Keeping a sense of proportion but losing all perspective: a critique of Gorard's notion of the 'Politician's Error'

In 1999 Stephen Gorard published an article in this journal in which he provided a trenchant critique of what he termed the `politician's error' in analysing differences in educational attainment. The main consequence of this error, he argued, has been the production of misleading findings in relation to trends in educational performance over time that have, in turn, led to misguided and potentially damaging policy interventions. By using gender differences in educational attainment as a case study, this article begins by showing how Gorard's notion of the politician's error has been largely embraced and adopted uncritically by those within the field. However, the article goes on to demonstrate how Gorard's own preferred way of analysing such differences – by calculating and comparing proportionate changes in performance between groups – is also inherently problematic and can lead to the production of equally misleading findings. The article will argue that there is a need to develop a more reliable and valid way of measuring trends in educational performance over time and will show that one of the simplest ways of doing this is to make use of existing, and widely accepted, measures of effect size.

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.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.