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Related Concept Videos

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...
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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...
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...
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...
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...

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Updated: Jun 28, 2026

Problem-Solving Before Instruction (PS-I): A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction (PS-I): A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

Multiple testing with minimal assumptions.

Peter H Westfall1, James F Troendle

  • 1Texas Tech University, Lubbock, TX, USA. peter.westfall@ttu.edu

Biometrical Journal. Biometrische Zeitschrift
|October 22, 2008
PubMed
Summary
This summary is machine-generated.

New resampling methods offer powerful and flexible multiple testing without data assumptions. These techniques control the Familywise Error Rate and apply broadly to multivariate data, including gene expression analysis.

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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

Published on: January 11, 2020

Related Experiment Videos

Last Updated: Jun 28, 2026

Problem-Solving Before Instruction (PS-I): A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction (PS-I): A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
12:18

A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment

Published on: January 11, 2020

Area of Science:

  • Statistics
  • Bioinformatics
  • Data Science

Background:

  • Multiple testing procedures are crucial for analyzing complex datasets.
  • Controlling the Familywise Error Rate (FWER) is essential to avoid false discoveries.
  • Existing methods may require strong assumptions about data distribution.

Purpose of the Study:

  • To present novel resampling-based methods for multiple testing.
  • To control the Familywise Error Rate (FWER) in the strong sense.
  • To clarify the role of subset pivotality in these procedures.

Main Methods:

  • Resampling techniques applied to multiple hypothesis testing.
  • Development of procedures with minimal to mild assumptions.
  • Analysis of multivariate, multiple group data (character or numeric).

Main Results:

  • Demonstrated powerful and flexible multiple testing procedures.
  • Showed no assumptions on the data-generating process are required.
  • Identified improvements possible with mild assumptions.
  • Clarified the subset pivotality condition.

Conclusions:

  • The presented methods offer a robust and adaptable approach to multiple testing.
  • Applicable to diverse datasets, notably gene expression data.
  • Provides a statistically sound framework without stringent prior data requirements.