Lecture

Hypothesis Testing: Neyman-Pearson Framework

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Description

This lecture by the instructor on October 25, 2021, covers the topic of hypothesis testing, focusing on the Neyman-Pearson framework. It explains the concepts of null and alternative hypotheses, test functions, critical regions, type I and type II errors, and the likelihood ratio test. The lecture delves into the Neyman-Pearson Lemma, the most powerful test, and the challenges in choosing tests when hypotheses are not singletons. It also discusses one-sided tests, multiparameter cases, and the likelihood ratio statistic. The lecture concludes with examples and considerations for asymptotic approximations in hypothesis testing.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing

Related concepts (31)

Statistical hypothesis testing

A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .

Null hypothesis

In scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.

Alternative hypothesis

In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc.

Likelihood-ratio test

In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

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