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Lecture

Statistical Hypothesis Testing

In course

MATH-232: Probability and statistics (for IC)

Cours d'introduction à la théorie des probabilités et aux statistiques. ...

Description

This lecture covers statistical hypothesis testing, focusing on confidence interval estimation, composite hypotheses, Pearson statistic, and multinomial distribution. It explains how to build confidence intervals, test adequation, and interpret p-values. The instructor discusses decision procedures, measures of evidence, and significance levels in hypothesis testing.

Instructors (2)

Raphaël Jean Berthier

Emmanuel Abbé

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing, Mathematical statistics

Related concepts (32)

Statistical significance

In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when .

Dirichlet-multinomial distribution

In probability theory and statistics, the Dirichlet-multinomial distribution is a family of discrete multivariate probability distributions on a finite support of non-negative integers. It is also called the Dirichlet compound multinomial distribution (DCM) or multivariate Pólya distribution (after George Pólya). It is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector , and an observation drawn from a multinomial distribution with probability vector p and number of trials n.

Dirichlet negative multinomial distribution

In probability theory and statistics, the Dirichlet negative multinomial distribution is a multivariate distribution on the non-negative integers. It is a multivariate extension of the beta negative binomial distribution. It is also a generalization of the negative multinomial distribution (NM(k, p)) allowing for heterogeneity or overdispersion to the probability vector. It is used in quantitative marketing research to flexibly model the number of household transactions across multiple brands.

Categorical distribution

In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified. There is no innate underlying ordering of these outcomes, but numerical labels are often attached for convenience in describing the distribution, (e.g. 1 to K).

P-value

In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience.

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