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Confidence Intervals01:21

Confidence Intervals

9.3K
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...
9.3K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

9.9K
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...
9.9K
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

8.8K
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...
8.8K
Prediction Intervals01:03

Prediction Intervals

2.5K
The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
2.5K
Confidence Coefficient01:24

Confidence Coefficient

9.2K
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...
9.2K
Finding Critical Values for Chi-Square01:18

Finding Critical Values for Chi-Square

3.4K
Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...
3.4K

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Related Experiment Video

Updated: May 3, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.2K

CONFIDENCE INTERVALS UNDER ORDER RESTRICTIONS.

Yongseok Park1, John D Kalbfleisch1, Jeremy M G Taylor1

  • 1University of Michigan at Ann Arbor.

Statistica Sinica
|February 8, 2014
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method for constructing confidence intervals (CIs) for ordered normal population means, improving accuracy and reducing width compared to existing techniques.

Keywords:
Elliptical unimodal distributionKey words and phrases: Convex combinationLinear orderingNormal distributionRestricted confidence interval

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Area of Science:

  • Statistics
  • Statistical Inference
  • Biostatistics

Background:

  • Constructing confidence intervals (CIs) for multiple independent normal population means under linear ordering constraints presents statistical challenges.
  • Existing methods (asymptotic distributions, likelihood ratio tests, bootstraps) exhibit limitations, especially when population means are close.

Purpose of the Study:

  • To develop a new, robust method for constructing accurate confidence intervals for ordered normal population means.
  • To address the shortcomings of traditional CI methods in constrained statistical inference problems.

Main Methods:

  • Proposed a novel approach using intermediate random variables derived from original observations.
  • Utilized CIs of these intermediate variables to refine and constrain CIs for the original population means.
  • Assessed performance under known variance ratios for two groups.

Main Results:

  • The proposed method demonstrates coverage rates that exceed and closely approximate the nominal level for two groups.
  • Simulation studies confirm that the new CIs maintain coverage rates near nominal levels while achieving reduced average widths.
  • The method was effectively illustrated using real-world data on antibiotic half-lives.

Conclusions:

  • The novel method provides improved confidence intervals for ordered normal means, outperforming traditional approaches.
  • This technique offers a more reliable statistical inference tool, particularly in scenarios with closely related population parameters.
  • The approach is practical and applicable, as shown by its successful application to antibiotic pharmacokinetic data.