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.

Ultraviolet oscillations in the chromosphere of the quiet Sun

Quiet-Sun oscillations in the four Transition Region and Coronal Explorer (TRACE) ultraviolet passbands centered on 1700, 1600, 1216, and 1550 Angstrom are studied using a wavelet-based technique. Both network and internetwork regions show oscillations with a variety of periods and lifetimes in all passbands. The most frequent network oscillation has a period of 283 s, with a lifetime of 2-3 cycles in all passbands. These oscillations are discussed in terms of upwardly propagating magnetohydrodynamic wave models. The most frequent internetwork oscillation has a period of 252 s, again with a lifetime of 2-3 cycles, in all passbands. The tendency for these oscillations to recur in the same position is discussed in terms of "persistent flashers." The network contains greater oscillatory power than the internetwork at periods longer than 300 s in the low chromosphere. This value is shown to decrease to 250 s in the high chromosphere. The internetwork also displays a larger number of short-lifetime, long-period oscillations than the network, especially in the low chromosphere. Both network and internetwork regions contain a small number of nonrecurring long-lifetime oscillations.