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Sign Test for Matched Pairs01:17

Sign Test for Matched Pairs

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The sign test for matched pairs offers a robust method for comparing two paired samples, often for the effects of an intervention in one of them. This method is very useful in situations where the underlying distribution of the data is unknown. The test compares two related samples—often pre- and post-treatment measurements on the same subjects—to determine if there are significant differences in their median values.
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McNemar's Test is a nonparametric statistical test used to determine if there is a significant difference in proportions between two related groups when the outcome is binary (e.g., yes/no, success/failure). It is beneficial when we have paired data, such as pre-test/post-test designs, where the same subjects are measured under two different conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in situations where subjects are...
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A Note on the Minimax Solution for the Two-Stage Group Testing Problem.

Yaakov Malinovsky1, Paul S Albert2

  • 1Assistant Professor, Department of Mathematics and Statistics, University of Maryland, Baltimore, MD 21250.

The American Statistician
|January 3, 2017
PubMed
Summary
This summary is machine-generated.

This study addresses the group size problem in group testing when the probability of an individual being affected (p) is unknown. It offers minimax and Bayesian solutions, recommending a group size of 8-13 for practical applications.

Keywords:
Loss functionOptimal designOptimization problem

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Area of Science:

  • Statistics
  • Biotechnology
  • Genetics
  • Medical Diagnostics

Background:

  • Group testing is crucial in various fields, including medicine and genetics.
  • The traditional Dorfman procedure is widely used, but often assumes known individual probabilities.
  • In practice, the probability (p) of an individual being affected is frequently unknown.

Purpose of the Study:

  • To develop solutions for determining optimal group sizes in group testing when individual probabilities (p) are unknown.
  • To present both minimax and Bayesian approaches for the group size problem.
  • To provide practical guidance for researchers and practitioners.

Main Methods:

  • Development of minimax solutions for group size determination with unknown probability (p).
  • Application of Bayesian strategies, specifically using Jeffreys' prior, for group size optimization.
  • Analysis of group size solutions under both unbounded and upper-bounded probability constraints.

Main Results:

  • The minimax solution for group size is 8 when the probability (p) is unbounded.
  • A Bayesian strategy with Jeffreys' prior yields an optimal group size of 13.
  • Solutions are also derived for scenarios where the probability (p) is bounded.

Conclusions:

  • A group size between 8 and 13 is recommended for practical group testing when probability (p) is unconstrained.
  • The study provides justification and computational tools for practitioners.
  • This research advances group testing methodologies for scenarios with uncertain individual probabilities.