One of the main applications of balance indices is in tests of nullmodels of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use this statistic in tests of this kind involving trees of any size. In this paper we obtain exact formulas for the variance under the Yule model of the Sackin, the...

Using the Kalbfleisch-Prentice marginal likelihood based on Cox's regression and life model, a computationally simple method is presented for testing general linear hypotheses of the form H o : ~ §= Q. The method, which does not require estimating §, is based on partitioning the asymptotic global chi-square statistic of Cox to produce the appropriate test statistic. Under H o ' this statistic a...

BACKGROUND: Many different test statistics have been proposed to test for spatial clustering. Some of these statistics have been widely used in various applications. In this paper, we use an existing collection of 1,220,000 simulated benchmark data, generated under 51 different clustering models, to compare the statistical power of several disease clustering tests. These tests are Besag-Newell'...

We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the examples explored, it is found to be comparable to that for the χ test. We discuss briefly how it may be possible to extend this test to multi-dimensional d...

This study has been performed in order to analyze the coordinated degree and evolving trends of the land intensive use and land eco-security based on the statistical data from 1998 to 2007 in Chengdu city by Synergetios theory and dynamic coordinated degrees model. Results show that during the study period, the level of land intensive use and land ecological security both rose in Chengdu, the f...

BACKGROUND The spatial scan statistic is widely used by public health professionals in the detection of spatial clusters in inhomogeneous point process. The most popular version of the spatial scan statistic uses a circular-shaped scanning window. Several other variants, using other parametric or non-parametric shapes, are also available. However, none of them offer information about the uncert...

South Africa has a population of 51.8 million people of which 7.5% over the age of five has a disability according to the latest census data (Statistics South Africa 2014). This statistic on the national prevalence of disability should be interpreted with caution since psychosocial and neurological disabilities are not accounted for (Statistics South Africa 2014). The most recent data on disabi...

Although the κ statistic has been used widely as an indicator of rater agreement, there have been some concerns about the existence of different definitions and some peculiar results involving skewed data. This note evaluates different definitions of κ and also demonstrates that the problem with directly comparing κ values, especially for skewed data, can be avoided by comparing their significa...

BACKGROUND Spatial scan statistics are widely used for spatial cluster detection, and several parametric models exist. For continuous data, a normal-based scan statistic can be used. However, the performance of the model has not been fully evaluated for non-normal data. METHODS We propose a nonparametric spatial scan statistic based on the Wilcoxon rank-sum test statistic and compared the per...

Suppose that U is a U-statistic of degree two based on N random observations drawn without replacement from a nite population. For the distribution of a standardized version of U we construct an Edgeworth expansion with remainder O(N ?1) provided that the linear part of the statistic satisses a Cram er type condition.