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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...
Types of Hypothesis Testing01:11

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.
Multiple Comparison Tests01:13

Multiple Comparison Tests

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...
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...
Null and Alternative Hypotheses01:16

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed  the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As  a result if you cannot accept the null, it requires some action.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the population that is...
Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...

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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
12:39

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

Published on: December 10, 2012

Unscaled Bayes factors for multiple hypothesis testing in microarray experiments.

Francesco Bertolino1, Stefano Cabras2, Maria Eugenia Castellanos3

  • 1Department of Mathematics and Informatics, University of Cagliari, via Ospedale 72, Cagliari, Italy.

Statistical Methods in Medical Research
|February 17, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian approach for multiple hypothesis testing, using Bayes factors alongside p-values. The method improves control over false positives and negatives, even with small sample sizes.

Keywords:
false discovery rateimproper priorslocal false discovery rate

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Area of Science:

  • Statistics
  • Bioinformatics
  • Genomics

Background:

  • Multiple hypothesis testing commonly relies on p-values.
  • Bayesian hypothesis testing utilizes Bayes factors for evidence assessment.
  • Existing methods may have limitations in controlling error rates.

Purpose of the Study:

  • To develop a new multiple hypothesis testing procedure integrating Bayes factors and p-values.
  • To address challenges with improper priors in Bayes factor calculations.
  • To improve the accuracy of statistical inference in multiple testing scenarios.

Main Methods:

  • Multiple hypothesis testing framed as a multiple model selection problem.
  • Utilizing unscaled Bayes factors derived from default improper priors.
  • Approximating the null distribution of unscaled Bayes factors using p-value information.
  • Integrating Bayes factors into Efron's multiple testing procedure.

Main Results:

  • Unscaled Bayes factors can be effectively used in comparative multiple hypothesis testing.
  • The proposed method approximates the null distribution of unscaled Bayes factors.
  • Simulation studies show reduced false positive and false negative rates compared to p-value-only methods.
  • The approach is validated in microarray data analysis.

Conclusions:

  • The integrated Bayes factor and p-value approach offers a robust alternative for multiple hypothesis testing.
  • This method demonstrates superior performance in controlling error rates, particularly in small sample sizes.
  • The procedure is applicable to complex biological data, such as microarray experiments.