The power of a statistical test is the probability that it will yield a statistically significant result given that the null hypothesis is false. In other words, it represents the chance that the study will be successful in detecting a true effect and is dependent on a number of factors, including the magnitude of the effect, the sample size and study design, and the specified false-positive ra...

Let's start with the most familiar context for pooling data (at least to students in introductory courses in statistics), viz., the pooling of sample variances in a t test of the significance of the difference between two independent sample means. The null hypothesis to be tested is that the means of two populations are equal (the populations from which the respective samples have been randomly...

Yuen's two-sample trimmed mean test statistic is one of the most robust methods to apply when variances are heterogeneous. The present study develops formulas for the sample size required for the test. The formulas are applicable for the cases of unequal variances, non-normality and unequal sample sizes. Given the specified alpha and the power (1-beta), the minimum sample size needed by the pro...

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-para...

Although the placebo effect is known to have a strong impact on the outcomes of clinical trials, methods for measuring it are limited to physiological observations. We propose a method of localizing, identifying and measuring placebo and treatment-induced networks in the brain using functional neuroimaging. Measuring the relative activation of these "placebo" brain networks serves as a proxy fo...

An advantage of the supremum log-rank over the standard log-rank statistic is an increased sensitivity to a wider variety of stochastic ordering alternatives. In this article, we develop a formula for sample size computation for studies utilizing the supremum log-rank statistic. The idea is to base power on the proportional hazards alternative, so that the supremum log rank will have the same p...

Johnson describes the lack of reproducibility of scientific studies, attributed, according to the author, to the low level of significance (1). We appreciate the quality of this work and its importance for the interpretation of statistical evidence. These results should be considered in statistical guidelines. Nevertheless, we would like to point out some important points not thoroughly discuss...

The ascertainment of the demographic and selective history of populations has been a major research goal in genetics for decades. To that end, numerous statistical tests have been developed to detect deviations between expected and observed frequency spectra, e.g., Tajima's D, Fu and Li's F and D tests, and Fay and Wu's H. Recently, Achaz developed a general framework to generate tests that det...

This procedure allows you to study the power and sample size of tests of equivalence of means of two correlated variables. Schuirmann’s (1987) two one-sided tests (TOST) approach is used to test equivalence. The paired t-test is commonly used in this situation. Other tests have been developed for the case when the data are not normally distributed. These additional tests include the Wilcoxon si...

A number of statistical tests for detecting population growth are described. We compared the statistical power of these tests with that of others available in the literature. The tests evaluated fall into three categories: those tests based on the distribution of the mutation frequencies, on the haplotype distribution, and on the mismatch distribution. We found that, for an extensive variety of...