Publication

Significance Tests

Stephan Morgenthaler
2025

Abstract

A hypothesis is an unverified assumption about a phenomenon, formulated and judged to be plausible by knowledgeable persons. Studies involving carefully planned and executed experiments play a leading role in the verification process. The methods used in the analysis of the data generated in such studies have been developed by statisticians and significance tests are a part of this branch of statistics. The idea at the core of this type of tests has a lot of appeal among experimental scientists, but has aroused some controversy in the recent statistical literature. The core idea consists in comparing the actual outcomes of the experiments with the outcomes to be expected if the hypothesis were false.

Official source

https://infoscience.epfl.ch/entities/publication/a9eaa864-fc93-4509-a632-5f94461af37f

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Stephan Morgenthaler
2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/a9eaa864-fc93-4509-a632-5f94461af37f

About this result

Related concepts (25)

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 .

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 .

One- and two-tailed tests

In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis.