Com fer una anàlisi quantitativa de dades de tipus descriptiu amb el paquet estadístic de l"SPSS?

En l"actualitat és difícil parlar de processos estadístics d"anàlisi quantitativa de dades sense fer referència a la informàtica aplicada a la recerca. Aquests recursos informàtics es basen sovint en paquets de programes informàtics que tenen l"objectiu d"ajudar al/a la investigador/a en la fase d"anàlisi de dades. En aquests moments un dels paquets més perfeccionats i complets és l"SPSS (Statistical Package for the Social Sciences). L"SPSS és un paquet de programes per tal de dur a terme l"anàlisi estadística de les dades. Constitueix una aplicació estadística força potent, de la qual s"han anat desenvolupant diverses versions des dels seus inicis, als anys setanta. En aquest manual les sortides d"ordinador que es presenten pertanyen a la versió 11.0.1. No obstant això, tot i que la forma ha anat variant des dels inicis, pel que fa al funcionament segueix essent molt similar entre les diferents versions. Abans d"iniciar-nos en la utilització de les aplicacions de l"SPSS és important familiaritzarse amb algunes de les finestres que més farem servir. En entrar a l"SPSS el primer que ens trobem és l"editor de dades. Aquesta finestra visualitza, bàsicament, les dades que anirem introduint. L"editor de dades inclou dues opcions: la Vista de les dades i la de les variables. Aquestes opcions es poden seleccionar a partir de les dues pestanyes que es presenten en la part inferior. La vista de dades conté el menú general i la matriu de dades. Aquesta matriu s"estructura amb els casos a les files i les variables a les columnes.

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically.

Com optimitzar una matriu de dades? Utilitats bàsiques de l"SPSS

Una vegada es disposa de les dades introduïdes al paquet estadístic de l"SPSS (Statistical Package of Social Science) en una matriu de dades, és el moment de plantejar-se optimitzar aquesta matriu per poder extreure el màxim rendiment a les dades, segons el tipus d"anàlisi que es pretengui dur a terme. Per a això, el mateix SPSS té una sèrie d"utilitats que poden ser de gran utilitat. Aquestes utilitats bàsiques poden diferenciar-se segons la seva funcionalitat entre: les utilitats per a l"edició de dades, les utilitats per a la modificació de variables i les opcions d"ajuda que ens brinda. A continuació es presenten algunes d"aquestes utilitats.

A measure of stability as a criterion for the verification and analysis of simulation models

The aim of this study is to define a new statistic, PVL, based on the relative distance between the likelihood associated with the simulation replications and the likelihood of the conceptual model. Our results coming from several simulation experiments of a clinical trial show that the PVL statistic range can be a good measure of stability to establish when a computational model verifies the underlying conceptual model. PVL improves also the analysis of simulation replications because only one statistic is associated with all the simulation replications. As well it presents several verification scenarios, obtained by altering the simulation model, that show the usefulness of PVL. Further simulation experiments suggest that a 0 to 20 % range may define adequate limits for the verification problem, if considered from the viewpoint of an equivalence test.

Análisis Discriminante mediante SPSS.

El análisis discriminante es un método estadístico a través del cual se busca conocer qué variables, medidas en objetos o individuos, explican mejor la atribución de la diferencia de los grupos a los cuales pertenecen dichos objetos o individuos. Es una técnica que nos permite comprobar hasta qué punto las variables independientes consideradas en la investigación clasifican correctamente a los sujetos u objetos. Se muestran y explican los principales elementos que se relacionan con el procedimiento para llevar a cabo el análisis discriminante y su aplicación utilizando el paquete estadístico SPSS, versión 18, para el desarrollo del modelo estadístico, las condiciones para la aplicación del análisis, la estimación e interpretación de las funciones discriminantes, los métodos de clasificación y la validación de los resultados.

Regional flows of domestic tourism in Spain = Flujos regionales del turismo doméstico en España

The paper analyses the regional flows of domestic tourism that took place in Spain in year 2000, contributing to the state of knowledge on tourism required by authorities and private firms when faced with decision making, for example, for regional infrastructure planning. Although tourism is one of the main income-generating economic activities in Spain, domestic tourism has received little attention in the literature compared to inbound tourism. The paper uses among others, gravitational model tools and concentration indices, to analyse regional concentration of both domestic demand and supply; tourism flows among regions, and the causes that may explain the observed flows and attractiveness between regions. Among the most remarkable results are the high regional concentration of demand and supply, and the role of population and regional income as explanatory variables. Also remarkable are the attractiveness of own region and neighbour ones, and that domestic tourism may be acting as a regional income redistributing activity

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principal component analysis allow to model compositional changes compared with a reference point. The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

Kriging coordinates: what does that mean?

Kriging is an interpolation technique whose optimality criteria are based on normality assumptions either for observed or for transformed data. This is the case of normal, lognormal and multigaussian kriging. When kriging is applied to transformed scores, optimality of obtained estimators becomes a cumbersome concept: back-transformed optimal interpolations in transformed scores are not optimal in the original sample space, and vice-versa. This lack of compatible criteria of optimality induces a variety of problems in both point and block estimates. For instance, lognormal kriging, widely used to interpolate positive variables, has no straightforward way to build consistent and optimal confidence intervals for estimates. These problems are ultimately linked to the assumed space structure of the data support: for instance, positive values, when modelled with lognormal distributions, are assumed to be embedded in the whole real space, with the usual real space structure and Lebesgue measure

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework. We present here a possible solution based on factor analysis of compositions illustrated with a case study. We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members. We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except fertilisers due to the heterogeneity of their composition. This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are intrinsic to the relative nature of compositional data

Major-elements trends in cenozoic volcanites of Hungary

Hungary lies entirely within the Carpatho-Pannonian Region (CPR), a dominant tectonic unit of eastern Central Europe. The CPR consists of the Pannonian Basin system, and the arc of the Carpathian Mountains surrounding the lowlands in the north, east, and southeast. In the west, the CPR is bounded by the Eastern Alps, whereas in the south, by the Dinaridic belt. (...)

The allometry of non-employment. What can compositional data analysis tell us about labour market performance across the UK's regions?

The low levels of unemployment recorded in the UK in recent years are widely cited as evidence of the country’s improved economic performance, and the apparent convergence of unemployment rates across the country’s regions used to suggest that the longstanding divide in living standards between the relatively prosperous ‘south’ and the more depressed ‘north’ has been substantially narrowed. Dissenters from these conclusions have drawn attention to the greatly increased extent of non-employment (around a quarter of the UK’s working age population are not in employment) and the marked regional dimension in its distribution across the country. Amongst these dissenters it is generally agreed that non-employment is concentrated amongst older males previously employed in the now very much smaller ‘heavy’ industries (e.g. coal, steel, shipbuilding). This paper uses the tools of compositiona l data analysis to provide a much richer picture of non-employment and one which challenges the conventional analysis wisdom about UK labour market performance as well as the dissenters view of the nature of the problem. It is shown that, associated with the striking ‘north/south’ divide in nonemployment rates, there is a statistically significant relationship between the size of the non-employment rate and the composition of non-employment. Specifically, it is shown that the share of unemployment in non-employment is negatively correlated with the overall non-employment rate: in regions where the non-employment rate is high the share of unemployment is relatively low. So the unemployment rate is not a very reliable indicator of regional disparities in labour market performance. Even more importantly from a policy viewpoint, a significant positive relationship is found between the size of the non-employment rate and the share of those not employed through reason of sickness or disability and it seems (contrary to the dissenters) that this connection is just as strong for women as it is for men

On the use of principal components in contemporany population genetics: a case study

In human Population Genetics, routine applications of principal component techniques are often required. Population biologists make widespread use of certain discrete classifications of human samples into haplotypes, the monophyletic units of phylogenetic trees constructed from several single nucleotide bimorphisms hierarchically ordered. Compositional frequencies of the haplotypes are recorded within the different samples. Principal component techniques are then required as a dimension-reducing strategy to bring the dimension of the problem to a manageable level, say two, to allow for graphical analysis. Population biologists at large are not aware of the special features of compositional data and normally make use of the crude covariance of compositional relative frequencies to construct principal components. In this short note we present our experience with using traditional linear principal components or compositional principal components based on logratios, with reference to a specific dataset

The agreement between ipsative and normative questionnaires using compositional data analysis techniques

The main instrument used in psychological measurement is the self-report questionnaire. One of its major drawbacks however is its susceptibility to response biases. A known strategy to control these biases has been the use of so-called ipsative items. Ipsative items are items that require the respondent to make between-scale comparisons within each item. The selected option determines to which scale the weight of the answer is attributed. Consequently in questionnaires only consisting of ipsative items every respondent is allotted an equal amount, i.e. the total score, that each can distribute differently over the scales. Therefore this type of response format yields data that can be considered compositional from its inception. Methodological oriented psychologists have heavily criticized this type of item format, since the resulting data is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians have kept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate both positions and addresses the similarities and differences between the two data collection methods. The ultimate objective is to formulate a guideline when to use which type of item format. The comparison is based on data obtained with both an ipsative and normative version of three psychological questionnaires, which were administered to 502 first-year students in psychology according to a balanced within-subjects design. Previous research only compared the direct ipsative scale scores with the derived ipsative scale scores. The use of compositional data analysis techniques also enables one to compare derived normative score ratios with direct normative score ratios. The addition of the second comparison not only offers the advantage of a better-balanced research strategy. In principle it also allows for parametric testing in the evaluation

A compositional statistical analysis of capital stock

Most of economic literature has presented its analysis under the assumption of homogeneous capital stock. However, capital composition differs across countries. What has been the pattern of capital composition associated with World economies? We make an exploratory statistical analysis based on compositional data transformed by Aitchinson logratio transformations and we use tools for visualizing and measuring statistical estimators of association among the components. The goal is to detect distinctive patterns in the composition. As initial findings could be cited that: 1. Sectorial components behaved in a correlated way, building industries on one side and , in a less clear view, equipment industries on the other. 2. Full sample estimation shows a negative correlation between durable goods component and other buildings component and between transportation and building industries components. 3. Countries with zeros in some components are mainly low income countries at the bottom of the income category and behaved in a extreme way distorting main results observed in the full sample. 4. After removing these extreme cases, conclusions seem not very sensitive to the presence of another isolated cases