**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Power of a test

Summary

In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis () when a specific alternative hypothesis () is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability of making a type II error by wrongly failing to reject the null hypothesis decreases.
Type I and type II errors
This article uses the following notation:
β = probability of a Type II error, known as a "false negative"
1 − β = probability of a "true positive", i.e., correctly rejecting the null hypothesis. "1 − β" is also known as the power of the test.
α = probability of a Type I error, known as a "false positive"
1 − α = probability of a "true negative", i.e., correctly not rejecting the null hypothesis
For a type II error probability of β, the corresponding statistical power is 1 − β. For example, if experiment E has a statistical power of 0.7, and experiment F has a statistical power of 0.95, then there is a stronger probability that experiment E had a type II error than experiment F. This reduces experiment E's sensitivity to detect significant effects. However, experiment E is consequently more reliable than experiment F due to its lower probability of a type I error. It can be equivalently thought of as the probability of accepting the alternative hypothesis () when it is true – that is, the ability of a test to detect a specific effect, if that specific effect actually exists. Thus,
If is not an equality but rather simply the negation of (so for example with for some unobserved population parameter we have simply ) then power cannot be calculated unless probabilities are known for all possible values of the parameter that violate the null hypothesis. Thus one generally refers to a test's power against a specific alternative hypothesis.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (105)

Related people (29)

Related units (7)

Related concepts (25)

Related lectures (61)

Related courses (18)

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).

Nonparametric statistics

Nonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).

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 .

Pitfalls in Empirical NLP Research

Explores pitfalls in NLP research, emphasizing the importance of standardized metrics and statistical testing.

Property Testing: Uniform Distribution

Covers property testing for uniform distributions and the importance of reliable predictions.

Understanding Statistics & Experimental Design

Provides an overview of basic probability theory, ANOVA, t-tests, central limit theorem, metrics, confidence intervals, and non-parametric tests.

BIO-449: Understanding statistics and experimental design

This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental d

MATH-131: Probability and statistics

Le cours présente les notions de base de la théorie des probabilités et de l'inférence statistique. L'accent est mis sur les concepts principaux ainsi que les méthodes les plus utilisées.

MATH-232: Probability and statistics

A basic course in probability and statistics

Roland John Tormey, Nihat Kotluk

Being able to work effectively in a team is a vital professional skill but how do students in different disciplines, engineering and hospitality, display their emotions when working together? We investigated their self-reported use of emotional labour stra ...

Despite the large body of academic work on machine learning security, little is known about the occurrence of attacks on machine learning systems in the wild. In this paper, we report on a quantitative study with 139 industrial practitioners. We analyze at ...

Cells are the smallest operational units of living systems. Through synthesis of various biomolecules and exchange of signals with the environment, cells tightly regulate their composition to realize a specific functional state. The transformation of a cel ...