Related papers: Test statistics and p-values
We theoretically analyze the problem of testing for $p$-hacking based on distributions of $p$-values across multiple studies. We provide general results for when such distributions have testable restrictions (are non-increasing) under the…
In many fields of research null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious…
The $T$-test is probably the most popular statistical test; it is routinely recommended by the textbooks. The applicability of the test relies upon the validity of normal or Student's approximation to the distribution of Student's statistic…
Nurses should rely on the best evidence, but tend to struggle with statistics, impeding research integration into clinical practice. Statistical significance, a key concept in classical statistics, and its primary metric, the p-value, are…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
In this paper, a problem of testing is discussed when the samples have been drawn from the normal distribution. The study of hypothesis testing is also extended to Baye's set up.
A definition for the statistical significance of a signal in an experiment is proposed by establishing a correlation between the observed p-value and the normal distribution integral probability, which is suitable for both counting…
The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue…
We discuss problems the null hypothesis significance testing (NHST) paradigm poses for replication and more broadly in the biomedical and social sciences as well as how these problems remain unresolved by proposals involving modified…
Mathematics is a limited component of solutions to real-world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect.…
An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.
After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for…
Standardness is a popular assumption in the literature on set estimation. It also appears in statistical approaches to topological data analysis, where it is common to assume that the data were sampled from a probability measure that…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
In traditional hypothesis testing one must pre-specify the significance level $\alpha$ to bound the `size' of the test: its probability to falsely reject the hypothesis. Indeed, a data-dependent selection of $\alpha$ would generally distort…
The randomized $p$-value, (nonrandomized) mid-$p$-value and abstract randomized $p$-value have all been recommended for testing a null hypothesis whenever the test statistic has a discrete distribution. This paper provides a unifying…