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The Karlin–Rubin Theorem for Uniformly Most Powerful 1 sided Tests
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Classroom Contents
Hypotheses Testing
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- 1 Hypotheses Testing: Statistical Nomenclature
- 2 Hypotheses Testing: Minimizing a linear combination of the type I and II errors
- 3 Hypotheses Testing: Neyman-Pearson Lemma with an Example
- 4 Hypotheses Testing: Simple vs Simple Hypotheses for a Normal Distribution
- 5 Hypotheses Testing: Simple vs Simple Hypotheses for Gamma and Poisson Distributions
- 6 Hypotheses Testing: R Simulation of Simple vs Simple Testing for a Gamma and Poisson Distributions
- 7 Testing for a Biased Die with an Approximate Alpha Level Test
- 8 Prove Pearson's Goodness of Fit Test Statistic limits to a Chi-sq Distribution
- 9 R Simulation Comparing 2 Tests. Goodness of Fit versus Normal Approximation to Test a Biased Die.
- 10 Bayesian Test for Simple vs Simple Hypotheses
- 11 Minimax Test for Simple vs Simple Hypotheses
- 12 Example with Most Powerful, Bayesian, and Minimax Test with Normal Data
- 13 Example with Gamma Data - Most Powerful, Bayesian, and Minimax Tests
- 14 Monotone Likelihood Ratio Property
- 15 Monotone Likelihood Ratio - Examples
- 16 Hypergeometric Distribution has the monotone likelihood ratio property
- 17 Illustration of a 1-sided UMP Test in the Normal Setting
- 18 The Karlin–Rubin Theorem for Uniformly Most Powerful 1 sided Tests
- 19 Corollary to the Neyman-Pearson Lemma: alpha less than power
- 20 Illustration of a 2 sided UMP test (part 1 of 3)
- 21 Illustration of a 2 sided UMP test (part 2 of 3)
- 22 Illustration of a 2 sided UMP test (part 3 of 3)
- 23 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 1 of 8): Normal Distribution
- 24 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 2 of 8): Using R Normal Distribution
- 25 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 3 of 8): Chi-square Distribution
- 26 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 4 of 8): Using R Chi-sq Distribution
- 27 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 5 of 8): Binomial Distribution
- 28 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 6 of 8): Using R Binomial Distribution
- 29 Comparing Adverse Event Rates Between Treatment Arms
- 30 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 7 of 8): Poisson Distribution
- 31 2-sided UMP Tests in the 1-Parameter Exponential Family (Part 8 of 8): Using R Poisson Distribution
- 32 A Generalization of the Neyman-Pearson Lemma
