Summary statistics, educational achievement gaps and the ecological fallacy

Summary statistics continue to play an important role in identifying and monitoring patterns and trends in educational inequalities between differing groups of pupils over time. However, this article argues that their uncritical use can also encourage the labelling of whole groups of pupils as ‘underachievers’ or ‘overachievers’ as the findings of group-level data are simply applied to individual group members, a practice commonly termed the ‘ecological fallacy’. Some of the adverse consequences of this will be outlined in relation to current debates concerning gender and ethnic differences in educational attainment. It will be argued that one way of countering this uncritical use of summary statistics and the ecological fallacy that it tends to encourage, is to make much more use of the principles and methods of what has been termed ‘exploratory data analysis’. Such an approach is illustrated through a secondary analysis of data from the Youth Cohort Study of England and Wales, focusing on gender and ethnic differences in educational attainment. It will be shown that, by placing an emphasis on the graphical display of data and on encouraging researchers to describe those data more qualitatively, such an approach represents an essential addition to the use of simple summary statistics and helps to avoid the limitations associated with them.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

Informal caregiving and mental ill health – differential relationships by workload, gender, age and area-remoteness in a UK region

Informal caregiving can be a demanding role which has been shown to impact on physical, psychological and social wellbeing. Methodological weaknesses including small sample sizes and subjective measures of mental health have led to inconclusive evidence about the relationship between informal caregiving and mental health. This paper reports on a study carried out in a UK region which investigated the relationship between informal caregiving and mental ill health. The analysis was conducted by linking three datasets, the Northern Ireland Longitudinal Study, the Northern Ireland Enhanced Prescribing Database and the Proximity to Service Index from the Northern Ireland Statistics and Research Agency. Our analysis used both a subjective measure of mental ill health, i.e. a question asked in the 2011 Census, and an objective measure, whether the respondents had been prescribed antidepressants by a General Practitioner between 2010 and 2012. We applied binary logistic multilevel modelling to these two responses to test whether, and for what sub-groups of the population, informal caregiving was related to mental ill health. The results showed that informal caregiving per se was not related to mental ill health although there was a strong relationship between the intensity of the caregiving role and mental ill health. Females under 50, who provided over 19 hours of care, were not employed or worked part-time and who provided care in both 2001 and 2011 were at a statistically significantly elevated risk of mental ill health. Caregivers in remote areas with limited access to shops and services were also at a significantly increased risk as evidenced by prescription rates for antidepressants. With community care policies aimed at supporting people to remain at home, the paper highlights the need for further research in order to target resources appropriately.

Fault Diagnosis in Internal Combustion Engines Using Nonlinear Multivariate Statistics

This paper presents a statistical-based fault diagnosis scheme for application to internal combustion engines. The scheme relies on an identified model that describes the relationships between a set of recorded engine variables using principal component analysis (PCA). Since combustion cycles are complex in nature and produce nonlinear relationships between the recorded engine variables, the paper proposes the use of nonlinear PCA (NLPCA). The paper further justifies the use of NLPCA by comparing the model accuracy of the NLPCA model with that of a linear PCA model. A new nonlinear variable reconstruction algorithm and bivariate scatter plots are proposed for fault isolation, following the application of NLPCA. The proposed technique allows the diagnosis of different fault types under steady-state operating conditions. More precisely, nonlinear variable reconstruction can remove the fault signature from the recorded engine data, which allows the identification and isolation of the root cause of abnormal engine behaviour. The paper shows that this can lead to (i) an enhanced identification of potential root causes of abnormal events and (ii) the masking of faulty sensor readings. The effectiveness of the enhanced NLPCA based monitoring scheme is illustrated by its application to a sensor fault and a process fault. The sensor fault relates to a drift in the fuel flow reading, whilst the process fault relates to a partial blockage of the intercooler. These faults are introduced to a Volkswagen TDI 1.9 Litre diesel engine mounted on an experimental engine test bench facility.

The Effects of Social Class and Ethnicity on Gender Differences in GCSE Attainment: A Secondary Analysis of the Youth Cohort Study of England and Wales 1997-2001

This article is based upon a secondary analysis of the Youth Cohort Study of England and Wales 1998 and examines the effects of social class and ethnicity on gender differences in GCSE attainment for those who left school in 1997 (n = 14,662). The article shows that both social class and ethnicity exert a far greater influence on the GCSE performance of boys and girls than gender. Moreover, the article also shows that an interaction effect is present between social class and gender and also between ethnicity and gender in relation to their impact upon GCSE attainment. More specifically, the findings suggest that a strong correlation exists such that the lower the overall levels of educational attainment for any group (whether that group is defined in terms of social class or ethnicity), the higher the gender differences that exist between those within that group.

Constructions of locality and gender and their impact on the educational aspirations of working class children

Over recent years the moral panic that has surrounded 'boys' underachievement' has tended to encourage crude and essentialist comparisons between all boys and all girls and to eclipse the continuing and more profound effects on educational achievement exerted by social class and 'race'/ethnicity. While there are differences in educational achievement between working class boys and girls, these differences are relatively minor when comparing the overall achievement levels of working class children with those from higher, professional social class backgrounds. This paper argues that a need exists therefore for researchers to fully contextualise the gender differences that exist in educational achievement within the over-riding contexts provided by social class and 'race'/ethnicity. The paper provides an example of how this can be done through a case study of 11-year-old children from a Catholic, working class area in Belfast. The paper shows how the children's general educational aspirations are significantly mediated by their experiences of the local area in which they live. However, the way in which the children come to experience and construct a sense of locality differs between the boys and girls and this, it is argued, helps to explain the more positive educational aspirations held by some of the girls compared to the boys. The paper concludes by considering the relevance of locality for understanding its effects on educational aspirations among other working class and/or minority ethnic communities.