相关论文: Confirming the Null: Remarks on Equivalence Testin…

There is a well-known problem in Null Hypothesis Significance Testing: many statistically significant results fail to replicate in subsequent experiments. We show that this problem arises because standard `point-form null' significance…

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…

In cell biology, statistical analysis means testing the hypothesis that there was no effect. This weak form of hypothesis testing neglects effect size, is universally misinterpreted, and is disastrously prone to error when combined with…

Randomization tests deliver exact finite-sample Type 1 error control when the null satisfies the randomization hypothesis. In practice, achieving these guarantees often requires stronger conditions than the null hypothesis of primary…

This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…

In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…

Not all experiments publish their results with a description of the correlations between the data points. This makes it difficult to do hypothesis tests or model fits with that data, since just assuming no correlation can lead to an over-…

Null hypothesis statistical significance testing (NHST) is the dominant approach for evaluating results from randomized controlled trials. Whereas NHST comes with long-run error rate guarantees, its main inferential tool -- the $p$-value --…

Statistical hypothesis testing, as formalized by 20th Century statisticians and taught in college statistics courses, has been a cornerstone of 100 years of scientific progress. Nevertheless, the methodology is increasingly questioned in…

The controversy about statistical significance vs. scientific relevance is more than 100 years old. But still nowadays null hypothesis significance testing is considered as gold standard in many empirical fields from economics and social…

The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…

The notions of null-sets and nullity are present in all discourses of mathematics. They are based on the dual-pair of notions of "almost-every" and "almost none". A notion of nullity corresponds to a choice of subsets that one interprets as…

We present a new test of hypothesis in which we seek the probability of the null conditioned on the data, where the null is a simplification undertaken to counter the intractability of the more complex model, that the simpler null model is…

This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…

The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

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…

Significance tests are probably the most extended form of inference in empirical research, and significance is often interpreted as providing greater informational content than non-significance. In this article we show, however, that…

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…

Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…