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Related Concept Videos

Bootstrapping01:24

Bootstrapping

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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Confidence Intervals01:21

Confidence Intervals

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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...
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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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Margin of Error01:27

Margin of Error

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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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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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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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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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Updated: Nov 29, 2025

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
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Interval Estimation for Minimal Clinically Important Difference and its Classification Error via a Bootstrap Scheme.

Zehua Zhou1, Jiwei Zhao1, Melissa Kluczynski2

  • 1Department of Biostatistics, School of Public Health and Health Professions, State University of New York at Buffalo, 3435 Main Street, Buffalo, NY 14214, United States.

Statistical Theory and Related Fields
|November 23, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a novel bootstrap method for estimating the minimal clinically important difference (MCID) and its accuracy. This approach provides interval estimations, improving upon existing point estimation methods for clinical trial analysis.

Keywords:
BootstrapClassification errorConfidence intervalMinimal clinically important differenceNon-convex optimizationm-out-of-n bootstrap

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Area of Science:

  • Clinical research methodology
  • Statistical analysis in healthcare
  • Patient-reported outcomes

Background:

  • Clinical researchers increasingly use minimal clinically important difference (MCID) over statistical significance for treatment effectiveness.
  • Patient-reported outcome data is more accessible, enhancing clinical relevance.
  • Current MCID determination methods, based on diagnostic measurements and large margin classification, provide only point estimations.

Purpose of the Study:

  • To introduce a novel bootstrap approach for estimating MCID.
  • To provide interval estimations for MCID and its classification error.
  • To develop an associated accuracy measure for performance assessment of MCID estimation.

Main Methods:

  • An m-out-of-n bootstrap approach is proposed.
  • The method provides interval estimations for MCID.
  • Classification error and accuracy measures are derived from the bootstrap intervals.

Main Results:

  • The proposed bootstrap method yields interval estimations for MCID.
  • The method allows for the assessment of MCID estimation performance through classification error and accuracy.
  • Simulation studies demonstrate the advantages of the proposed method.

Conclusions:

  • The m-out-of-n bootstrap approach offers a robust method for interval estimation of MCID.
  • This technique enhances the performance assessment of MCID in clinical trials.
  • The method was illustrated using data from the chondral lesions and meniscus procedures (ChAMP) trial.