Decompositions for 2-Ratios-Parameter Symmetry Model in Square Contingency Tables with Ordered Categoriesat

For square contingency tables with ordered categories, Agresti (1983) considered the linear diagonals-parameter symmetry model. An extended model including that model is proposed which has only one more parameter than that model. The model also includes the conditional symmetry model considered by McCullagh (1978). Decompositions for the proposed model and Agresti's model are given.     

A Multiplicative Model Imposed More Restrictions on the Quasi-Symmetry Model for the Analysis of Square Contingency Tables

For the analysis of square contingency tables, this note proposes a multiplicative model imposed more restrictions on CAUSSINUS ' (1965) quasi-symmetry (QS) model. The model is not so strict as in the quasi-double symmetry model considered by TOMIZAWA (1985b). The proposed model has the structure of the QS about the main diagonal plus an extended QS about the reverse diagonal of the square contingency table. The model is applied to the data on unaided vision of students in a university in Japan.     

Linear Diagonals‐Parameter Symmetry and Quasi‐Symmetry Models for Cumulative Probabilities in Square Contingency Tables with Ordered Categories

For the analysis of square contingency tables with ordered categories, Caussinus (1965) considered the quasi‐symmetry (QS) model, Goodman (1979) considered the diagonals‐parameter symmetry (DPS) model, and Agresti (1983) considered the linear diagonals‐parameter symmetry (LDPS) model. These models show the structures of symmetry for cell probabilities. Tomizawa (1993) proposed another DPS model which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. This paper proposes another LDPS and QS models that have the corresponding similar multiplicative forms for cumulative probabilities instead of cell probabilities. Special cases of the proposed models include symmetry. Two kinds of unaided distance vision data and endometrial cancer data are analyzed using these models. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contingency Table Browser ? prediction of early stage protein structure

The Early Stage (ES) intermediate represents the starting structure in protein folding simulations based on the Fuzzy Oil Drop (FOD) model. The accuracy of FOD predictions is greatly dependent on the accuracy of the chosen intermediate. A suitable intermediate can be constructed using the sequence-structure relationship information contained in the so-called contingency table − this table expresses the likelihood of encountering various structural motifs for each tetrapeptide fragment in the amino acid sequence. The limited accuracy with which such structures could previously be predicted provided the motivation for a more indepth study of the contingency table itself. The Contingency Table Browser is a tool which can visualize, search and analyze the table. Our work presents possible applications of Contingency Table Browser, among them − analysis of specific protein sequences from the point of view of their structural ambiguity.     

Apluteal development of the sea urchin Holopneustes purpurescens Agassiz (Echinodermata: Echinoidea: Euechinoidea)

The external features of a shortened, apluteal development (lacking a pluteus larva) are described. Some features are unusual for echinoids. The large egg is distinctively marked by dark and pale coloured yolk. The sperm entry point is marked by a dark yolk spot and the first cleavage plane in most embryos is through the meridian on which the sperm entry point lies. Dark yolk in the animal hemisphere segregates largely to one blastomere in the two-cell embryo and pale yolk segregates to the other as a result of yolk movements during the first cell cycle. Progeny of the pale-yolk blastomere form adult oral structures and progeny of the dark-yolk blastomere form adult aboral structures. There is no feeding planktonic pluteus larva. The gastrula develops into a demersal vestibula larva with bilateral symmetry. The plane of symmetry is coincident with the Carpenter axis that defines a plane of symmetry through the madreporite in adult echinoderms. The coincidence shows that the anterior ambulacrum is vegetal with respect to egg polarity and the interradius originating at the madreporite is animal. The bilateral symmetry of the vestibula offers insight into the origin of radial symmetry in echinoderms and the body plan of an echinoderm ancestor.     

Symmetry: A guide to its application in 2D electron crystallography

A defining property of a crystal is its symmetry. This mini-review sets out to summarize all aspects that define 2D crystallographic symmetry as applied to the study of macromolecular structure. It begins by defining molecular point symmetries, before covering crystallographic symmetry operations in 2D, common notation, a summary of crystallographic plane groups and theoretical methods and important considerations for the identification and application of symmetry in 2D crystal images for 3D structure determination. While many of the concepts covered here may be equally applicable to point symmetry and space group symmetry in 3D, this review has been written from the perspective of 2D electron crystallography and deals specifically with symmetry operations and crystallographic space groups in 2D crystal projection images.     

Post-imaging fiducial markers aid in the orientation determination of complexes with mixed or unknown symmetry

During the entry process many icosahedral viruses must adopt a lower-order symmetry or incur a symmetry mismatch to release their genome through a single site. A membrane model system in which poliovirus was bound to receptor-decorated liposomes was used to pioneer techniques that studied the break in the symmetry of the initial attachment complex by cryo-electron microscopy. Novel methods involving a fiducial marker for the membrane contact point were developed to objectively determine the symmetry of this complex and provide a starting model to initiate a bootstrap orientation refinement. Here we analyze how errors in the subjective assignment of this position affect the determination of symmetry, and the accuracy of calculating Euler angles for each raw image. In this study we have optimized the method and applied it to study the membrane-attachment complex of Semliki Forest virus (SFV), a model system for enveloped virus fusion. The resulting reconstruction of the SFV-membrane complex with a fiducial provides the first experimental evidence that this pre-fusion cell entry intermediate approaches the membrane along the viral 5-fold axis. The analysis reported here, and its subsequent application to enveloped virus fusion, indicate that this is a robust tool for solving the structures of mixed-symmetry complexes.     

Considering of certain relevant information in the analysis of contingency tables. A three-step procedure

A heuristic three-step procedure for analysing multidimensional contingency tables is given to meet the requirements of a mixed analysis from both hypotheses-ruled and data-ruled type. The first-step provides the structure of relationships among the attributes by fitting an appropriate unsaturated log-linear model to the data of the given contingency table. Restriction to elementary hierarchical models allows to get them by combining pairs of conditional independence. The result of the first step may be regarded as a certain validisation of real model ideas. In the second step the significant pairs of conditional dependence are analysed in regard to the levels of the condition complex. Only such significant pairs are to be considered, in general, where the condition complex does not include the response variable. The third-step may test special subtests in that significant two-dimensional tables found in step two or may extend the general statements by partitioning, the corresponding test statistics in additive components. Application examples demonstrate the general line of action.     

Pre-post Treatment Evaluation by Symmetry Testing in Square Contingency Table

Starting from an r × r contingency table derived from ordinal pre- and post treatment observations, the traditional Bowker symmetry test is suggested to be replaced by one of the following alternatives (1) a globals test of general improvement, (2) a set of simultaneous symmetry tests of differential improvement without assuming general improvement under H₀ and (3) a set of simultaneous symmetry tests beyond assuming general improvement under H₀. The tests are illustrated by a bivariate example of observing neuroticism and introversion binarily (+, -) before and after Rogerian psychotherapy in a sample of clients.     

Judgments of causal efficacy under constant and changing interevent contingencies

How do people judge constant and varying interevent contingencies? In two experiments, 150 college students rated the efficacy of a potential cause (an experimental fertilizer) of an effect (a plant's blooming). The prevailing probabilistic interevent relation could remain constant for the entirety of the problem or it could change without warning at the midway point: by contingency reversal, by shifting from noncontingency to contingency, or by shifting from contingency to noncontingency. Participants’ trial-by-trial ratings sensitively tracked the prevailing positive, negative, and noncontingent interevent relations, even those that entailed an unsignaled change in contingency. Changes in specific cells of the 2 × 2 contingency table differentially affected participants’ response to the altered interevent relations. All of this evidence was well described by an associative account of contingency and causal judgments.     

The origin of chirality in protein amino acids

We discuss the origin of the chirality of protein amino acids from the point of view of a phase transition from a racemic mixture into an optically pure state. We assume that Bose–Einstein condensation may act as an amplification mechanism. The original theory is due to Salam. We suggest a new role for the phase transition. Following Quack we distinguish parity violation of two kinds (de facto and de lege symmetry breaking). While the Salam phase transition corresponds to parity violation of the second kind (de lege), the phase transition we discuss in this work corresponds to parity violation of what we may call a third kind. This is suggested by recent experimental phenomena which correlate chiral symmetry breaking and pattern formation (spontaneous symmetry breaking that separates an initial racemic mixture into right- and left-handed space domains by means of a substrate). Tentative comments are given on the eventual design of possible experiments that may test this new hypothesis. © 1994 Wiley-Liss, Inc.     

The Probability Density Functions of the Contingency Coefficients,defined by KRAMER and PEARSON,in a 2-Dimensional Frequency Distribution of Grouped Bivariate Normal Variables. I

Two general measures for the degree of association in a contingency table are the contingency coefficients defined by PEARSON and KRAMER. In the case of a standardized bivariate normal distribution with correlation coefficient of the variables, whose realizations constitute the rows and columns of the table, the density functions of the two listed association measures are derived.     

Exploring contingency tables with correspondence analysis

An algorithm for correspondence analysis is described and implementedin SAS/IML (SAS Institute, 1985a). The technique is shown, throughthe analysis of several biological examples, to supplement thelog-linear models approach to the analysis of contingency tables,both in the model identification and model interpretation stagesof analysis. A simple two-way contingency table of tumor datais analyzed using correspondence analysis. This example emphasisesthe relationships between the parameters of the log-linear modelfor the table and the graphical correspondence analysis results.The technqiue is also applied to a three-way table of surveydata concerning ulcer patients to demonstrate applications ofsimple correspondence analysis to higher dimensional tableswith fixed margins. Finally, the diets and foraging behaviorsof birds of the Hubbard Brook Forest are each analyzed and thena simultaneous display of the two separate but related tablesis constructed to highlight relationships between the tables. Received on August 29, 1988; accepted on April 25, 1989     

Configural Frequency Analysis (CFA) Revisited — a New Look at an Old Approach

Configural frequency analysis (CFA) is a widely used method for the identification of types and syndromes in contingency tables. However, the type model of CFA shows some major deficiencies. In this paper, we propose an alternative modeling of types eliminating the shortcomings of CFA. Basically, a type is modeled as a combination of traits or symptoms that deviates from the pattern of association holding true for the complementary configurations of the contingency table. The new approach is formulated in terms of a log-linear model. It is shown that parameter estimation can be performed with methods known from the analysis of incomplete contingency tables. Test procedures for confirmatory analysis and methods for exploratory search for type configurations are developed. We illustrate the methodology with two practical examples.     

Identifying population units that comply with capture-recapture assumptions in an open community of alpine grasshoppers

Population units which are homogeneous with respect to capture-recapture assumptions are identified by applying 11 contingency table tests to grasshopper data according to various site, species, growth stage and sex groupings. The results of 2337 contingency table analyses have permitted a definition of the biological, spatial and temporal characteristics of those groupings which were found to be homogeneous. The same analyses suggest that dispersal rates and dispersal patterns pose the greatest single difficulty in defining population homogeneity within an open community. The effects of failures in capture-recapture assumptions are discussed in relation toJolly's 1965 stochastic model. A more detailed presentation of the study is available from the author on request.     

The Relative Power of Two Asymptotic Multivariate Tests for Homogeneity in a Contingency Table

In a three way contingency table two multivariate tests for homogeneity have been proposed by the author (1983) a the “catanova” test, which is a trace “metric” test and b the “multinova” test which is determinant based. Both tests are asymptotically distributed as chi-square. In this paper, the power values of the tests are compared and conditions are given for preference of each test.     

Chiral symmetry conservation principle

We show a chiral symmetry conservation principle based on chemical kinetics using stochastic results. Suppose the chiral symmetry conservation is evoked, and our universe can be considered globally asymmetric. In that case, there are at least two mirrored asymmetric universes if all the chiral properties are strongly correlated. However, if the chiral correlations are weak or nonexistent, there are possibly Many-(Chiral-Symmetry)-Worlds. Alternatively, if our universe is only locally asymmetric, there could be a single universe with segregated chiral regions. The possible mechanisms of the primordial chiral symmetry breaking can only be found if the chiral symmetry is not truly conserved by assuming the initial racemic conditions. In that case, our universe is asymmetric and could be alone. On the other hand, if the chiral symmetry is conserved, there is no chance of finding the primordial chiral symmetry breaking. Based on this conservation (or not), it is possible to infer two opposite hypotheses, where two general scenarios about the chiral universes are possible.     

One Degree of Freedom for Non-Additivity in a Contingency Table and Its Multivariate Extension

The paper develops a chi-square test with one degree of freedom for row-column interaction in a contingency table. Use is made of the JOHNSON-GRAYBILL [1972] model which is herein generalized to a twoway multiple response situation. Some of the merits of the new test over the better-known tests for the same hypothesis are discussed.     

Test of Independence Against a Class of Ordered Alternatives in an R × C Contingency Table

Test procedures are developed for testing the hypotheses of independence in a two-way contingency table against a class of ordered alternatives defined in terms of pooled crossproduct ratios. The alternatives hypotheses of “positive dependence” defines new notions of dependence. The distribution of the test statistics is obtained. Admissibility of the test is deduced and power comparison with some known test procedures are given. A numerical example is presented to illustrate the techniques developed.