Related papers: Smaller $p$-values via indirect information
In meta analysis, multiple hypothesis testing and many other methods, p-values are utilized as inputs and assumed to be uniformly distributed over the unit interval under the null hypotheses. If data used to generate p-values have discrete…
The large-scale multiple testing inherent to high throughput biological data necessitates very high statistical stringency and thus true effects in data are difficult to detect unless they have high effect sizes. One solution to this…
Adaptive experiments use preliminary analyses of the data to inform further course of action and are commonly used in many disciplines including medical and social sciences. Because the null hypothesis and experimental design are…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
We present the expected values from p-value hacking as a choice of the minimum p-value among $m$ independents tests, which can be considerably lower than the "true" p-value, even with a single trial, owing to the extreme skewness of the…
Selective inference is a subfield of statistics that enables valid inference after selection of a data-dependent question. In this paper, we introduce selectively dominant p-values, a class of p-values that allow practitioners to easily…
The mid-p-value is a proposed improvement on the ordinary p-value for the case where the test statistic is partially or completely discrete. In this case, the ordinary p-value is conservative, meaning that its null distribution is larger…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
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…
Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…
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…
A hypothesis testing and an interval estimation are studied for the common mean of several lognormal populations. Two methods are given based on the concept of generalized p-value and generalized confidence interval. These new methods are…
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…
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…
This article addresses issues of model criticism and model comparison in Bayesian contexts, and focusses on the use of the so-called posterior predictive p-values (ppp values). These involve a general discrepancy or conflict measure and…
$\textbf{Motivation:}$ Small $p$-values are often required to be accurately estimated in large-scale genomic studies for the adjustment of multiple hypothesis tests and the ranking of genomic features based on their statistical…
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…
Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…
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…
Verifying that a statistically significant result is scientifically meaningful is not only good scientific practice, it is a natural way to control the Type I error rate. Here we introduce a novel extension of the p-value - a…