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Related Concept Videos

P-value01:10

P-value

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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...
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Decision Making: P-value Method01:09

Decision Making: P-value Method

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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...
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Bonferroni Test01:10

Bonferroni Test

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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...
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Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

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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%...
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Fisher's Exact Test01:08

Fisher's Exact Test

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Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
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Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

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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...
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Accurate and Ultra-Efficient p-Value Calculation for Higher Criticism Tests.

Wenjia Wang1, Yusi Fang1, Chung Chang2

  • 1Department of Biostatistics, University of Pittsburgh.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|August 30, 2024
PubMed
Summary

This study introduces an efficient computational strategy for the higher criticism (HC) method, improving its use in data science for detecting weak signals. The new R package "HCp" enables large-scale inferences, including COVID-19 outbreak detection.

Keywords:
analytical approximationasymptotic rare and weak modelhigher criticismimportance samplingp-value computation

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Area of Science:

  • Data Science
  • Statistical Methods
  • Computational Statistics

Background:

  • The higher criticism (HC) method is crucial for detecting rare and weak signals in data science.
  • Computational challenges hinder HC application with large numbers of p-values or repeated tests.
  • Existing computational methods for HC have significant limitations, especially under stringent significance levels.

Purpose of the Study:

  • To develop an accurate and highly efficient computing strategy for four variations of the higher criticism (HC) method.
  • To address computational bottlenecks and numerical issues in existing HC methods.
  • To provide a scalable solution for HC applications in large-scale data analysis.

Main Methods:

  • Proposed an unbiased cross-entropy-based importance sampling method (IS) for benchmarking.
  • Developed a modified SetTest method (MST) to resolve numerical issues.
  • Introduced an ultra-fast approach (UFI) using pre-calculated tables and cubic spline interpolation.
  • Integrated MST, UFI, and existing methods into the R package "HCp".

Main Results:

  • The proposed strategy demonstrates high efficiency and accuracy for HC computations.
  • The R package "HCp" supports virtually any number of p-values and small p-values.
  • The method was successfully applied to COVID-19 surveillance for spatio-temporal outbreak detection.
  • Simulations confirmed the viability of the strategy for large-scale inferences.

Conclusions:

  • The developed computing strategy significantly enhances the applicability of the higher criticism method.
  • The "HCp" R package provides a robust tool for large-scale statistical inference.
  • The approach is effective for real-world applications like disease surveillance and outbreak detection.