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Related Concept Videos

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...
DNA Microarrays02:34

DNA Microarrays

Microarrays are high-throughput and relatively inexpensive assays that can be automated to analyze large quantities of data at a time. They are used in genome-wide studies to compare gene or protein expression under two varied conditions, such as healthy and diseased states. Microarrays consist of glass or silica slides on which probe molecules are covalently attached through surface functionalization. Most commonly, the slides are prepared through the chemisorption of silanes to silica...
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...
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...
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...

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Methodology for Accurate Detection of Mitochondrial DNA Methylation
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Published on: May 20, 2018

A moment-based method for estimating the proportion of true null hypotheses and its application to microarray gene

Yinglei Lai1

  • 1Department of Statistics and Biostatistics Center, The George Washington University, Washington, DC 20052, USA. ylai@gwu.edu

Biostatistics (Oxford, England)
|January 25, 2007
PubMed
Summary

This study introduces a new nonparametric method for estimating true null hypotheses proportions, crucial for multiple hypothesis testing adjustments like the false discovery rate. The method offers optimal performance and addresses identifiability challenges in statistical analysis.

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Area of Science:

  • Statistics
  • Bioinformatics
  • Computational Biology

Background:

  • Advances in experimental technologies enable large-scale variable screening.
  • Multiple hypothesis testing adjustments, such as the false discovery rate, are essential.
  • Estimating the proportion of true null hypotheses is a persistent challenge due to nonparametric model identifiability issues.

Purpose of the Study:

  • To propose a novel, nonparametric method for estimating the proportion of true null hypotheses.
  • To address the identifiability problem in nonparametric models for hypothesis testing.
  • To provide a simple, explicit formula for practical application.

Main Methods:

  • A moment-based estimation method is developed.
  • Sample splitting is incorporated to enhance robustness.
  • Approximation of mixture distributions is used for heterogeneous p-value distributions.

Main Results:

  • The proposed method achieves optimal performance under homogeneous p-value distributions.
  • Identifiability is achieved even with heterogeneous p-value distributions through approximation.
  • Simulation studies demonstrate superior performance compared to existing methods.

Conclusions:

  • The developed moment-based method with sample splitting provides an effective solution for estimating true null hypothesis proportions.
  • The method is robust, nonparametric, and offers a simple explicit formula.
  • Successful application to microarray gene expression data highlights its utility in bioinformatics.