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.

Is childhood type 1 diabetes a wealth-related disease? An ecological analysis of European incidence rates

Aims/Hypothesis: To describe the epidemiology of childhood-onset Type 1 (insulin-dependent) diabetes in Europe, the EURODIAB collaborative group has established prospective, geographically-defined registers of children diagnosed under 15 years. A total of 16,362 cases were registered by 44 centres during the period 1989-1994. The registers cover a population of approximately 28 million children with most European countries represented. Methods In most centres a primary and a secondary source of ascertainment were used so that the completeness of registration could be assessed by the capture-recapture method. Ecological correlation and regression analyses were used to study the relationship between incidence and various environmental, health and economic indicators. Findings: The standardised average annual incidence rate during the period 1989-94 ranged from 3.2 cases per 100,000 per annum in the Former Yugoslavian Republic of Macedonia to 40.2 cases per 100,000 per annum in Finland. Indicators of national prosperity such as infant mortality (r= -0.64) and gross domestic product (r= 0.58) were most strongly and significantly correlated with incidence rate, and previously-reported associations with coffee consumption (r= 0.51), milk consumption (r= 0.58) and latitude (r= 0.40) were also observed. Conclusion/Interpretation: The wide variation in childhood type 1 diabetes incidence rates within Europe could be partially explained by indicators of national prosperity. These indicators could reflect differences in environmental risk factors such as nutrition or lifestyle that are important in determining a country's incidence rate.

A new look at the pulsating DB white dwarf GD 358: Line-of-sight velocity measurements and constraints on model atmospheres

We report on our findings of the bright, pulsating, helium atmosphere white dwarf GD 358, based on time-resolved optical spectrophotometry. We identify 5 real pulsation modes and at least 6 combination modes at frequencies consistent with those found in previous observations. The measured Doppler shifts from our spectra show variations with amplitudes of up to 5.5 km s-1 at the frequencies inferred from the flux variations. We conclude that these are variations in the line-of-sight velocities associated with the pulsational motion. We use the observed flux and velocity amplitudes and phases to test theoretical predictions within the convective driving framework, and compare these with similar observations of the hydrogen atmosphere white dwarf pulsators (DAVs). The wavelength dependence of the fractional pulsation amplitudes (chromatic amplitudes) allows us to conclude that all five real modes share the same spherical degree, most likely, l=1. This is consistent with previous identifications based solely on photometry. We find that a high signal-to-noise mean spectrum on its own is not enough to determine the atmospheric parameters and that there are small but significant discrepancies between the observations and model atmospheres. The source of these remains to be identified. While we infer Teff =24 kK and log g ~ 8.0 from the mean spectrum, the chromatic amplitudes, which are a measure of the derivative of the flux with respect to the temperature, unambiguously favour a higher effective temperature, 27 kK, which is more in line with independent determinations from ultra-violet spectra.