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Related Concept Videos

Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
Decision Making: Traditional Method01:14

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
Critical Region, Critical Values and Significance Level01:16

Critical Region, Critical Values and Significance Level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the test...
Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.

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Related Experiment Video

Updated: May 9, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Statistical properties of an early stopping rule for resampling-based multiple testing.

Hui Jiang1, Julia Salzman

  • 1Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, Michigan 48109, U.S.A. , jianghui@umich.edu.

Biometrika
|July 12, 2013
PubMed
Summary

This study introduces an efficient early stopping rule for resampling-based multiple hypothesis testing. The method significantly reduces computation time with minimal impact on hypothesis rejection accuracy.

Keywords:
BootstrapEarly stoppingFalse discovery rate controlMultiple hypothesis testingResampling

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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances

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Selecting Multiple Biomarker Subsets with Similarly Effective Binary Classification Performances
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Area of Science:

  • Statistics
  • Computational Biology
  • Bioinformatics

Background:

  • Resampling methods are crucial for multiple hypothesis testing.
  • Large numbers of tests in fields like genomics lead to extensive computation times.

Purpose of the Study:

  • To develop a computationally efficient method for multiple hypothesis testing.
  • To reduce the runtime of resampling-based procedures without compromising accuracy.

Main Methods:

  • Introduced a novel early stopping rule for resampling.
  • The rule allows termination of resampling on a subset of tests.
  • Error bounds for multiple hypothesis testing were derived.

Main Results:

  • The proposed method significantly reduces computational load.
  • Demonstrated a low probability of differing rejected hypotheses compared to full resampling.
  • Simulations confirmed superior computational savings over existing methods.

Conclusions:

  • The early stopping rule offers a practical solution for large-scale multiple hypothesis testing.
  • This approach enhances the efficiency of statistical analyses in computationally intensive research areas.
  • The method provides a favorable balance between speed and statistical validity.