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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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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.
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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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Confidence Coefficient01:24

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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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Prediction Intervals01:03

Prediction Intervals

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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. 
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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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A Two-interval Forced-choice Task for Multisensory Comparisons
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Confidence intervals for policy evaluation in adaptive experiments.

Vitor Hadad1, David A Hirshberg2, Ruohan Zhan3

  • 1Stanford Graduate School of Business, Stanford University, Stanford, CA 94305; athey@stanford.edu vitorh@stanford.edu.

Proceedings of the National Academy of Sciences of the United States of America
|April 20, 2021
PubMed
Summary
This summary is machine-generated.

Adaptive experimental designs improve trial efficiency but can bias data. This study introduces new test statistics using adaptive reweighting to reduce variance and improve accuracy for unbiased parameter estimation.

Keywords:
adaptive experimentationcentral limit theoremfrequentist inferencemultiarmed banditspolicy evaluation

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Adaptive experimental designs enhance randomized trial efficiency.
  • However, adaptively collected data can introduce bias and heavy tails in common estimators.
  • This poses challenges for hypothesis testing, especially for parameters not directly targeted by data collection.

Purpose of the Study:

  • To develop robust test statistics for adaptive experimental designs.
  • To address bias and variance issues in estimators from adaptively collected data.
  • To enable accurate hypothesis testing for parameters not targeted by the data-collection mechanism.

Main Methods:

  • Introduced a class of test statistics for adaptive designs.
  • Employed adaptive reweighting of terms in an augmented inverse propensity-weighting estimator.
  • Controlled the contribution of each term to the estimator's variance.

Main Results:

  • The proposed reweighting scheme reduces overall variance.
  • The resulting test statistic is asymptotically normal.
  • Numerical experiments validated the accuracy of estimates and confidence intervals (CIs).

Conclusions:

  • The novel methods offer improved performance over existing alternatives.
  • Demonstrated favorable comparisons in mean squared error, coverage, and CI size.
  • Provides a statistically sound approach for analyzing data from adaptive randomized trials.