相关论文: Note on the One and Two-Sided Z Tests

Below, we summarize the appearances and possible uses of the two-sided approach and the two-sided counting in the most diverse areas of (secondary) school mathematics.

In observational studies of discrimination, the most common statistical approaches consider either the rate at which decisions are made (benchmark tests) or the success rate of those decisions (outcome tests). Both tests, however, have…

This short note contains some definitions and formulas about the power of an observable in statistically separating different classes of events.

Null hypothesis significance testing remains popular despite decades of concern about misuse and misinterpretation. We believe that much of the problem is due to language: significance testing has little to do with other meanings of the…

We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.

The Zygmund functions form an intermediate class between Lipschitz and H\"older functions; their second order divided differences are uniformly bounded. It is well known that for $d \geq 1$ the graph of any Lipschitz function $f:\R^d…

Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…

A single parameter cubic composite test for odd positive integers is given which relies on the discriminant always being a square integer. This test has no known counterexample despite extensive verifications. As well as a comparison with…

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of…

Indirect evidence is crucial for successful statistical practice. Sometimes, however, it is better used informally. Future efforts should be directed toward understanding better the connection between statistical methods and scientific…

We revisit the problem of property testing for convex position for point sets in $\mathbb{R}^d$. Our results draw from previous ideas of Czumaj, Sohler, and Ziegler (ESA 2000). First, the algorithm is redesigned and its analysis is revised…

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…

With limited resources, scientific inquiries must be prioritized for further study, funding, and translation based on their practical significance: whether the effect size is large enough to be meaningful in the real world. Doing so must…

We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio…

The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…

The theory of testing statistical functionals is developed for non-parametric two-sample problems. For differentiable real-valued statistical functionals, some tests for the one-sided and two-sided cases are proposed and studied. The…

Two--sided bounds are constructed for a probability density function of a weighted sum of chi-square variables. Both cases of central and non-central chi-square variables are considered. The upper and lower bounds have the same dependence…

Empirical phi-divergence test-statistics have demostrated to be a useful technique for the simple null hypothesis to improve the finite sample behaviour of the classical likelihood ratio test-statistic, as well asfor model misspecification…

Statistical significance testing of differences in values of metrics like recall, precision and balanced F-score is a necessary part of empirical natural language processing. Unfortunately, we find in a set of experiments that many commonly…

Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…