Applications and Tabulations of the Multivariate t Distribution with ρ = 0

Quantiles of the multivariate t distribution with ρ = 0 are tabulated. Some applications are discussed.     

A Multivariate Procedure for Comparing Mean Vectors for Populations with Unequal Regression Coefficient and Residual Covariance Matrices

In fisheries research there is a need to compare vectors of means of continuous random response variables adjusted for concomitant variations of covariables for populations that have unequal regression coefficient and residual covariance matrices. A multivariate procedure that provides an extended comparison of vectors of adjusted means is presented. An example is presented using a real data set. The procedure is quite general and applicable to many other fields of research.     

A Note on Measures of Multivariate Kurtosis

We propose a measure of multivariate kurtosis suggested from Mardia's measure of multivariate skewness b₁,p, and examine its relationship both to Mardia's measure of multivariate kurtosis b₂,p, and to a smooth test of multivariate kurtosis ǔ₄².     

Optimum Design in Multivariate Stratified Sampling

The procedure of determining the optimum sample size in each stratum in stratified sampling for several variables is expressed and solved as a multistage decision process through dynamic programming. Using data published elsewhere, the dynamic programming approach was shown to give results identical to those obtained by some other already suggested approaches. The advantage is that dynamic programming can more easily handle problems involving several strata and/or variables.     

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.     

On the Performance of the SPRT for Correlation Coefficient: Normal and Mixtures of Normal Populations

The sequential probability ratio test (SPRT) for the correlation coefficient is examined in the normal and non-normal situations. In the latter case, we evaluate the robustness of the normal procedure when sampling from the mixtures of normal distributions. Two models are introduced for this type of nonnormality. It is shown that in the case of moderate nonnormality, the normal procedure is robust while for extreme nonnormality, the normal procedure is not recommended.     

Multivariate analysis of Gigantopithecus mandibles

Multivariate analysis of measurements of the teeth and mandibles of Gigantopithecus species has been conducted, using several methods. Results indicate Gigantopithecus is an aberrant form, less related to australopithecines and gorillas than the latter are to each other. Gracile and robust australopithecines differ considerably more than do male and female gorillas.     

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。     

Multivariate regression trees for analysis of abundance data

Multivariate regression tree methodology is developed and illustrated in a study predicting the abundance of several cooccurring plant species in Missouri Ozark forests. The technique is a variation of the approach of Segal (1992) for longitudinal data. It has the potential to be applied to many different types of problems in which analysts want to predict the simultaneous cooccurrence of several dependent variables. Multivariate regression trees can also be used as an alternative to cluster analysis in situations where clusters are defined by a set of independent variables and the researcher wants clusters as homogeneous as possible with respect to a group of dependent variables.     

Multivariate analysis of polypeptide synthesis in field-grown maize inbreds and hybrids

Summary A leaf disc method is described to permit the localized incorporation of ³⁵S-l-methionine into polypeptides synthesized in individual leaves of maize plants grown in the field. The method of incorporation employs minimal external manipulation of the intact leaf, is simple, repeatable, and may be used at any plant age after leaf emergence. Incorporation (cpm/g protein) in 12 leaves per plant was compared among three inbred (Oh43, W23, M14) and three F₁ hybrid (Oh43/M14, W23/M14, Oh43/W23) genotypes. The incorporation was 40% higher (hybrid versus inbred) in 9 of the 12 leaves studied. Samples from leaf 07 (7th leaf numbered from base of plant) for four inbreds (Oh43, M14, B73, Mol 7) and two pairs of reciprocal F₁ hybrids (Oh43/M14, M14/Oh43; B73/Mo17, Mo17/B73) were labelled in situ using the leaf disc method. Each cultivar was sampled at three different ages in each of 1985, 1986, and 1987. High-resolution, two-dimensional isoelectric focusing sodium-dodecyl-sulfate polyacrylamide gel electrophoresis and fluorography were used to display the polypeptides synthesized in the samples. Multivariate methods — Principal Coordinate Analysis, Cluster Analysis, and Standard Deviation Distance — were used to analyze variation and to identify trends in the variation for year, genotype, and age sampled. Our analyses disclose a hierarchy to polypeptide synthesis variation in maize leaves: differences in polypeptide synthesis are greater for year-to-year comparisons than differences due to sample age, which in turn are greater than differences for inbred versus hybrid comparisons.     

A Class of Multivariate Survival Functions Characterized by Minimum and Marginal Distribution

This paper characterizes a class of multivariate survival functions in terms of the minimum and marginal distributions.     

Multivariate analysis of bacterial volatile compound profiles for discrimination between selected species and strains in vitro

Volatile compounds (VCs) are produced by all microorganisms as part of their normal metabolism. The aim of this study was to determine whether bacterial VC profiles could be used to discriminate between selected bacterial species and strains in vitro.Selected Ion Flow Tube Mass Spectrometry (SIFT-MS) was used to quantify the concentration of 23 microbial VCs within the head-space of various bacterial monocultures, during both the logarithmic and stationary growth phases. In comparison with existing techniques, SIFT-MS enables quantitative, high throughput, real-time head-space analysis to be performed, without need for sample preparation. The results show that most VCs were produced by > 1 bacterial species or strain, and some were produced by all strains tested. Multivariate analysis using similarity matrices, cluster analysis and multidimensional scaling (MDS) was used to determine whether there was a characteristic VC profile at either the species or strain level. Significant discrimination of all bacterial species and strains was achieved by analysing the VC profiles, and the relative similarity of VC profiles could be differentiated in 2 or 3 dimensional space. This study has shown that there are significant differences in the volatile profiles obtained from various bacterial monocultures grown in vitro, and that the analysis techniques herein employed have the potential to differentiate samples at the strain level.     

Multivariate analysis of anthropometric data and classifications of British Columbian natives

Anthropometric data collected in native populations of British Columbia in the late 19th century by Franz Boas were analyzed by two multivariate techniques. Multivariate analysis of variance was used to test physical classificatory units devised by Boas and an ad hoc classification based on local cultural units. Both were found to have some empirical validity. Mahalanobis' D (Mahalanobis, '30) was computed between pairs of local groups, for both sexes. From these a matrix of differences was prepared and diagrams drawn to illustrate phenetic relationships among samples. By this means one cluster of groups, Interior B.C. peoples, could be distinguished and other local samples appeared distinctly different from each other. It was concluded that in the absence of genealogical data by which to identify local populations, local cultural units are preferable to more inclusive units for making empirical comparisons and classifications.     

On Kernel Methods of Estimating Marginal Radial and Angular Probability Density Functions

Spatial point patterns which possess a natural origin are considered. Two ways of estimating the marginal radial and angular probability density functions associated with the stochastic process underlying such a pattern are presented. These methods are based on one and two-dimensional kernel functions respectively. The angular density estimate can be used to detect angular trend and to test for angular uniformity within a particular sector about the origin. The two methods of estimation produce essentially the same results. That based on the one-dimensional kernel is recommended because it is computationally simpler.     

Multivariate analysis of vegetational variation in different habitats at Omayed,Egypt

The application of indicator species analysis has proved useful in classifying stands into groupings coinciding with topographic variations. 41 indicator pseudo-species are identified in the vegetation along a phytosociological gradient: some are characteristic of specific habitats, and the others indicate transition between groups of habitats.The use of qualitative estimations (transformed density records) in multivariate analysis in the present study indicates that they may be more preferable than quantitative estimations, because of their easy and fast recording in the field, and the less comprehensive computations, while yielding precise results.The X-axis of the reciprocal averaging ordination is related to the salinity and fertility gradients, while the Y-axis reflects soil texture.The phytosociological gradients of the canonical variate axes reflect essentially contrasts between groups of species, each correlated with one or the other of the environmental gradients.Comparing the results obtained by the two ordination methods (reciprocal averaging and canonical variates) we find that the first method detects the overall phytosociological changes along strong environmental gradients which would be helpful in studying large surveys. On the other hand, the second technique, which is mainly predictive, is more sensitive to changes within both the phytosociological and environmental gradients and can detect the impact of these changes on the overall variance of each gradient.Nomenclature follows Täckholm (1964).The authors are grateful to Dr J. Jeffers and Mr and Mrs P. Howard of the Institute of Terrestrial Ecology, England, for their help with applying the multivariate techniques to the vegetation data.     

Multivariate analyses of polypeptide synthesis in developing maize embryos

Summary Variation in polypeptide synthesis was examined in developing maize embryos of two inbred and two hybrid genotypes. Multivariate analyses were used to evaluate the variation among two-dimensional, electrophoretic separations of polypeptides. Several features of the data set were revealed. Similar developmental patterns were exhibited by all genotypes and no evidence was obtained for differential rates of development for inbreds and hybrids. The differential synthesis of two subsets of polypeptides during embryo development was observed. The multivariate methods employed in this study were a valuable aid in interpreting the results from a large and complex data set.