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Hypotheses Testing

statisticsmatt via YouTube

Overview

Dive into a comprehensive 6-hour tutorial on hypotheses testing, covering statistical nomenclature, error minimization, and the Neyman-Pearson Lemma. Explore simple vs. simple hypotheses for various distributions, including Normal, Gamma, and Poisson. Learn to test for biased dice, prove Pearson's Goodness of Fit Test, and compare different testing methods through R simulations. Examine Bayesian and Minimax tests, the monotone likelihood ratio property, and uniformly most powerful tests. Investigate 2-sided UMP tests in the 1-parameter exponential family for Normal, Chi-square, Binomial, and Poisson distributions, with practical applications using R. Conclude with a generalization of the Neyman-Pearson Lemma, providing a thorough understanding of advanced hypotheses testing concepts and techniques.

Syllabus

Hypotheses Testing: Statistical Nomenclature.
Hypotheses Testing: Minimizing a linear combination of the type I and II errors.
Hypotheses Testing: Neyman-Pearson Lemma with an Example.
Hypotheses Testing: Simple vs Simple Hypotheses for a Normal Distribution.
Hypotheses Testing: Simple vs Simple Hypotheses for Gamma and Poisson Distributions.
Hypotheses Testing: R Simulation of Simple vs Simple Testing for a Gamma and Poisson Distributions.
Testing for a Biased Die with an Approximate Alpha Level Test.
Prove Pearson's Goodness of Fit Test Statistic limits to a Chi-sq Distribution.
R Simulation Comparing 2 Tests. Goodness of Fit versus Normal Approximation to Test a Biased Die..
Bayesian Test for Simple vs Simple Hypotheses.
Minimax Test for Simple vs Simple Hypotheses.
Example with Most Powerful, Bayesian, and Minimax Test with Normal Data.
Example with Gamma Data - Most Powerful, Bayesian, and Minimax Tests.
Monotone Likelihood Ratio Property.
Monotone Likelihood Ratio - Examples.
Hypergeometric Distribution has the monotone likelihood ratio property.
Illustration of a 1-sided UMP Test in the Normal Setting.
The Karlin–Rubin Theorem for Uniformly Most Powerful 1 sided Tests.
Corollary to the Neyman-Pearson Lemma: alpha less than power.
Illustration of a 2 sided UMP test (part 1 of 3).
Illustration of a 2 sided UMP test (part 2 of 3).
Illustration of a 2 sided UMP test (part 3 of 3).
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 1 of 8): Normal Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 2 of 8): Using R Normal Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 3 of 8): Chi-square Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 4 of 8): Using R Chi-sq Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 5 of 8): Binomial Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 6 of 8): Using R Binomial Distribution.
Comparing Adverse Event Rates Between Treatment Arms.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 7 of 8): Poisson Distribution.
2-sided UMP Tests in the 1-Parameter Exponential Family (Part 8 of 8): Using R Poisson Distribution.
A Generalization of the Neyman-Pearson Lemma.

Taught by

statisticsmatt

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