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Related Concept Videos

Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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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%...
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Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
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Multiple Comparison Tests01:13

Multiple Comparison Tests

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Multiple comparison test, abbreviated as MCT, is a post hoc analysis generally performed after comparing multiple samples with one or more tests. An MCT will help identify a significantly different sample among multiple samples or a factor among multiple factors.
It would be easy to compare two samples using a significance alpha level of 0.05. In other words, there is only one sample pair to be compared. However, it would be difficult to identify a significantly different sample if the number...
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Bonferroni Test01:10

Bonferroni Test

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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...
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Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

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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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Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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OPTIMAL FALSE DISCOVERY RATE CONTROL FOR LARGE SCALE MULTIPLE TESTING WITH AUXILIARY INFORMATION.

Hongyuan Cao1, Jun Chen2, Xianyang Zhang3

  • 1Florida State University.

Annals of Statistics
|May 4, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical framework to improve power in large-scale multiple testing by using auxiliary information. The method enhances true positive detection while controlling the false discovery rate, outperforming existing approaches.

Keywords:
EM algorithmFalse discovery rateIsotonic regressionLocal false discovery rateMultiple testingPool-Adjacent-Violators algorithmPrimary 62G07, 62G10secondary 62C12

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Area of Science:

  • Statistical Inference
  • High-Dimensional Data Analysis
  • Bioinformatics

Background:

  • Large-scale multiple testing is a critical challenge in high-dimensional statistics.
  • Auxiliary information, reflecting hypothesis structures, is often available and can enhance statistical power.
  • Existing methods may not fully leverage available auxiliary information for optimal results.

Purpose of the Study:

  • To propose a novel framework for large-scale multiple testing that effectively utilizes auxiliary information.
  • To develop an optimal rejection rule maximizing true positives under controlled false discovery rate.
  • To improve statistical power in high-dimensional inference by incorporating structural relationships among hypotheses.

Main Methods:

  • A two-group mixture model with hypothesis-specific prior probabilities of being null.
  • A shape-constrained relationship between auxiliary information and prior null probabilities.
  • A robust Expectation-Maximization (EM) algorithm for simultaneous estimation of prior probabilities and alternative hypothesis distributions.

Main Results:

  • The proposed method demonstrates superior statistical power compared to state-of-the-art competitors.
  • The framework effectively controls the average false discovery rate.
  • Both theoretical analysis and extensive simulations confirm the method's advantages.

Conclusions:

  • The developed framework offers a powerful approach to large-scale multiple testing by integrating auxiliary information.
  • The method provides significant improvements in detecting true positives while maintaining strict error control.
  • Applicability is demonstrated using real-world data from genome-wide association studies.