Analysis of Academy School Performance in the 2011 and 2012 GCSEs

The Local Government Association (LGA) commissioned NFER to undertake statistical analysis of school level GCSE data provided by the Department of Education and accessible from their website. The purpose of the analysis was to determine whether there was any differential progress between Key Stage 2 and Key Stage 4 that can be associated with schools status. This report highlights analysis undertaken on the 2011 and 2012 GCSE results with future analysis on the 2013 and 2014 results also planned. Additional analyses looking at changes over time were also carried out.Analysis at the school level used average attainment at Key Stage 2 as measure of prior attainment and as a way to control for schools having different pupil intakes. Pupil progress was measured between KS2 and average GCSE points score. Two measures of GCSE attainment were used, average total point score (capped) and the proportion of pupil achievbing 5+ A* to C grades. Other school level factors that may have been associated with a variation in pupil progress were also included within the models. These included the proportion of pupils on free school meals and the proportion of pupils with special educational needs, as well as geographical location.Key Findings:In 2011 and 2012 schools with academy status made, on average, more progress between KS2 and GCSE than non academy status schools.Peformance, and interpretation, altered when excluding equivalent qualifications.There was no long term change in performance associated with academy status

Mean-Dispersion Preferences and Constant Absolute Uncertainty Aversion

We axiomatize, in an Anscombe-Aumann framework, the class of preferences that admit a representation of the form V(f) = mu - rho(d), where mu is the mean utility of the act f with respect to a given probability, d is the vector of state-by-state utility deviations from the mean, and rho(d) is a measure of (aversion to) dispersion that corresponds to an uncertainty premium. The key feature of these mean-dispersion preferences is that they exhibit constant absolute uncertainty aversion. This class includes many well-known models of preferences from the literature on ambiguity. We show what properties of the dispersion function rho(dot) correspond to known models, to probabilistic sophistication, and to some new notions of uncertainty aversion.Ambiguity aversion, Translation invariance, Dispersion, Uncertainty, Probabilistic sophistication

Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large $d$-dimensional array $A$ and a fixed $d$-dimensional pattern $P$ over a finite alphabet, we say that $A$ is $P$-free if it does not contain a copy of the forbidden pattern $P$ as a consecutive subarray. The distance of $A$ to $P$-freeness is the fraction of entries of $A$ that need to be modified to make it $P$-free. For any $\epsilon \in [0,1]$ and any large enough pattern $P$ over any alphabet, other than a very small set of exceptional patterns, we design a tolerant tester that distinguishes between the case that the distance is at least $\epsilon$ and the case that it is at most $a_d \epsilon$, with query complexity and running time $c_d \epsilon^{-1}$, where $a_d < 1$ and $c_d$ depend only on $d$. To analyze the testers we establish several combinatorial results, including the following $d$-dimensional modification lemma, which might be of independent interest: for any large enough pattern $P$ over any alphabet (excluding a small set of exceptional patterns for the binary case), and any array $A$ containing a copy of $P$, one can delete this copy by modifying one of its locations without creating new $P$-copies in $A$. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data. They serve as a first step towards a general understanding of local properties of multi-dimensional arrays, as any such property can be characterized by a fixed family of forbidden patterns

Decomposable Choice Under Uncertainty

Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savage's axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. It also enables Nash behavior in games of incomplete information to be decentralized to the agent-normal form. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agent's induced preferences over lotteries satisfy betweenness.Sure-thing principle, decomposability, uncertainty, computation, dynamic programming solvability, agent-normal form games, non-expected utility, betweenness

Preference for Information and Dynamic Consistency

We provide necessary and sufficient conditions for a dynamically consistent agent always to prefer more informative signals (in single-agent problems). These conditions do not imply recursivity, reduction or independence. We provide a simple definition of dynamically consistent behavior, and we discuss whether an intrinsic information lover (say, an anxious person) is likely to be dynamically consistent.Information, non-expected utility, dynamic consistency, randomization, anxiety