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Related Concept Videos

Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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...
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...
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...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
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...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...

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Related Experiment Video

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DNA Microarrays: Sample Quality Control, Array Hybridization and Scanning
09:27

DNA Microarrays: Sample Quality Control, Array Hybridization and Scanning

Published on: March 15, 2011

Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data

Jing Qiu1, J T Gene Hwang

  • 1Department of Statistics, University of Missouri-Columbia Columbia, Missouri 65211, USA. qiujing@missouri.edu

Biometrics
|April 4, 2007
PubMed
Summary

This study introduces a new empirical Bayes method for simultaneous confidence intervals, significantly improving accuracy for large-scale parameter inference in fields like microarray analysis. The novel approach offers shorter intervals with better coverage probabilities compared to traditional methods.

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Area of Science:

  • Statistics
  • Bioinformatics
  • Genomics

Background:

  • Simultaneous inference for a large number (N) of parameters presents a significant statistical challenge.
  • In specific applications like microarray experiments, interest is often focused on inference for the K most extreme parameter estimates.
  • Developing reliable simultaneous confidence intervals for these selected parameters is crucial.

Purpose of the Study:

  • To develop a method for constructing simultaneous confidence intervals for the K most extreme parameter estimates.
  • To address the issue of low coverage probabilities associated with naive simultaneous confidence intervals.
  • To improve the efficiency and reliability of statistical inference in high-dimensional data.

Main Methods:

  • An empirical Bayes approach, also described as a random effect model, was employed.
  • The method focuses on constructing simultaneous confidence intervals for a subset of K parameters.
  • The performance was evaluated in scenarios with large N and small K, typical for genomic data.

Main Results:

  • The proposed empirical Bayes method yields simultaneous confidence intervals with improved coverage probabilities.
  • For typical microarray data parameters (N=10,000, K=100), the new intervals were found to be substantially shorter (up to 77%) than naive intervals.
  • This indicates enhanced precision and efficiency in estimation.

Conclusions:

  • The empirical Bayes approach provides a robust solution for constructing simultaneous confidence intervals for extreme parameters.
  • This method offers a significant advantage over naive approaches, particularly in high-dimensional statistical inference.
  • The findings are directly applicable to improving analyses in fields such as genomics and bioinformatics.