In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be accep...

Increased emphasis on aircraft inspection to ensure aviation safety has resulted in the need for a better trained workforce of aircraft maintenance personnel. As almost 90% of inspection is visual in nature, it has led to the development of computer simulators to train human inspectors performing the inspection task. However, the lack of immersion and interaction has led to limited effectivenes...

The Wilcoxon-Mann-Whitney statistic is commonly used for a distribution-free comparison of two groups. One requirement for its use is that the sample sizes of the two groups are fixed. This is violated in some of the applications such as medical imaging studies and diagnostic marker studies; in the former, the violation occurs since the number of correctly localized abnormal images is random, w...

In this paper we show Whitney’s fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivial...

There are so many excellent review papers describing the principles of C o m p t o n spectrometry that they may be considered almost as a bible for anyone wishing to work in this field. Here I want to quote the book edited by Williams [1], papers by Coope r [2 -4 ] and more recent papers of Mann inen [5] and Sharma [6]. The use of circularly polarized synchrot ron radiat ion to so-called magnet...

Let {X1, . . . , Xm} and {Y1, . . . , Yn} be two samples independent of each other, but the random variables within each sample are stationary associated with one dimensional marginal distribution functions F and G, respectively. We study the properties of the classical WilcoxonMann-Whitney statistic for testing for stochastic dominance in the above set up.