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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
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Types of Hypothesis Testing01:11

Types of Hypothesis Testing

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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...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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Test for Homogeneity01:23

Test for Homogeneity

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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

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The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
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Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

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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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Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models.

Rong Ma1,2,3, T Tony Cai1,2,3, Hongzhe Li1,2,3

  • 1University of Pennsylvania Perelman School of Medicine, Philadelphia, 19104 United States.

Journal of the American Statistical Association
|August 23, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new statistical tests for high-dimensional logistic regression, improving analysis of binary outcomes. The methods offer optimal performance and control false discovery rates in large-scale testing.

Keywords:
False discovery rateGlobal testingLarge-scale multiple testingMinimax lower bound

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Area of Science:

  • Statistics
  • Biostatistics
  • Genomics

Background:

  • High-dimensional logistic regression is crucial for binary outcome data analysis.
  • Challenges exist in global and multiple testing of regression coefficients in high dimensions.

Purpose of the Study:

  • To develop and evaluate novel statistical tests for global and multiple testing in high-dimensional logistic regression.
  • To establish asymptotic properties and optimality of the proposed tests.
  • To apply these methods to a real-world metabolomics dataset.

Main Methods:

  • Construction of a test statistic using generalized low-dimensional projection for bias correction.
  • Derivation of the asymptotic null distribution for global testing.
  • Development of multiple testing procedures to control False Discovery Rate (FDR) and Falsely Discovered Variables (FDV).

Main Results:

  • The proposed global test is asymptotically minimax optimal over a specific sparsity range.
  • The multiple testing procedures effectively control FDR and FDV asymptotically.
  • Simulation studies demonstrate superior performance compared to existing methods.

Conclusions:

  • The developed statistical tests provide powerful and optimal solutions for high-dimensional logistic regression.
  • These methods enhance the analysis of complex biological data, such as in metabolomics studies.
  • The approach offers robust control over errors in large-scale hypothesis testing.