A Geneaology of Correspondence Analysis: Part 2 - The Variants

In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analysethe association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development ofcorrespondence analysis across all areas of research

Modes of assessing a Student’s performance in statistical subjects – A brief look at the pro’s and con’s

The role of assessment tasks in statistics subjects plays a very important role in determining the level of understanding of the material being taught. There are many options that are available to the teacher, all of which are either beneficial or counterproductive for the students understanding of statistics. This poster will explore some of these options, and in particular, its use in first year service teaching units which is how most students learn of statistics

Where statistics teaching can go wrong

Statistics is an abstract subject and getting students motivated is, with the exception of a handful of students, a very challenging task. At present there is a growing demand in the research of Statistics teaching mainly aimed at addressing this difficulty. This paper addresses some associated problems and possible solutions to enthusiastic and dedicated teachers

Manipulating the alpha level cannot cure significance testing

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable

The Emergence and Early Evolution of Biological Carbon-Fixation

The fixation of into living matter sustains all life on Earth, and embeds the biosphere within geochemistry. The six known chemical pathways used by extant organisms for this function are recognized to have overlaps, but their evolution is incompletely understood. Here we reconstruct the complete early evolutionary history of biological carbon-fixation, relating all modern pathways to a single ancestral form. We find that innovations in carbon-fixation were the foundation for most major early divergences in the tree of life. These findings are based on a novel method that fully integrates metabolic and phylogenetic constraints. Comparing gene-profiles across the metabolic cores of deep-branching organisms and requiring that they are capable of synthesizing all their biomass components leads to the surprising conclusion that the most common form for deep-branching autotrophic carbon-fixation combines two disconnected sub-networks, each supplying carbon to distinct biomass components. One of these is a linear folate-based pathway of reduction previously only recognized as a fixation route in the complete Wood-Ljungdahl pathway, but which more generally may exclude the final step of synthesizing acetyl-CoA. Using metabolic constraints we then reconstruct a “phylometabolic” tree with a high degree of parsimony that traces the evolution of complete carbon-fixation pathways, and has a clear structure down to the root. This tree requires few instances of lateral gene transfer or convergence, and instead suggests a simple evolutionary dynamic in which all divergences have primary environmental causes. Energy optimization and oxygen toxicity are the two strongest forces of selection. The root of this tree combines the reductive citric acid cycle and the Wood-Ljungdahl pathway into a single connected network. This linked network lacks the selective optimization of modern fixation pathways but its redundancy leads to a more robust topology, making it more plausible than any modern pathway as a primitive universal ancestral form

The aggregate association index

Recently (Beh, 2008, JSPI) presented an index that helps to identify how likely two dichotomous categorical variables may be associated given only the aggregate (or marginal) information. Such an index was referred to as the aggregate association index. This paper will further consider some of the issues concerned with that index. These include variations of the original index as well as adaptations for quantifying the possibility that there exists a statistically significant positive or negative association between the two dichotomous variables

Elliptical confidence regions for simple correspondence analysis

Confidence regions for simple correspondence analysis allow for the identification of categories that are consistent with independence, and those that are not. This paper describes a procedure for constructing elliptical regions which takes into account the unequal weighting of each of the axes of the plot

Simple correspondence analysis : a bibliographic review

Over the past few decades correspondence analysis has gained an international reputation as a powerful statistical tool for the graphical analysis of contingency tables. This popularity stems from its development and application in many European countries, especially France, and its use has spread to English speaking nations such as the United States and the United Kingdom. Its growing popularity amongst statistical practitioners, and more recently those disciplines where the role of statistics is less dominant, demonstrates the importance of the continuing research and development of the methodology. The aim of this paper is to highlight the theoretical, practical and computational issues of simple correspondence analysis and discuss its relationship with recent advances that can be used to graphically display the association in two-way categorical data

Partitioning Pearson's chi-squared statistic for singly ordered two-way contingency tables

This paper presents a partition of Pearson's chi-squared statistic for singly ordered two-way contingency tables. The partition involves using orthogonal polynomials for the ordinal variable while generalized basic vectors are used for the non-ordinal variable. The benefit of this partition is that important information about the structure of the ordered variable can be identified in terms of locations, dispersion and higher order components. For the non-ordinal variable, it is shown that the squared singular values from the singular value decomposition of the transformed dataset can be partitioned into location, dispersion and higher order components. The paper also uses the chi-squared partition to present an alternative to the maximum likelihood technique of parameter estimation for the log-linear analysis of the contingency table