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Lecture

Statistical Tests: Wald and p-values

In course

MATH-240: Statistics

Ce cours donne une introduction au traitement mathématique de la théorie de l'inférence statistique en utilisant la notion de vraisemblance comme un thème central. ...

Description

This lecture covers the concepts of statistical tests, focusing on the Wald test and p-values. The instructor explains the calculation and interpretation of p-values, the Wald test based on likelihood, and the relationship between Neyman-Pearson and p-values. Examples and practical considerations are provided to understand the significance of test results.

Instructors (2)

Yoav Zemel

Victor Panaretos

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing

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 .

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.

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 .

Texas Instruments

Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globally. It is one of the top 10 semiconductor companies worldwide based on sales volume. The company's focus is on developing analog chips and embedded processors, which account for more than 80% of its revenue.

Martinique

Martinique (ˌmɑːrtᵻˈniːk , maʁtinik; Matinik or Matnik; Kalinago: Madinina or Madiana) is an island which is a single territorial collectivity of the French Republic. It is also part of the European Union as an Outermost Region within the Special territories of members of the European Economic Area, but is not part of the Schengen Area and the European Union Customs Union. As part of the French (Antilles) West Indies, Martinique is located in the Lesser Antilles of the West Indies in the eastern Caribbean Sea.

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