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.

Choice and use of standards for dynamic headspace trapping and application to the analysis of the volatiles of baked potato

When attempting to quantify the volatile components of a food isolated by dynamic headspace trapping onto an adsorbent, the analyst has to select the most appropriate compounds to use as standards and at which stage of the analysis to add them. Factors to be borne in mind include the volatility of the standard, the response of the GC detector, and whether to add the standard to the sample or to the adsorbent trap. This chapter considers the issues and describes the application of one chosen method to the quantitation of the volatile components of baked potato.