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.     

Stein's Two-Stage Test in Linear Models

After a brief presentation of Stein's two-sample test there is shown an improved procedure for general linear hypotheses analogous to the improvement of the two-sample-t-test described by Stein. The example of an analysis of variance in an one-way layout demonstrates the execution of the procedure as well as the problems that occur with the determination of the test parameters n₀ and z. For these problems there is finally suggested a practicable way of solution.     

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。     

Nutrients and limiting factors

The terms nutrient and limiting factor summarise the results of an experiment in which increase in supply results in an increased response. By extension they are often — perhaps usually — used when the user believes that were such an experiment made it would have this characteristic. If the supply is further increased the response diminishes and may, eventually, become negative. Nutrient and limiting factor therefore apply, strictly, only when the circumstances are specified: they cannot be attached to a particular substance without qualification. The claim that nitrogen is a nutrient (or limiting factor) is incomplete. All nutrients are limiting factors, but the reverse is not true. The widespread belief that only one factor can limit a complex process at one time is demonstrably false in general, though it may sometimes be true in particular cases.     

应用于家畜育种试验中的组内常相关方差分析

在家畜育种中,不同杂交组合试验的比较,如果采用常规的方差分析方法,由于遗传相关的存在,来自同一家系内的样本,个体之间具有相关性,会产生第一类错误．为此,本文从理论上讨论具有组内常相关性样本的方差分析,导出了新的F检验统计量．并举例在家畜育种试验中的应用．     

Linear Discriminant Functions and Problems of Hybridization

A discriminant analysis method for frequency data for hybridization based on weighted multivariate analysis of variance is given for allotting an individual to one of groups.     

内蒙古锡林郭勒高原大针茅种群分株构件数量性状的地理变异研究

采用单因素方差分析、变异组分分析和分形几何学的原理和方法,对内蒙古锡林郭勒盟不同气候条件下的三个大针茅种群分株构件数量性状进行了研究,并结合它们所在生境特点对所得结果进行了分析。结果显示：（1）整个生长季内,不同种群大针茅营养枝高度的生长模式不同;营养枝高度和生殖枝高度在种群间差异显著,且多数变异存在于种群之间;（2）在不同生长期内,大针茅种群地上部干重与植株高度之间存在显著的分形关系;在无强度干扰的情况下,大针茅种群营养枝分形维数的大小与大针茅营养枝地上部干重的累积程度是一致的;但在长期严重干旱条件下,分形维数值表现为快速增加;（3）整个生长季内,同一生境条件下大针茅种群营养枝地上部干重与植株高度之间也存在显著的分形关系,且不同样地间分形维数值差异显著。不同生境条件下大针茅种群分株构件数量性状的差异是对所在生境长期适应、自然选择的结果。     

Increased power with modified forms of the Levene (Med) test for heterogeneity of variance

While the conventional Levene (Med) test is a widely used and robust test for detecting heterogeneity of variance, it does not take notice of either the linear dependencies among the residuals involved or the possibility of a mean (or median)-variance relationship. This paper explores the substantial improvements in power possible by investigating the benefits both of removing such linear dependencies (structural zeros) and of modeling (even roughly) such relationships.     

Techniques for the objective detection of pattern in chlorophyll samples at different temporal scales: an example using data from Lough Hyne, a seasonally stratified inlet

Chlorophyll concentrations in coastal systems are frequently variable to the extent that identifying the scales where pattern occurs is very difficult. Judgements on the temporal structure of data sets are frequently rather subjective. By examining the temporal structure of chlorophyll variation in Lough Hyne with hierarchical techniques, it was possible to identify the important temporal scales objectively. Suggestions can also be made about appropriate sampling programmes for similar coastal systems. There was significant variation in measured chlorophyll concentrations between seasons and between months within seasons. High chlorophyll concentrations were more likely during spring and autumn, as would be predicted from the seasonal cycle of stratification in the lough. Seasonality could also be detected in the tidal inflow to the lough from adjacent coastal waters. More intensive sampling during the summer did not reveal any temporal structure in surface water samples. However, there were 14 day periodicities associated with measurements of depth integrated chlorophyll, oxygen, salinity, water column stability and attenuation coefficient. It is suggested that these periodicities are consistent with spring neap tidal forcing. No interannual variation in chlorophyll concentrations was detected. Examination of the power in the analysis of variance suggested that the monthly sampling frequency was unlikely to have detected differences of less than 145% between the means of pairs of years. A sampling interval of less than a week would be needed to have confidence in detecting differences of 50% between annual means.     

Response of liver and heart trace elements in rats to the interaction between dietary zinc and iron

An analysis of the interaction between dietary iron (Fe) and zinc (Zn) was performed by using data from Sprague-Dawley rats in a 5 x 4 fully crossed factorially arranged experiment. The concentrations of 9 trace elements from the liver and 10 from the heart were determined and subjected to diverse statistical analyses and were classified by their response to the interaction between dietary Fe and Zn. The interaction was studied by using analysis of variance (ANOVA), discriminant analysis, and logistic regression to determine the direction of interaction; that is, did dietary Fe affect dietary Zn or did dietary Zn affect dietary Fe? The use of discriminant analysis allowed for using multiple parameters (rather than a single parameter) to determine possible interactions between Fe and Zn. Thus, two main levels of interaction were studied: the separate response of each tissue mineral and the response of some grouped minerals. The responses studied were the effect of dietary Zn on tissue trace element parameters, the effect of dietary Fe on the parameters, the effect of dietary Zn on combined (grouped) parameters, and the effect of dietary Fe on combined parameters. As determined by ANOVA, only three individual trace elements--liver Fe, Cu, and Mo--were significantly affected by the interaction between Fe and Zn. However, a broader interaction between Fe and Zn is revealed when groups of, rather than single, trace elements arestudied. For example, an interaction between dietary Fe and Zn affects the weighted linear combination of heart Ca, Cu, K, Mg, Mn, P, and Zn. This article presents the hypothesis that grouped parameters may be useful as status indicators. The complete dataset can be found at http://www.gfhnrc.ars. usda.gov/fezn.     

Statistical methods suitable for the analysis of plant tissue culture data

Statistical analyses are an essential part of biological research. Statistical methods are available to biological researchers that range from very simple to extremely complex. Therefore, caution should be used when selecting a statistical method. When possible it is best to avoid complicated statistical procedures that are difficult to interpret and may hinder the researcher's ability to make treatment comparisons. Instead a method should be chosen that compliments a logical and practical treatment design. Statistics should be used as a tool to compare treatments of interest and should not dictate the treatments. Experimental designs should take into account the eventual analysis, otherwise one could conceive of a design that could not be analyzed or, when analyzed, would not answer the desired questions. Therefore, time should be spent before conducting an experiment to plan an experimental design and analysis that best compliments the treatment scheme and questions to be answered. The purpose of this paper is to present examples of experimental designs, means separation procedures, data transformations and presentation methods suitable for plant cell and tissue culture data.Abbreviations ANOVA analysis of variance - BA benzyladenine - CV coefficient of variation - DF degrees of freedom - IAA indole-3-acetic acid - IBA indole-3-butyric acid - LOF lack-of-fit - MSE mean square error - P-ITB phenyl indole-3-thiolobutyrate - S standard deviation - SE standard error of the mean - TDZ thidiazuron     

巢式设计的多元分析

本文把经典巢式设计的统计分析方法由单变量推广到多变量,使得试验或调查的多性状数据能综合在一起进行分析,以得出考虑了性状间相关性在内的统计结论并用一烟草栽培试验数据示明具体步骤。     

Nuovi reperti di intersessualità nelle Cucurbitacee

Abstract

The aim of this paper is to investigate differences in plant species composition between managed and unmanaged forests, and to assess if these difference give rise to a higher plant diversity in the unmanaged forest. Furthermore our aim is to relate forest structure to differences in plant species composition, identifying the structural attributes more strongly related to the unmanaged forest vegetation. We compared an old-growth forest and a managed highforest in the Abruzzo Lazio and Molise National Park (Central Italy). Plant species composition and diversity, deadwood components and live structure have been analyzed. We used permutational multivariate analysis of variance to test the response of species composition to management factor; furthermore, we compared species richness and beta diversity. Redundancy analysis has been used to relate plant species abundances to structural variables; the importance of dead and living wood components has been compared through variation partitioning. Plant species composition proved to be significantly different in the two sites, and the old-growth stand showed a higher plant diversity. From a structural point of view, we found differences especially in the amount and quality of deadwood, and in the diameter class distribution. These variables are also the most important in determining the old-growth stand plant species composition according to redundancy analysis. Variation partitioning confirmed the greater importance of the deadwood variables. Our results suggest that including deadwood surveys in traditional forest inventories could help in finding forests with both structural and floristic old-growth properties to be considered in conservation programmes. The imitation of natural dynamics, through the creation of gaps avoiding deadwood removal, could be an effective strategy for restoring old-growth conditions, also in terms of plant diversity.     

Technical note: Measures of differentiation for quantitative traits

Studies of anthropological genetics and bioarcheology often examine the degree of among-group variation in quantitative traits such as craniometrics and anthropometrics. One comparative index of among-group differentiation is the minimum value of Wright's $F_{\mathrm{ST}}$ as estimated from quantitative traits. This measure has been used in certain population-genetic applications such as comparison with $F_{\mathrm{ST}}$ estimated from genetic data, although some inferences are limited by how well the data and study design fit the underlying population-genetic model. In many cases, all that is needed is a simple measure of among-group variation. One such measure is $R^2$, the proportion of total phenotypic variation accounted for by among-group phenotypic variation, a measure easily obtained from analysis of variance and regression methods. This paper shows that $R^2$ and minimum $F_{\mathrm{ST}}$ are closely related as $\mathrm{Min}{F}_{\mathrm{ST}}\approx R^2/\left(2-R^2\right)$. $R^2$ is computationally easy and may be useful in cases where all we need is a simple measure of relative among-group differentiation.     

Applications of a Vectorized MANOVA-Model

If the observation matrix of n independent p-dimensional normal vectors with common covariance matrix is transformed into an np-vector, linear models and hypotheses on the expectations can be formulated, that are not attainable in standard MANOVA or GMANOVA models. The distribution of an earlier proposed test procedure for this vectorized model is derived for p = 2, and its application is demonstrated for crossover and repeated measurement designs. Numerical results are compared in situations, in which both the standard and the vectorized model are applicable.     

Mathematical methods for the acquisition of changes in vecps

Procedures such as principal component analysis, autocorrelation and cross-correlation, Fourier analysis, Wiener filtering, which have been used so far for the mathematical analysis of VECP mainly serve purpose of quantization and frequency analysis of signals and the evaluation of their intraindividual and interindividual variability. Although some of the above methods are also employed for the differentiation of VECPs, it seems that methods of primarily comparative character are better suited for the classification of different signal forms. This paper reports on results obtained by multivariate analysis of variance.