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.

Error sensitive historical GIS: Identifying areal interpolation errors in time series data

Historical GIS has the potential to re-invigorate our use of statistics from historical censuses and related sources. In particular, areal interpolation can be used to create long-run time-series of spatially detailed data that will enable us to enhance significantly our understanding of geographical change over periods of a century or more. The difficulty with areal interpolation, however, is that the data that it generates are estimates which will inevitably contain some error. This paper describes a technique that allows the automated identification of possible errors at the level of the individual data values.

Identification of three novel Phyllomedusa sauvagei dermaseptins (sVI-sVIII) by cloning from a skin secretion-derived cDNA library

The defensive skin secretions of many amphibians contain a wide spectrum of biologically active compounds, particularly antimicrobial peptides that act as a first line of defence against bacterial infection. Here we describe for the first time the identification of three novel dermaseptin-related peptides (dermaseptins sVI–sVIII) whose primary structures were deduced from cDNAs cloned from a library constructed from lyophilised skin secretion of the South American hylid frog, Phyllomedusa sauvagei. The molecular masses of each were subsequently confirmed by interrogation of archived LC/MS files of fractionated skin secretion followed by automated Edman degradation sequencing. The heterogeneity of primary structures encountered in amphibian skin antimicrobial peptides may in part be explained by individual variation—a factor essential for selective functional molecular evolution and perhaps, ultimately in speciation.