Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certain assumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur in the proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p. There are many statistical tests being used to check whether empirical marker data obeys the Hardy-Weinberg principle. Among these are the classical xi-square test (with or without continuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combination with Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE) are numerical in nature, requiring the computation of a test statistic and a p-value. There is however, ample space for the use of graphics in HWE tests, in particular for the ternary plot. Nowadays, many genetical studies are using genetical markers known as Single Nucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the counts one typically computes genotype frequencies and allele frequencies. These frequencies satisfy the unit-sum constraint, and their analysis therefore falls within the realm of compositional data analysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotype frequencies can be adequately represented in a ternary plot. Compositions that are in exact HWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected in a statistical test are typically “close" to the parabola, whereas compositions that differ significantly from HWE are “far". By rewriting the statistics used to test for HWE in terms of heterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted in the ternary plot. This way, compositions can be tested for HWE purely on the basis of their position in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphical representations where large numbers of SNPs can be tested for HWE in a single graph. Several examples of graphical tests for HWE (implemented in R software), will be shown, using SNP data from different human populations

La incontinencia urinaria en el cáncer de próstata: diseño de un programa de rehabilitación

Este trabajo presenta el diseño e implementación de un programa progresivo de rehabilitación basado en los ejercicios musculares del suelo pélvico, incorporando el trabajo muscular de fuerza contrarresistencia. El disenño del estudio es casi experimental.La muestra es de 33 participantes en fase de tratamiento. Las variables de estudio son las antropométricas, las relacionadas con la evolución de la incontinencia urinaria(IU (intensidad, dificultad, frecuencia y limitación de las actividades),la obesidad, fatiga y dolor,la fuerza muscular y la calidad de vida(CdV). Para evaluar el cambio intrasujeto se tomaron medidas pretest(semana 0)y postest(semana24. En el análisis estadístico se utilizan las pruebas t Student-Fisher, Wilcoxon oU de Mann Whitney y el test del w2. El análisis se realiza con el programa SPSS versión 15. El nivel de significación escogido es del 5%. Al finalizar las 24 semanas del programa se identifica una disminución significativa de las variables antropométricas índice de cintura cadera (p¼0,003), perímetro de cintura(pr0,001) y porcentaje de masa de grasa(pr0,001); de las variables de IU: intensidad(pr0,0001), frecuencia y dificultad y su relación con la limitación de las actividades (pr0,0001), así como la relación existente entre la mejora de IU y la mejora de la CdV(p¼0,039). Queda científicamente demostrada la eficacia del programa progresivo de fuerza para disminuir la IU. La mejora de la CdV del hombre mayor con cáncer de prósstata viene mediada por la mejora de la continencia urinaria

Incongruence between test statistics and P values in medical papers

Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers. Methods: We checked the congruence of statistical results reported in all the papers of volumes 409–412 of Nature (2001) and a random sample of 63 results from volumes 322–323 of BMJ (2001). We also tested whether the frequencies of the last digit of a sample of 610 test statistics deviated from a uniform distribution (i.e., equally probable digits).Results: 11.6% (21 of 181) and 11.1% (7 of 63) of the statistical results published in Nature and BMJ respectively during 2001 were incongruent, probably mostly due to rounding, transcription, or type-setting errors. At least one such error appeared in 38% and 25% of the papers of Nature and BMJ, respectively. In 12% of the cases, the significance level might change one or more orders of magnitude. The frequencies of the last digit of statistics deviated from the uniform distribution and suggested digit preference in rounding and reporting.Conclusions: this incongruence of test statistics and P values is another example that statistical practice is generally poor, even in the most renowned scientific journals, and that quality of papers should be more controlled and valued

El coneixement de la llengua catalana i la llengua castellana per part de l'alumnat estranger escolaritzat a l'educació primària de Catalunya: factors explicatius i relacions d'interdependència lingüística.

La tesi presenta els resultats de coneixement de català i castellà de 515 alumnes estrangers escolaritzats a Catalunya al finalitzar sisè de primària durant el curs 2006/07. En concret, analitza la incidència d'algunes variables en el seu coneixement lingüístic (el temps d'estada, la llengua inicial, l'escolaritat prèvia, el nivell educatiu familiar, el context sociolingüístic del centre, la concentració d'alumnat estranger per aula, els usos de les diferents llengües a l'entorn social, escolar i familiar, entre altres) i també estudia les relacions d'interdependència lingüística (Cummins, 1979) que es produeixen entre les llengües que aquest alumnat aprèn des de l'escola. Les proves utilitzades avaluen diferents habilitats relacionades amb el coneixement de llengua oral i escrita de català i castellà. El tractament que es fa de les dades és estadístic. Les conclusions apunten alguns dels elements que cal considerar pel tractament educatiu i lingüístic de la infància i l'adolescència estrangera escolaritzada a Catalunya.