The adequacy of different robust statistical tests in comparing two independent groups

In the current study, we evaluated various robust statistical methods for comparing two independent groups. Two scenarios for simulation were generated: one of equality and another of population mean differences. In each of the scenarios, 33 experimental conditions were used as a function of sample size, standard deviation and asymmetry. For each condition, 5000 replications per group were generated. The results obtained by this study show an adequate type error I rate but not a high power for the confidence intervals. In general, for the two scenarios studied (mean population differences and not mean population differences) in the different conditions analysed, the Mann-Whitney U-test demonstrated strong performance, and a little worse the t-test of Yuen-Welch.

Aprendizaje elemental a pesar de entrenamiento configuracional en una tarea de navegación

Se entrenó a unas ratas a encontrar una plataforma invisible definida por una configuración de dos objetos en la mitad de los ensayos y por una segunda configuración de dos objetos en la otra mitad. Los objetos estaban espaciados alrededor del borde de la piscina. Las dos configuraciones se presentaron con la misma frecuencia cada día, entremezcladas semi-al azar. En el Experimento 1, las configuraciones de las ratas fueron A y B (configuración 1), y B y C (configuración 2). B era un objeto común a ambas configuraciones. Al final de esta fase los animales recibieron ensayos de prueba en los que se colocaba a una rata en la piscina sin la plataforma y se registraba el tiempo que pasaba en el cuadrante de la plataforma. Los animales tuvieron ensayos de prueba con las configuraciones del entrenamiento, con los objetos por separado, y con una nueva configuración, A y C (una prueba de integración). Tanto ante las configuraciones del entrenamiento como en presencia de B, las ratas pasaron una cantidad de tiempo sustancial buscando la plataforma en el cuadrante de la plataforma; no se obtuvo ningún otro efecto en las otras pruebas. En el Experimento 2 se introdujeron varios cambios metodológicos y se replicaron los principales resultados del Experimento 1. Concluimos que tras un entrenamiento configuracional como el empleado, la navegación de las ratas hacia una plataforma invisible estuvo controlada por un aprendizaje elemental, por B.

Blocking and unblocking in a navigation task

Rodrigo, Chamizo, McLaren, & Mackintosh (1997) demonstrated the blocking effect in a navigational task using a swimming pool: rats initially trained to use three landmarks (ABC) to find an invisible platform learned less about a fourth landmark (X) added later than did rats trained from the outset with these four landmarks (ABCX). The aim of the experiment reported here was to demonstrate unblocking using a similar procedure as in the previous work. Three groups of rats were initially trained to find an invisible platfom in the presence of three landmarks: ABC for the Blocking and Unblocking groups and LMN for the Control group. Then, all animals were trained to find the platform in the presence of four landmarks, ABCX. In this second training, unlike animals in the Blocking group to which only a new landmark (X) was added in comparison to the first training, the animals in the Unblocking group also had a change in the platform position. In the Control group, both the four landmarks and the platform position were totally new at the beginning of this second training. As in Rodrigo et al. (1997) a blocking effect was found: rats in the Blocking group learned less with respect to the added landmark (X) than did animals in the Control group. However, rats in the Unblocking group learned about the added landmark (X) as well as did animals in the Control group. The results are interpreted as an unblocking effect due to a change in the platform position between the two phases of training, similarly to what is normal in classical conditioning experiments, in which a change in the conditions of reinforcement between the two training phases of a blocking design produce an attenuation or elimination of this effect. These results are explained within an error-correcting connectionist account of spatial navigation (McLaren, 2002).

Proceso de transformación de las concepciones del profesorado sobre la resolución de problemas matemáticos

The aim of this study is to analyze the transformation of Primary School teachers’ conceptions about mathematical problem solving. We performed a study with 18 teachers from three public schools: in each class (from 1º to 6º) there were two interventions, and we were interviewed teachers before and after them. The results have show identified changes in: 1) teacher’s expectations about students’ abilities; classroom management; perception of diversity; mathematical strategies used by students; communication in the classroom; causes of the problems encountered; and relevance process of problem solving in mathematics teaching. The transformation of teachers’ conceptions is due to the following factors: a) awareness of the practice; b) systematic reflection; c) the contrast between different ways to work solving problems in math class

Repensando la formación inicial del profesorado para abordar el tratamiento a la diversidad cultural y lingüística en el aula = Rethinking initial teacher education for linguistic and cvltural diversity in the classroom

In recent decades, European educational systems are facing many challenges related to the treatment of cultural and linguistic diversity. The need to address this diversity requires new approaches to education; this in turn requires changes in the way we prepare teachers for the new reality they face in their classrooms. In this article we highlight some of the major problems that initial teacher training has to address in order to enable teachers to deal effectively, respectfully, and fairly with students whose linguistic and cultural background is different from their own. We also present several models for teacher education from Europe and North America based on clearly identified teacher competences for linguistic and cultural diversity

Is contextual-potentiated eating dependent on caloric density of food?

One experiment tested whether a specific context could elicit eating in rats as a result of Pavlovian conditioning and whether this effect depended on the caloric density of food. Thirty two deprived rats experienced two contexts. They had access to food in context A, but no food was available in context B. During conditioning, half of the animals received high density caloric food (HD groups) whereas the other half, low density caloric food (LD groups). Then, half of the rats in each type of food group was tested in context A and the other half in context B. The results demonstrated an effect of context conditioning only in HD groups. These findings suggest the relevance of both contextual conditioning and caloric density of food in eating behaviour. Implications for the aetiology of binge eating will be discussed.

Como si fuera posible recoger sentimientos = As if it were possible to collect suffering

Se trata de una propuesta como resultado del trabajo conjunto entre la escuela de Arte Pigment y el ESPAI ZERO1 del Museu Comarcal de la Garrotxa, destinado exclusivamente a exposiciones temporales de creación contemporánea y como continuidad de propuestas anteriores de colaboración: REPLICA23 y SONESNAT JUNIOR. Com si fos possible recollir el sofriment es un proyecto de la artista Anna Manel.la, y se consideró una propuesta interesante y un reto para conversar, intercambiar y crear con los alumnos sobre el tema de la exposición: la muerte y el sufrimiento. Asimismo porque es una artista conocida por los alumnos de la escuela Pigment, ya que anteriormente habían realizado un proyecto de apadrinamiento de esculturas y habitualmente ella participa en programas divulgativos en la escuela. El trabajo desarrollado centra el aprendizaje en la creación y en la investigación artística como ejes de los procesos de conceptualización con el objetivo de atender las dinámicas y los estímulos característicos de los niños. Facilitando procesos de búsqueda, exploración y manipulación sin condicionantes y promoviendo procesos autónomos en los que los mismos niños se planteen dudas e interrogantes y se enfrenten a situaciones cada vez mas complejas

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Some last thoughts on compositional data analysis

One of the disadvantages of old age is that there is more past than future: this, however, may be turned into an advantage if the wealth of experience and, hopefully, wisdom gained in the past can be reflected upon and throw some light on possible future trends. To an extent, then, this talk is necessarily personal, certainly nostalgic, but also self critical and inquisitive about our understanding of the discipline of statistics. A number of almost philosophical themes will run through the talk: search for appropriate modelling in relation to the real problem envisaged, emphasis on sensible balances between simplicity and complexity, the relative roles of theory and practice, the nature of communication of inferential ideas to the statistical layman, the inter-related roles of teaching, consultation and research. A list of keywords might be: identification of sample space and its mathematical structure, choices between transform and stay, the role of parametric modelling, the role of a sample space metric, the underused hypothesis lattice, the nature of compositional change, particularly in relation to the modelling of processes. While the main theme will be relevance to compositional data analysis we shall point to substantial implications for general multivariate analysis arising from experience of the development of compositional data analysis…

Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research. Moreover, there appear to be few mathematical and statistical researchers working on compositional biomedical problems. Like the earth and environmental sciences, biomedicine has many problems in which the relevant scienti c information is encoded in the relative abundance of key species or categories. I introduce three problems in cancer research in which analysis of compositions plays an important role. The problems involve 1) the classi cation of serum proteomic pro les for early detection of lung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostic tumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it's role in breast cancer patient prognosis. For each of these problems I outline a partial solution. However, none of these problems is \solved". I attempt to identify areas in which additional statistical development is needed with the hope of encouraging more compositional data analysts to become involved in biomedical research

Spatial Analysis of Cell Composition Data

A version of Matheron’s discrete Gaussian model is applied to cell composition data. The examples are for map patterns of felsic metavolcanics in two different areas. Q-Q plots of the model for cell values representing proportion of 10 km x 10 km cell area underlain by this rock type are approximately linear, and the line of best fit can be used to estimate the parameters of the model. It is also shown that felsic metavolcanics in the Abitibi area of the Canadian Shield can be modeled as a fractal

Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areas of applications of statistics. For compositional data the necessary theoretical adaptation has been provided, with illustrative applications, by Aitchison (1990) and Aitchison and Greenacre (2002). These papers were restricted to the interpretation of simple compositional data sets. In many situations the problem has to be described in some form of conditional modelling. For example, in a clinical trial where interest is in how patients’ steroid metabolite compositions may change as a result of different treatment regimes, interest is in relating the compositions after treatment to the compositions before treatment and the nature of the treatments applied. To study this through a biplot technique requires the development of some form of conditional compositional biplot. This is the purpose of this paper. We choose as a motivating application an analysis of the 1992 US President ial Election, where interest may be in how the three-part composition, the percentage division among the three candidates - Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethnic composition and on the urban-rural composition of the state. The methodology of conditional compositional biplots is first developed and a detailed interpretation of the 1992 US Presidential Election provided. We use a second application involving the conditional variability of tektite mineral compositions with respect to major oxide compositions to demonstrate some hazards of simplistic interpretation of biplots. Finally we conjecture on further possible applications of conditional compositional biplots

Analyzing shapes as compositions of distances

We propose to analyze shapes as “compositions” of distances in Aitchison geometry as an alternate and complementary tool to classical shape analysis, especially when size is non-informative. Shapes are typically described by the location of user-chosen landmarks. However the shape – considered as invariant under scaling, translation, mirroring and rotation – does not uniquely define the location of landmarks. A simple approach is to use distances of landmarks instead of the locations of landmarks them self. Distances are positive numbers defined up to joint scaling, a mathematical structure quite similar to compositions. The shape fixes only ratios of distances. Perturbations correspond to relative changes of the size of subshapes and of aspect ratios. The power transform increases the expression of the shape by increasing distance ratios. In analogy to the subcompositional consistency, results should not depend too much on the choice of distances, because different subsets of the pairwise distances of landmarks uniquely define the shape. Various compositional analysis tools can be applied to sets of distances directly or after minor modifications concerning the singularity of the covariance matrix and yield results with direct interpretations in terms of shape changes. The remaining problem is that not all sets of distances correspond to a valid shape. Nevertheless interpolated or predicted shapes can be backtransformated by multidimensional scaling (when all pairwise distances are used) or free geodetic adjustment (when sufficiently many distances are used)

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given

CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts is divided into two new groups, and a balancing axis in the simplex between both groups is defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in a dendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process; (c) the decomposition of the total variance into balance components associated with each binary partition; (d) a box-plot of each balance. This representation is useful to help the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independently of the number of parts of the sample