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Testing a Claim about Population Proportion

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...

P-value

P-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. P-value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.
A large P-value calculated from the data indicates to not reject the null hypothesis. But a higher P-value does not mean that the null hypothesis is true. The smaller the P-value, the more...

Decision Making: P-value Method

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can...

Distributions to Estimate Population Parameter

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...

Testing a Claim about Mean: Unknown Population SD

Testing a Claim about Mean: Unknown Population SD

A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
Estimating a population mean requires the samples to be approximately normally distributed. The data should be collected from the randomly selected samples having no sampling bias. There is no specific requirement for sample size. But if the sample size is less than 30, and we don't know the population standard deviation, a different approach is used;...

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...

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Related Experiment Video

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Methodology for Accurate Detection of Mitochondrial DNA Methylation

Methodology for Accurate Detection of Mitochondrial DNA Methylation

Published on: May 20, 2018

A parametric model to estimate the proportion from true null using a distribution for p-values.

Chang Yu¹, Daniel Zelterman²

¹Department of Biostatistics, Vanderbilt University Medical Center, Nashville, TN 37232, U.S.A.

Computational Statistics & Data Analysis

|August 23, 2017

Summary

This summary is machine-generated.

This study derives the distribution of p-values under the alternative hypothesis for chi-squared tests. This new parametric method robustly estimates the proportion of null hypothesis p-values in microarray data.

Keywords:

distribution of p-values microarray studies mixture model proportion from the null hypothesis

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Area of Science:

Bioinformatics
Statistical genetics
Computational biology

Background:

Microarray studies yield numerous p-values from gene expression comparisons, necessitating accurate estimation of the proportion of null hypothesis p-values.
Current methods, often employing two-component mixture models, face challenges with complex data structures.
Understanding p-value distributions under alternative hypotheses is crucial for reliable statistical inference.

Purpose of the Study:

To derive the distribution of p-values under the alternative hypothesis for the chi-squared test.
To develop a novel parametric framework for estimating the proportion of null hypothesis p-values.
To evaluate the performance of the new method against existing approaches using simulations and real data.

Main Methods:

Derivation of the p-value distribution under the alternative hypothesis for the chi-squared test.
Development of a parametric estimation method utilizing this derived distribution.
Conducting simulation studies to compare the new method with five recent statistical approaches.
Application of the method to a real microarray dataset.

Main Results:

The newly derived distribution provides a basis for a robust parametric estimation of the null proportion.
Simulation studies demonstrate superior or comparable performance of the new method across various scenarios, including correlated p-values and complex mixture alternatives.
The method proved effective in analyzing a real microarray dataset, highlighting its practical utility.

Conclusions:

The derived p-value distribution under the alternative hypothesis offers a significant advancement in statistical methodology for high-dimensional data.
The proposed parametric method provides a robust and accurate approach for estimating the proportion of null hypothesis p-values in microarray analyses.
This work contributes to more reliable interpretation of gene expression data and facilitates improved biological discoveries.