A Combined Invariant Test for a Null Variance Ratio

This paper investigates the properties of a test that combines the Wald and LMPI (locally most powerful invariant) tests of variance components in unbalanced mixed models. The combined test statistic is easily computed and its null distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the degree of imbalance of the design. Numerical methods are used to show that the approximation is accurate over a wide range of conditions and that the efficiency of the combined test, relative to the power envelope, is satisfactorily high overall.     

An Analysis of Variance of Nominal Data

This paper considers a common problem in analysis of variance where the responses to a set of treatments are nominal (i.e. are recorded in frequencies) with no underlying metric. Reasoning by analogy from standard analysis of variance of a two-way classification we develop chi-square tests for significance of treatments and interactions. Two tests are proposed for interaction and their asymptotic properties are studied.     

On the Application of the Analysis ct Variance in the Identification of Dadoxylon woods

This paper suggests that the analysis of variance could be used to the distinction of Da- doxylon-like woods and some quantitave characters of Dadoxylon taiyuanensis, Amyelon radicans, A. xui, A. equivius and Billigea resinosa, for example, diameter of ray cells and tracheids, height of rays, and diameter ratio of ray to tracheid, are compared and discussed. The comparision and discussion show quantitave character is more useful to identification of fossil plants than others if analysis Of variance is used.     

The Effect of Categorization on a Simple Analysis of Variance Model

Many statistical procedures assume a continuous model in spite of the fact that observations are necessarily discrete. Here we consider a simple ANOVA model—one factor with fixed effects—and assess the effect of categorisation by simulating sizes and calculating asymptotic relative efficiencies. Even for severe categorisation the effects are small.     

利用单元内方差分析法估计遗传参数的探讨

在遗传力的估计过程中,需将多种非遗传因素的影响从公畜间方差或者母畜间方差中剔除。在我国常使用的是盛志廉教授提出的单元内同胞相关法。本文对该法从理论上进行了更详细的证明,并将其推广到两层分类方差分析时的情况。同时还给出了当公母畜彼此间有亲缘关系时,利用单元内方差分析估计遗传力的方法。这些方法既可使遗传力的估计简便,又具有多因方差分析的功用。     

Causal Efficacy and the Analysis of Variance

The causal impacts of genes and environment on any one biological trait are inextricably entangled, and consequently it is widely accepted that it makes no sense in singleton cases to privilege either factor for particular credit. On the other hand, at a population level it may well be the case that one of the factors is responsible for more variation than the other. Standard methodological practice in biology uses the statistical technique of analysis of variance to measure this latter kind of causal efficacy. In this paper, I argue that: 1) analysis of variance is in fact badly suited to this role; and 2) a superior alternative definition is available that readily reconciles both the entangled-singleton and the population-variation senses of causal efficacy.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

Profile Analysis of Variance as a Tool for Analyzing Correlated Responses in Experimental Ecology

In ecological studies experiments are often designed in which the variables to be compared are not statistically independent. Examples include repeated measures of the same response by the same individual at different times, measurement of several traits on the same individual, and measurements taken from two or more types of organisms present together in the same experimental unit (e.g.) plot, cage, pond, etc.). This type of design violates several assumptions of the standard analysis of variance. These assumptions are examined and profile analysis, a modification of the standard analysis of variance which does not depend upon these assumptions, is presented. Simple instructions for performing profile analysis of variance using two common statistical packages for mainframe computers are provided in an appendix.     

生物实验数据的两因素方差分析

结合实例详细地叙述了生物实验数据的两因素方差分析计算方法,具有较强的实用意义。并介绍了如何分析计算结果。     

经纬杂交试验分析新法—一般最小二乘

经纬杂交试验主要涉及地方品种。这些品种具有两个显著特点:一是品种之内纯合程度较差,二是品种之间纯合程度不同。所以对于不同杂交组合而言,相应于观测值的误差效应不仅很大而且服从不同的分布;此时若再利用正规最小二乘进行分析,必然不能得到正确结果。本文根据客观特点,依据新的模型和最优线性无偏估计原理,对于这种试验提出了一种新的分析方法——一般最小二乘分析。这种方法只需首先估计各个组合的方差,然后用它对重复数和观测值进行校正,再按正规最小二乘分析步骤分析即可,所以并不复杂。具体使用有一实例说明。     

The Polynomial Model in the Multivariate Analysis of Variance

Assuming that the independent variables (factors) are quantitative, there exist besides the coding schemes generally used for the multivariate analysis of variance (dummy-coded or effect-coded design matrices) the so-called polynomial models. The advantage of these polynomial models are the full rank design matrices, which allow a more comprehensible analysis, i.e. the unambiguous interpretation of tested hypotheses and simultaneous confidence intervals.     

Adaptive Quantile Estimation and its Application in Analysis of Biological Signals

Quantiles and their estimations are the basis for solving numerous problems of statistics. The paper presents adaptive recursive estimation methods for this statistical parameter. Its specifical properties are investigated and the possibilities of applications in computer assisted analysis of biological signals are demonstrated even satisfying real time requirements.     

Stochastically Independent Components in the Analysis of Variance

In this paper an analysis of a sum of squares for linear hypothesis in a fixed linear model is presented. The analysis is based on a partition of sum of squares into independent components. These components are treated as sums of squares for hypotheses implied by an overall one. In the special case components of a sum of squares are distributed with one degree of freedom each and hypotheses concern single parametric functions. In the model not of full rank the form of a sum of squares is transformed before partitioning. The case of the model for cross classification is considered in details. Next the cases of the model of full rank and the one with restrictions on parameters are discussed. The model for balanced design with unweighted restrictions on parameters is considered in details. In this case sume of squares for orthogonal contrasts are obtained from analysis of the sum of squares for hypothesis concerning main or interaction effects.     

On the Use of the Shapiro‐Wilk Test in Two‐Stage Adaptive Inference for Paired Data from Moderate to Very Heavy Tailed Distributions

Paired data arises in a wide variety of applications where often the underlying distribution of the paired differences is unknown. When the differences are normally distributed, the t‐test is optimum. On the other hand, if the differences are not normal, the t‐test can have substantially less power than the appropriate optimum test, which depends on the unknown distribution. In textbooks, when the normality of the differences is questionable, typically the non‐parametric Wilcoxon signed rank test is suggested. An adaptive procedure that uses the Shapiro‐Wilk test of normality to decide whether to use the t‐test or the Wilcoxon signed rank test has been employed in several studies. Faced with data from heavy tails, the U.S. Environmental Protection Agency (EPA) introduced another approach: it applies both the sign and t‐tests to the paired differences, the alternative hypothesis is accepted if either test is significant. This paper investigates the statistical properties of a currently used adaptive test, the EPA's method and suggests an alternative technique. The new procedure is easy to use and generally has higher empirical power, especially when the differences are heavy‐tailed, than currently used methods.     

一株斜纹夜蛾核型多角体病毒毒力及基因组酶切的研究

一株斜纹夜蛾核型多角体病毒毒力及基因组酶切的研究王晓容,刘明富,刘润忠,兰萍章,张友清（中国科学院武汉病毒研究所,武汉４３００７１）关键词斜纹夜蛾,核多角体病毒,毒力测定,限制酶分析斜纹夜蛾（Ｓｐｏｄｏｐｌｅｒａｌｉｔｕｒａ）是重要的农业害虫之一。关...     

A Bootstrap Procedure for Adaptive Selection of the Test Statistic in Flexible Two‐Stage Designs

Adaptive two‐stage designs allow a data‐driven change of design characteristics during the ongoing trial. One of the available options is an adaptive choice of the test statistic for the second stage of the trial based on the results of the interim analysis. Since there is often only a vague knowledge of the distribution shape of the primary endpoint in the planning phase of a study, a change of the test statistic may then be considered if the data indicate that the assumptions underlying the initial choice of the test are not correct. Collings and Hamilton proposed a bootstrap method for the estimation of the power of the two‐sample Wilcoxon test for shift alternatives. We use this approach for the selection of the test statistic. By means of a simulation study, we show that the gain in terms of power may be considerable when the initial assumption about the underlying distribution was wrong, whereas the loss is relatively small when in the first instance the optimal test statistic was chosen. The results also hold true for comparison with a one‐stage design. Application of the method is illustrated by a clinical trial example.     

The Method of Unweighted Means in Unbalanced Analysis of Variance

For factorial experiments with unbalanced data the method of unweighted means is an alternate method of analysis which is computationally simpler than likelihood ratio based F-tests. The quality of the null approximation to the F-distribution of the statistic for the method of unweighted means and the power of this test relative to the likelihood ratio test are discussed. Recommendations are made of when in the course of data analysis the superior operating characteristics of the likelihood ratio test may not outweigh the computational simplicity of the method of unweighted means test.     

具有亲缘关系矩阵的混合模型的方差组分迭代估计——应用于计算BLUP的方差比值和遗传参数

论述的是来自非均街资料的混合模型中具有亲缘关系矩阵时利用迭代法估计方差组分问题。这篇文章表明计算程序是可行的,只要能够按照混合模型中固定效应的结构矩阵和Henderson方法3的固定效应的假设条件正确地计算二次型约化平方和,就可获得较为精确的方差组分估计值;而且表明方差初始比值k偏高或偏低,不影响迭代求解的最后结果,这是因为在迭代过程中可以通过结构矩阵x'x和x'x的控制而自行调整。这些方差组分不仅可应用于选种种畜用的BLUP计算,还可用来估计遗传参数。