How much more evidence is there in a ‘highly significant’ p-value of 0.01 relative to one ‘just significant’ at 0.05? Why does the replication of an experiment lead, on average, to a higher p-value than the one just obtained? To answer such questions one must go beyond the traditional p-value which is conditional on the data and thus interpretable only in the context of the experiment just perf...

We consider the problem of testing each of m null hypotheses with a sequential permutation procedure in which the number of draws from the permutation distribution of each test statistic is a random variable. Each sequential permutation p-value has a null distribution that is nonuniform on a discrete support. We show how to use a collection of such p-values to estimate the number of true null h...

The projection pursuit index defined by a sum of squares of the third and the fourth sample cumulants is known as the moment index proposed by Jones and Sibson [14]. Limiting distribution of the maximum of the moment index under the null hypothesis that the population is multivariate normal is shown to be the maximum of a Gaussian random field with a finite Karhunen-Loève expansion. An approxim...

OBJECTIVES/HYPOTHESIS The present tutorial is the seventh in a series of Tutorials in Clinical Research. The specific purpose of the tutorial (Part A) and its sequel (Part B) is to introduce and explain three commonly used statistical tools for assessing contrast in the comparison between two groups. STUDY DESIGN Tutorial. METHODS The authors met weekly for 10 months discussing clinical res...

This research is motivated by one of our survey studies to assess the potential influence of introducing zebra mussels to the Lake Mead National Recreation Area, Nevada. One research question in this study is to investigate the association between the boating activity type and the awareness of zebra mussels. A chi-squared test is often used for testing independence between two factors with nomi...

The standard method for p-value computation of spatial scan statistics, with adjustments for covariate effects, is to conduct Monte Carlo simulations with these effects estimated under the null hypothesis of no clustering. However when the covariates are geographically unbalanced, the proposed Monte Carlo p-value estimates are too conservative, with corresponding loss of power, due to excessive...

In the field of psychology, the practice of p value null-hypothesis testing is as widespread as ever. Despite this popularity, or perhaps because of it, most psychologists are not aware of the statistical peculiarities of the p value procedure. In particular, p values are based on data that were never observed, and these hypothetical data are themselves influenced by subjective intentions. More...

This paper considers p-value based step-wise rejection procedures for testing multiple hypotheses. The existing procedures have used constants as critical values at all steps. With the intention of incorporating the exact magnitude of the p-values at the earlier steps into the decisions at the later steps, this paper applies a different strategy that the critical values at the later steps are d...

We derive Thouless-Anderson-Palmer (TAP) equations for quantum disordered systems. We apply them to the study of the paramagnetic and glassy phases in the quantum version of the spherical p spin-glass model. We generalize several useful quantities (complexity, threshold level, etc.) and various ideas (configurational entropy crisis, etc), that have been developed within the classical TAP approa...

We present a new method to efficiently estimate very large numbers of p-values using empirically constructed null distributions of a test statistic. The need to evaluate a very large number of p-values is increasingly common with modern genomic data, and when interaction effects are of interest, the number of tests can easily run into billions. When the asymptotic distribution is not easily ava...