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Related Concept Videos

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.
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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.
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Uncertainty: Confidence Intervals00:54

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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...
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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.
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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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Critical Values

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A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
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Simultaneous confidence intervals for contrasts of quantiles.

Lawrence S Segbehoe1, Frank Schaarschmidt2, Gemechis D Djira1

  • 1Department of Mathematics and Statistics, South Dakota State University, Brookings, SD, USA.

Biometrical Journal. Biometrische Zeitschrift
|September 9, 2021
PubMed
Summary

This study introduces a new statistical method for creating simultaneous confidence intervals for quantiles, crucial for skewed data common in health and social sciences. The method performs well, offering a practical tool for analyzing complex datasets.

Keywords:
asymptoticconfidence intervalskernel densitymultiple contrastsquantiles

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Area of Science:

  • Statistics
  • Biostatistics
  • Quantitative Social Science

Background:

  • Standard statistical inference often assumes data normality, limiting its application to skewed distributions common in health and social sciences.
  • Existing methods for simultaneous inference on quantiles, especially for multiple contrasts in a one-way layout, are scarce and not user-friendly.
  • There is a need for accessible methods to analyze quantile comparisons in non-normal data.

Purpose of the Study:

  • To develop an easy-to-use asymptotic method for constructing simultaneous confidence intervals for multiple contrasts of quantiles.
  • To extend this methodology to handle right-censored time-to-event data in survival analysis.
  • To evaluate the performance of the proposed method and a bootstrap alternative.

Main Methods:

  • Development of an asymptotic statistical method for simultaneous confidence intervals.
  • Application of the method to differences and ratios of quantiles.
  • Extension to survival analysis with right-censored data.
  • Simulation studies to assess small-sample performance (coverage probabilities, interval widths).

Main Results:

  • The proposed asymptotic method provides good coverage probabilities for simultaneous confidence intervals across various distributions.
  • The method demonstrates effective performance comparable to bootstrap methods in simulations.
  • The developed statistical techniques have been implemented in a user-friendly R package.

Conclusions:

  • The new asymptotic method offers a reliable approach for constructing simultaneous confidence intervals for quantile contrasts, even with skewed data.
  • The extension to survival data enhances its applicability in health and social science research.
  • The R package facilitates the practical use of these advanced statistical techniques for data analysis.