One of the simplest and most widely used multiple comparison tests is the Bonferroni adjustment (test). It is applicable to the following situations: 1) Regardless of whether or not the sample sizes of each group are equal. 2) When the family of interest is the particular set of comparisons (not all pair-wise comparisons). We can easily obtain the results of the Bonferroni comparison by multipl...

Testing linear combinations of normal group means with unequal variances and possibly unequal samples sizes using a t-statistic is a well known problem for which the effective degrees of freedom are unknown. ? and ? set forth their approximations based on the ratio of combinations of fourth moments, and their methodology remains the de facto standard. We propose a new approach that extends thei...

BACKGROUND In this article, we discuss the purpose of sample size calculation in clinical trials, the need for it, and the methods by which it is accomplished. Study samples that are either too small or too large are unacceptable, for clinical, methodological, and ethical reasons. The physicians participating in clinical trials should be directly involved in sample size planning, because their ...

BACKGROUND In healthcare research, outcomes with skewed probability distributions are common. Sample size calculations for such outcomes are typically based on estimates on a transformed scale (e.g. log) which may sometimes be difficult to obtain. In contrast, estimates of median and variance on the untransformed scale are generally easier to pre-specify. The aim of this paper is to describe ho...

When sample sizes are small, it becomes challenging for an asymptotic test requiring diverging to maintain accurate Type I error rate. In this paper, we consider one-sample, two-sample and ANOVA tests mean vectors when data high-dimensional but very small. We establish t-distributions of the proposed U-statistics, which only require dimensionality diverge be fixed no less than 3. The rates a wi...