An approximate degrees of freedom test for heteroscedastic two-way ANOVA

Heteroscedastic two-way ANOVA are frequently encountered in real data analysis. In the literature, classical F-tests are often blindly employed although they are often biased even for moderate heteroscedasticity. To overcome this problem, several approximate tests have been proposed in the literature. These tests, however, are either too complicated to implement or do not work well in terms of size controlling. In this paper, we propose a simple and accurate approximate degrees of freedom (ADF) test. The ADF test is shown to be invariant under affine-transformations, different choices of contrast matrix for the same null hypothesis, or different labeling schemes of cell means. Moreover, it can be conducted easily using the usual F-distribution with one unknown degree of freedom estimated from the data. Simulations demonstrate that the ADF test works well in various cell sizes and parameter configurations but the classical F-tests work badly when the cell variance homogeneity assumption is violated. A real data example illustrates the methodologies.     

用柱面坐标系求解傅科摆运动

用柱面坐标系对傅科摆进行定量求解,简明扼要,结论直观,避免了有关文献中用复数或坐标变换求解的繁琐计算。     

A Two Sample Test for Mean Vectors with Unequal Covariance Matrices

In this paper, we consider testing the equality of two mean vectors with unequal covariance matrices. In the case of equal covariance matrices, we can use Hotelling’s T² statistic, which follows the F distribution under the null hypothesis. Meanwhile, in the case of unequal covariance matrices, the T² type test statistic does not follow the F distribution, and it is also difficult to derive the exact distribution. In this paper, we propose an approximate solution to the problem by adjusting the degrees of freedom of the F distribution. Asymptotic expansions up to the term of order N^{? 2} for the first and second moments of the U statistic are given, where N is the total sample size minus two. A new approximate degrees of freedom and its bias correction are obtained. Finally, numerical comparison is presented by a Monte Carlo simulation.     

On randomness, determinism and computability

This paper discusses the meaning and relationship of randomness and determinism. A fundamental development of chaotic dynamical systems is given with examples. Such systems are seen to exhibit randomness in the usual sense of unpredictability. The formal definition of randomness in terms of algorithmic incompressibility is also discussed. The role of recursion in computability and randomness is also discussed.     

Clinical Pastoral Education (CPE) and the Professional Identity of the Dual Degrees Student

Abstract

Students in dual degree programs have an additional task of negotiating dual professional identities. While students do this somewhat successfully, it seems they do it without any deliberate or systematic help from either their divinity or social work curricula. This article suggests that the divinity requirement for Clinical Pastoral Education (CPE) can serve as an integrating element of the curriculum and examines perceived identity blocks that may make this possible.     

F-tests with a rare pathology

ANOVA is routinely used to compare pathologies. Nevertheless, in many situations, the sample dimensions may not be known when planning the study. This is specially relevant when one of the pathologies is rare. Thus, the sample size for that pathology or for all pathologies must be considered as random. Sample selection for the non-rare pathologies may be carried out to increase the balance of the model. This leads to F-tests with random non-centrality parameters and random degrees of freedom for the errors. The distribution of such tests statistics is obtained.     

A note on the power of the f-test for testing linear hypothesis with elliptic t errors

The power of the classical .F-test for testing the regression coefficient of a general linear model with elliptic t error variable depends on the degrees of freedom of the t- distribution. In this note it is shown that the power of the F-test based on t-distribution is greater than the normal based test at smaller level of significance.     

联系度在决策中的应用

介绍了集对分析的一个重要概念——联系度，讨论了用联系度进行单个方案决策及多个方案评优决策的方法。     

水中有限长功能梯度材料圆柱壳声辐射研究

研究了径向简谐集中力激励下的水中功能梯度复合材料有限长圆柱壳的振动和声辐射问题。从有限长功能梯度材料振动方程出发，利用模态叠加法，推导出了圆柱壳在径向集中力激励下，平面振动平均振速和声辐射效率表达式。通过数值仿真计算了不同梯度指数下圆柱壳的平均振速、辐射功率和辐射效率。为功能梯度材料圆柱壳声辐射的研究提供了一种有效方法。     

论夸张修辞的“实”与“度”

关于夸张修辞的研究,目前多集中于“实”与“度”的争议,这在广告等实用言语中涉及对是艺术还是虚假的界定.产生争议的原因是,不同论者所说“实”含义不同,所说“度”也含义不同.总之“实”与“度”的概念含义区分不清.所谓夸张不能背离现实之“实”,应指被夸张事物是否具有所夸张表达的某种性质、特征;所谓言过其实之“实”,应指对事物某种性质特征夸张表达超过其可能达到的极限程度.这样,说“夸张”既要“言过其实”,又要“不能背离现实”在逻辑上才不至于矛盾.