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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

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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.
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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Knowing What Counts: Unbiased Stereology in the Non-human Primate Brain
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Conditionally unbiased estimation in the normal setting with unknown variances.

David S Robertson1, Ekkehard Glimm2,3

  • 1MRC Biostatistics Unit, University of Cambridge, Cambridge, UK.

Communications in Statistics: Theory and Methods
|June 21, 2019
PubMed
Summary

This study develops new statistical estimators for adaptive two-stage trials to correct selection bias, even with unknown variances and unequal sample sizes.

Keywords:
62-07Selection biasTwo-stage sampleUniformly minimum variance conditionally unbiased estimation

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Adaptive two-stage trials are crucial for efficient clinical research.
  • Selection bias can compromise the integrity of trial results.
  • Existing methods for bias correction often assume known variances, which is unrealistic.

Purpose of the Study:

  • To extend uniformly minimum variance conditionally unbiased estimators (UMVCUEs) for adaptive two-stage trials.
  • To address selection bias in settings with unknown variances.
  • To accommodate multiple selected candidates and unequal sample sizes across trial stages.

Main Methods:

  • Building upon prior work on UMVCUEs for normally distributed data with unknown common variance.
  • Developing novel estimators for scenarios involving multiple candidate selections.
  • Incorporating unequal sample sizes between the first and second stages of the trial.

Main Results:

  • The proposed UMVCUEs effectively correct for selection bias in adaptive two-stage trials.
  • The estimators are valid even when population variances are unknown.
  • The methodology accommodates complex trial designs with multiple candidates and varying sample sizes.

Conclusions:

  • The developed estimators provide a robust solution for bias correction in adaptive two-stage trials.
  • This work enhances the reliability of statistical inference in clinical trials with complex designs.
  • The findings are applicable to a broader range of practical clinical trial scenarios.