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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

Description:

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.

Hypotheses Testing

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#Mathematics #Statistics & Probability #Programming #Domain-Specific Languages (DSL) #R Programming