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Accuracy and Errors in Hypothesis Testing

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...

Errors In Hypothesis Tests

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.

Bonferroni Test

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 Testing

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.

Comparing Experimental Results: Student's t-Test

Comparing Experimental Results: Student's t-Test

The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic is calculated from the standard deviation, mean, and number of measurements in the data set at a selected confidence interval and then compared to a table of critical values at this confidence level. If the test statistic is smaller than the critical value, the null hypothesis is accepted. In this case, we state that the difference between the...

Multiple Comparison Tests

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...

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Related Experiment Video

Updated: Jun 16, 2026

Three Differential Expression Analysis Methods for RNA Sequencing: limma, EdgeR, DESeq2

Three Differential Expression Analysis Methods for RNA Sequencing: limma, EdgeR, DESeq2

Published on: September 18, 2021

Balancing Type One and Two Errors in Multiple Testing for Differential Expression of Genes.

Alexander Gordon¹, Linlin Chen, Galina Glazko

¹Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina, U.S.A.

Computational Statistics & Data Analysis

|February 18, 2010

Summary

This summary is machine-generated.

A novel procedure balances type I and II errors in gene expression testing. This method identifies differentially expressed genes by minimizing asymmetric distances between gene sets, improving accuracy in biological data analysis.

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Area of Science:

Bioinformatics
Statistical Genetics
Computational Biology

Background:

Significance testing for differential gene expression is crucial in genomics.
Balancing Type I and Type II errors remains a challenge in gene selection.

Purpose of the Study:

To introduce a new procedure for balancing Type I and Type II errors in differential gene expression testing.
To develop a method for selecting candidate genes that best represents multiple gene lists.

Main Methods:

A collection of gene lists, F(k), approximating differentially expressed genes is generated.
An asymmetric distance metric is introduced to measure closeness between gene lists, accounting for error costs.
An optimal gene set, S(*), is identified by minimizing the average asymmetric distance to all sets in F(k).

Main Results:

The minimization problem is solved explicitly, yielding a frequency criterion for gene inclusion.
The proposed method was tested using resampling on real microarray data with introduced expression shifts.
The procedure effectively identifies differentially expressed genes while balancing statistical error types.

Conclusions:

The new procedure offers a robust approach to significance testing for differential gene expression.
This method provides a data-driven criterion for gene selection, enhancing biological discovery.
The asymmetric distance metric allows for flexible error cost management in genomic analyses.