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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

11.7K
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...
11.7K
Confidence Intervals01:21

Confidence Intervals

10.7K
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...
10.7K
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

10.0K
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...
10.0K
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

8.9K
A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
8.9K
The Uncertainty Principle04:08

The Uncertainty Principle

31.9K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
31.9K
Confidence Coefficient01:24

Confidence Coefficient

10.6K
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...
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Related Experiment Video

Updated: Feb 2, 2026

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

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Improving confidence intervals for normed test scores: Include uncertainty due to sampling variability.

Lieke Voncken1, Casper J Albers2, Marieke E Timmerman2

  • 1Department Psychometrics & Statistics, Faculty of Behavioural and Social Sciences, University of Groningen, Grote Kruisstraat 2/1, 9712, TS Groningen, The Netherlands. l.voncken@rug.nl.

Behavior Research Methods
|November 8, 2018
PubMed
Summary

This study introduces a new method to calculate confidence intervals (CIs) for test scores, accounting for norming uncertainty. The proposed approach using Generalized Additive Models for Location, Scale, and Shape (GAMLSS) provides more accurate CIs for continuous norming.

Keywords:
Box-Cox power exponential distributionContinuous normingGAMLSSPosterior simulationPsychological tests

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Area of Science:

  • Psychometrics
  • Statistical Modeling

Background:

  • Test publishers typically provide confidence intervals (CIs) for normed test scores, but these often only reflect test unreliability.
  • Uncertainty arising from sampling variability during the norming phase is frequently overlooked.

Purpose of the Study:

  • To propose and evaluate a flexible statistical method for calculating confidence intervals (CIs) that incorporates uncertainty due to norming variability.
  • To assess the performance of this method in continuous norming scenarios with diverse score distributions.

Main Methods:

  • Utilized Generalized Additive Models for Location, Scale, and Shape (GAMLSS) for a flexible modeling approach.
  • Conducted a comprehensive simulation study to evaluate CI quality under various conditions (e.g., sample size, predictor values, score extremity).

Main Results:

  • The proposed GAMLSS-based method demonstrated good quality of confidence intervals across most simulated conditions.
  • The method effectively addresses the uncertainty stemming from norm sampling fluctuations.

Conclusions:

  • The developed method provides a robust way to express uncertainty due to norm sampling in continuous norming.
  • Recommends adoption by test developers to enhance the accuracy of CIs and aid practitioners in fair person assessment.