Neyman–Pearson theory of hypothesis testing

E212555

hypothesis testing framework statistical theory

The Neyman–Pearson theory of hypothesis testing is a foundational statistical framework that formalizes how to construct and evaluate tests for competing hypotheses using concepts like Type I and Type II errors and power.

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All labels observed (7)

Label	Occurrences
Neyman–Pearson lemma	5
Neyman–Pearson framework for hypothesis testing	1
Neyman–Pearson hypothesis testing framework	1
Neyman–Pearson lemma for simple hypotheses	1
Neyman–Pearson theory of hypothesis testing canonical	1
Neyman–Pearson theory of testing statistical hypotheses	1
On the problem of the most efficient tests of statistical hypotheses	1

How this entity was disambiguated

This entity first appeared as the object of triple T1902499 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Neyman–Pearson theory of hypothesis testing
Context triple: [Abraham Wald, contributedTo, Neyman–Pearson theory of hypothesis testing]

A. Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
B. Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
C. A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
D. The Probability Approach in Econometrics
The Probability Approach in Econometrics is Trygve Haavelmo’s landmark work that founded modern econometrics by rigorously formulating economic relationships within a probabilistic, statistical framework.
E. Innovations approach to detection and estimation
"Innovations approach to detection and estimation" is a seminal work by Thomas Kailath that develops a powerful stochastic framework for solving signal detection and parameter estimation problems, particularly in control and communication systems.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Neyman–Pearson theory of hypothesis testing
Target entity description: The Neyman–Pearson theory of hypothesis testing is a foundational statistical framework that formalizes how to construct and evaluate tests for competing hypotheses using concepts like Type I and Type II errors and power.

A. Gaussian law of error
The Gaussian law of error is a fundamental statistical principle stating that measurement errors tend to follow a normal (bell-shaped) distribution, forming the basis of much of probability theory and statistical inference.
B. Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
C. A Treatise on Probability
A Treatise on Probability is John Maynard Keynes’s influential 1921 work that develops a logical and philosophical theory of probability, challenging classical and frequency-based interpretations.
D. The Probability Approach in Econometrics
The Probability Approach in Econometrics is Trygve Haavelmo’s landmark work that founded modern econometrics by rigorously formulating economic relationships within a probabilistic, statistical framework.
E. Innovations approach to detection and estimation
"Innovations approach to detection and estimation" is a seminal work by Thomas Kailath that develops a powerful stochastic framework for solving signal detection and parameter estimation problems, particularly in control and communication systems.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	hypothesis testing framework ⓘ statistical theory ⓘ
appliesTo	composite hypotheses ⓘ simple versus simple hypothesis tests ⓘ
assumes	probabilistic model for data ⓘ repeated sampling framework ⓘ
basedOn	likelihood principle in restricted sense ⓘ
contrastsWith	Fisherian significance testing ⓘ
coreResult	Neyman–Pearson lemma for simple hypotheses ⓘ linked to: Neyman–Pearson theory of hypothesis testing
defines	acceptance region ⓘ most powerful test for simple hypotheses ⓘ power function of a test ⓘ rejection region ⓘ size of a test ⓘ
developedBy	Egon Pearson ⓘ Jerzy Neyman ⓘ
emphasizes	control of Type I error probability ⓘ maximization of power subject to size constraint ⓘ
field	mathematical statistics ⓘ statistical inference ⓘ statistics ⓘ
focusesOn	long-run error frequencies ⓘ pre-specified testing rules ⓘ
goal	construct tests with maximum power for a given significance level ⓘ
hasPart	Neyman–Pearson lemma ⓘ linked to: Neyman–Pearson theory of hypothesis testing most powerful test concept ⓘ uniformly most powerful test concept ⓘ
incompatibleWith	Bayesian decision-theoretic interpretation in strict sense ⓘ
influenced	classical statistical inference ⓘ frequentist hypothesis testing ⓘ
namedAfter	Egon Pearson ⓘ Jerzy Neyman ⓘ
provides	framework for designing critical regions ⓘ optimality criteria for hypothesis tests ⓘ
relatedTo	confidence interval construction via duality ⓘ likelihood ratio test ⓘ uniformly most powerful unbiased tests ⓘ
timePeriod	1930s ⓘ
usedIn	nonparametric hypothesis testing ⓘ parametric hypothesis testing ⓘ
usesConcept	Type I error ⓘ Type II error ⓘ alternative hypothesis ⓘ critical region ⓘ likelihood ratio ⓘ null hypothesis ⓘ significance level ⓘ test power ⓘ

How these facts were elicited