Exploration and reduction of data using principal component analysis

In a data set with two variables only, a scatterplot between the two variables can be easily plotted to represent the data visually. When the number of variables in the data set is large, however, it is more difficult to represent visually. The method of principal component analysis (PCA) can sometimes be used to represent the data faithfully in few dimensions (eg. three or less), with little or no loss of information. This reduction in dimensionality is best achieved when the original variables are highly correlated, positively or negatively. In this case, it is quite conceivable that 20 or 30 original variables can be adequately represented by two or three new variables, which are suitable combinations of the original ones, and which are called principal components. Principal components are uncorrelated between themselves, so that each component describes a different dimension of the data. The principal components can also be arranged in descending order of their variance. The first component has the largest variance, and is the most important, followed by the second component with the second largest variance, and so on. The first two components can then be evaluated for each case in the data set and plotted against each other in a scattergraph, the score for the first component being plotted along the horizontal axis, the score of the second component being plotted on the vertical axis. This scatterplot is a parsimonious two-dimensional picture of the variables and cases in the original data set. We illustrate the method by applying it to simulated datasets, and to a dataset containing national track record times for males and females in various countries.peer-reviewe

Francesco Azopardi : a Maltese musician and theorist : new evidence about his career and didactic writings

Francesco Azopardi (1748-1809) lived in Malta during the second half of the eighteenth century. He was professionally trained in Naples for four years and remained in this city working as a composer, teacher and conductor until 1774. The Cathedral authorities subsequently employed Azopardi in Malta as an organist. His duties included composition, playing the organ and teaching singers. Azopardi's workload increased significantly following the retirement of his predecessor Benigno Zerafa. Azopardi was a prolific composer and he composed new music regularly for the liturgical services of the Cathedral Church. In addition, he taught many students including Nicolo lsouard and produced two important composition treatises for his students.peer-reviewe

Psychological interventions in post-partum depression : a critical analysis

Non-pharmacological interventions are often the preferred treatment modalities in perinatal mothers suffering from mental health problems. Cognitive-behavioural therapy (CBT) and inter-personal therapy (IPT) are the two main evidence-based psychological treatment interventions in the management of post-partum depression. Various studies have been conducted-to-date to assess the efficacy and effectiveness of both CBT and IPT in this specialised group, yet there is no data contrasting the two. This report aims to provide a comparative critical evaluation of the evidence base for the two interventions, including their respective strengths and limitations. Research possibly indicates a stronger evidence base for IPT in the treatment of depression post-delivery, perhaps as a result of larger scale studies having been performed for this treatment modality. Nonetheless, valuable positive outcomes for CBT-treated individuals have been observed. Consequently, a number of recommendations for future research will be put forward with the main objective of advancing the literature in this area of expertise.peer-reviewe

Some tentative suggestions for a children's museum

The need for a Children's Museum or, at least, for some sort of Museum-School Service has been felt for some time in education circles in Malta. At a time when stress is put on environmental studies and extra-curricula activities the setting up of such a service has become increasingly important. This report contains suggestions for a Children's Museum devoted primarily to Maltese Archaeology, History and Folklore. Museums are usually planned for an adult public and, therefore, often lack appeal to children. The conventional arrangement of show-case after show-case with methodically arranged, carefully labelled exhibits is meaningless to children. These need a special type of museum where show-cases are reduced to a minimum and the display is organized in a way that will stimulate interest and excite imagination. It is a basic principle in education that memory depends on the kind of material to be remembered; the more meaningful the material the more easily is it assimilated.peer-reviewe

Rationalisation of the biochemistry laboratory : which way forwards?

The eternal problem faced in service provision is that of coping with an ever-increasing work-load within the relative constraints of keeping costs down to a minimum. The reasons for the increase in the work-load are multiple and include the need to expand the repertoire of tests available if so justified. The justification in medical practice is not only limited to evidence-based proof of the use of medicinals, but is also extendable to the usage of laboratory tests. Regrettably, laboratory usage still appears to be rooted in the mentality that if the test is available, then its request may just be justified in the case that it throws up an abnormal result. This article aims to look at some commonly requested and possibly overrequested tests as well as discusses the value of emerging tests that may well help the rationalisation of other over-stretched medical services.peer-reviewe

Measuring reliability and consistency in contingency tables

The association between two categorical variables is very often assessed by making a cross-tabulation and calculating the x2 statistic for that table. However there are many other related parameters which can be used to assess subtle patterns in the table. In this article we will discuss parameters which can be fruitfully used in situations such as the test-retest method for the reliability of questions in a pilot questionnaire ; the measurement of the change of people’s attitude with time ; the comparison of two medical diagnoses of a given patient ; the prediction of heart disease status using an independent risk scale.peer-reviewe

The evolving link between learning and assessment : from 'transmission check' to 'learning support'

Learning and assessment are now considered as two sides of the same coin we simply cannot speak of one without also referring to the other. This paper, which traces the evolution of the link between learning and assessment, explores what led to our shift in understanding of the learning process from the behaviourist to the constructivist model, and the implications that this 'revolution ' has had for assessment. Making assessment at the service of learning is subsequently identified as the challenge ahead for the educational community.peer-reviewe

Stimulus & response : fieldwork in science

From time to time students at the faculty of Education are asked to air their views on particular educational topics which the editors propose to them. In this issue of the journal we reproduce the ideas of two students about the value of fieldwork in science.peer-reviewe

Square compactness and the filter extension property

We show that the consistency strength of κ being 2κ-square compact is at least weak compact and strictly less than indescribable. This is the first known improvement to the upper bound of strong compactness obtained in 1973 by Hajnal and Juhasz

Using inquiry-based learning to support the mathematical learning of students with SEBD

This paper, which draws on action research methodology, explores the use of inquirybased learning (IBL) in the teaching of mathematics to students with social, emotional and behavioural difficulties (SEBD). The year-long study was conducted in a Form 3 secondary class that grouped 13 male students with SEBD in a Maltese secondary school. After first creating an IBL-friendly classroom environment in the initial months, the actual implementation of IBL pedagogy in class began in the second term and spread over a 15 week period. The data included teacher observations that were recorded in a reflective research journal, two sessions of in-depth interviews with students, student journal writing, samples of students’ work and student marks in the school-based halfyearly and annual mathematics examinations. The findings indicate that the use of IBL in the mathematics classroom can benefit students with SEBD in a number of ways. These include infusing a sense of enjoyment during lessons, improved student behaviour and motivation to learn, and facilitating the learning of mathematics which generally translated in higher achievement levels.peer-reviewe