR) analysis for high-precision clocks.

Related Experiment Videos

Last Updated: May 30, 2026

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients
07:06

Binocular Dynamic Visual Acuity in Eyeglass-Corrected Myopic Patients

Published on: March 29, 2022

Area of Science:

  • Metrology and Precision Measurement
  • Statistical Signal Processing
  • Timekeeping Technology

Background:

  • The dynamic Allan variance (DAVAR) surface quantifies high-precision clock stability over time.
  • Experimental DAVAR evaluation exhibits random fluctuations due to estimation processes.
  • Differentiating these fluctuations from actual clock anomalies is crucial for reliable timekeeping.

Purpose of the Study:

  • To develop methods for assigning statistical significance to DAVAR estimator fluctuations.
  • To introduce techniques for identifying variations caused by clock anomalies.
  • To enhance the reliability of high-precision clock stability analysis.

Main Methods:

  • Development of confidence surfaces to statistically validate DAVAR estimator fluctuations.
  • Introduction of detection surfaces to identify anomalies in the DAVAR surface.
  • Validation of the proposed methods using numerical simulations.

Main Results:

  • Successfully developed confidence surfaces to quantify the statistical significance of random DAVAR fluctuations.
  • Introduced detection surfaces capable of revealing variations indicative of clock anomalies.
  • Numerical simulations confirmed the efficacy of the developed surfaces.

Conclusions:

  • The confidence and detection surfaces provide a robust framework for analyzing DAVAR data.
  • These tools enable better discrimination between noise and actual clock performance issues.
  • The findings are fundamental for advancing the stability assessment of high-precision clocks.