Lecture

Statistical Hypothesis Testing

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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)

Emmanuel Abbé

Teaching & PhD PhD Students Denys Pushkin, Ortal Yona Senouf, Vladyslav Shashkov Past EPFL PhD Students Elisabetta Cornacchia, Aryo Lotfi Courses Reasoning in artificial intelligence MATH-700 Large language models have raised the potential of artificial intelligence in various applications, including science and mathematics, but their reasoning capabilities remain under investigations. This class focuses on defining, measuring and improving the reasoning capabilities of such AI models. Awa

Raphaël Jean Berthier

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing, Mathematical statistics

Related concepts (32)

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 .

Chi-squared test

A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in influencing the test statistic (values within the table). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof.

Student's t-test

A t-test is a type of statistical analysis used to compare the averages of two groups and determine if the differences between them are more likely to arise from random chance. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and therefore a nuisance parameter).

Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).

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 .

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