Related papers: Test statistics and p-values

A pervasive issue in statistical hypothesis testing is that the reported $p$-values are biased downward by data "peeking" -- the practice of reporting only progressively extreme values of the test statistic as more data samples are…

The e-value is swiftly rising in prominence in many applications of hypothesis testing and multiple testing, yet its relationship to classical testing theory remains elusive. We unify e-values and classical testing into a single 'continuous…

A definition for the statistical significance by constructing a correlation between the normal distribution integral probability and the p-value observed in an experiment is proposed, which is suitable for both counting experiment and…

P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for…

We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter…

Despite their importance in supporting experimental conclusions, standard statistical tests are often inadequate for research areas, like the life sciences, where the typical sample size is small and the test assumptions difficult to…

In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding…

The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…

We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…

The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often…

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

Increasing accessibility of data to researchers makes it possible to conduct massive amounts of statistical testing. Rather than follow a carefully crafted set of scientific hypotheses with statistical analysis, researchers can now test…

Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…

Increased availability of data and accessibility of computational tools in recent years have created unprecedented opportunities for scientific research driven by statistical analysis. Inherent limitations of statistics impose constrains on…

Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…

Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach…

Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need…

We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…

Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…