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Related Concept Videos

Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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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...
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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Known Standard Deviation01:16

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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.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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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...
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Analysis of population pharmacokinetic data involves studying the behavior of drugs within diverse populations to understand their pharmacokinetic parameters. Traditional pharmacokinetic methods typically involve collecting samples from a few individuals and estimating these parameters. While these methods are commonly used, they have limitations in capturing the variability in drug response among individuals or heterogeneous populations. Population pharmacokinetics is employed to address these...
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Interval estimation of a population mean using existing knowledge or data on effect sizes.

Changyu Shen1

  • 1Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, USA.

Statistical Methods in Medical Research
|May 9, 2018
PubMed
Summary

This study introduces a new interval estimation method, the FB interval, for medical research. It improves inferential accuracy and interpretation by using effect size knowledge, offering a hybrid approach for population mean estimation.

Keywords:
Bayesconfidence intervaleffect sizeempirical Bayesfrequentist

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Area of Science:

  • Statistics
  • Medical Research
  • Biostatistics

Background:

  • Bayes and empirical Bayes methods are common in medical research for population mean inference.
  • Existing methods often simplify joint prior distributions, complicating interpretation and potentially reducing accuracy.
  • Difficulty in specifying or estimating joint prior distributions for mean and variance parameters is a key challenge.

Purpose of the Study:

  • To propose a novel framework for interval estimation that addresses limitations of current Bayesian methods.
  • To introduce a method with an interpretable interval that combines Frequentist and Bayesian principles.
  • To develop a new quantity, the hybrid effect size, for constructing intervals when population variance is unknown.

Main Methods:

  • Developed a new interval estimation framework termed the FB interval.
  • Introduced the concept of a hybrid effect size for interval construction.
  • Utilized existing knowledge or data on effect size for parameter estimation.

Main Results:

  • The proposed FB interval offers an interpretation that aligns with both Frequentist and Bayesian statistical philosophies.
  • The hybrid effect size effectively mediates the construction of the FB interval, particularly when population variance is unknown.
  • Simulation studies and a real data example demonstrate the method's utility and performance.

Conclusions:

  • The FB interval provides a valuable alternative for population mean estimation in medical research.
  • The hybrid effect size is a key innovation for robust interval construction.
  • This framework enhances inferential accuracy and interpretability compared to traditional simplified Bayesian approaches.