Assessing pupil and school performance by non-parametric and parametric techniques

Often observations are nested within other units. This is particularly the case in the educational sector where school performance in terms of value added is the result of school contribution as well as pupil academic ability and other features relating to the pupil. Traditionally, the literature uses parametric (i.e. it assumes a priori a particular function on the production process) Multi-Level Models to estimate the performance of nested entities. This paper discusses the use of the non-parametric (i.e. without a priori assumptions on the production process) Free Disposal Hull model as an alternative approach. While taking into account contextual characteristics as well as atypical observations, we show how to decompose non-parametrically the overall inefficiency of a pupil into a unit specific and a higher level (i.e. a school) component. By a sample of entry and exit attainments of 3017 girls in British ordinary single sex schools, we test the robustness of the non-parametric and parametric estimates. We find that the two methods agree in the relative measures of the scope for potential attainment improvement. Further, the two methods agree on the variation in pupil attainment and the proportion attributable to pupil and school level.

Statnote 15: the non-parametric correlation coefficients

If in a correlation test, one or both variables are small whole numbers, scores based on a limited scale, or percentages, a non-parametric correlation coefficient should be considered as an alternative to Pearson’s ‘r’. Kendall’s t and Spearman’s rs are similar tests but the former should be considered if the analysis is to be extended to include partial correlations. If the data contain many tied values, then gamma should be considered as a suitable test.

The effect of corruption on FDI:a parametric and non-parametric analysis

This paper analyses the effect of corruption on Multinational Enterprises' (MNEs) incentives to undertake FDI in a particular country. We contribute to the existing literature by modelling the relationship between corruption and FDI using both parametric and non-parametric methods. We report that the impact of corruption on FDI stock is different for the different quantiles of the FDI stock distribution. This is a characteristic that could not be captured in previous studies which used only parametric methods. After controlling for the location selection process of MNEs and other host country characteristics, the result from both parametric and non-parametric analyses offer some support for the ‘helping-hand’ role of corruption.

COOPER-framework:a unified process for non-parametric projects

Practitioners assess performance of entities in increasingly large and complicated datasets. If non-parametric models, such as Data Envelopment Analysis, were ever considered as simple push-button technologies, this is impossible when many variables are available or when data have to be compiled from several sources. This paper introduces by the 'COOPER-framework' a comprehensive model for carrying out non-parametric projects. The framework consists of six interrelated phases: Concepts and objectives, On structuring data, Operational models, Performance comparison model, Evaluation, and Result and deployment. Each of the phases describes some necessary steps a researcher should examine for a well defined and repeatable analysis. The COOPER-framework provides for the novice analyst guidance, structure and advice for a sound non-parametric analysis. The more experienced analyst benefits from a check list such that important issues are not forgotten. In addition, by the use of a standardized framework non-parametric assessments will be more reliable, more repeatable, more manageable, faster and less costly. © 2010 Elsevier B.V. All rights reserved.

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios. © 2011 Elsevier Inc.

A non-parametric data envelopment analysis approach for improving energy efficiency of grape production

Grape is one of the world's largest fruit crops with approximately 67.5 million tonnes produced each year and energy is an important element in modern grape productions as it heavily depends on fossil and other energy resources. Efficient use of these energies is a necessary step toward reducing environmental hazards, preventing destruction of natural resources and ensuring agricultural sustainability. Hence, identifying excessive use of energy as well as reducing energy resources is the main focus of this paper to optimize energy consumption in grape production.In this study we use a two-stage methodology to find the association of energy efficiency and performance explained by farmers' specific characteristics. In the first stage a non-parametric Data Envelopment Analysis is used to model efficiencies as an explicit function of human labor, machinery, chemicals, FYM (farmyard manure), diesel fuel, electricity and water for irrigation energies. In the second step, farm specific variables such as farmers' age, gender, level of education and agricultural experience are used in a Tobit regression framework to explain how these factors influence efficiency of grape farming.The result of the first stage shows substantial inefficiency between the grape producers in the studied area while the second stage shows that the main difference between efficient and inefficient farmers was in the use of chemicals, diesel fuel and water for irrigation. The use of chemicals such as insecticides, herbicides and fungicides were considerably less than inefficient ones. The results revealed that the more educated farmers are more energy efficient in comparison with their less educated counterparts. © 2013.

In-situ infrared spectroscopy as a non-invasive technique to study carbon sequestration at high pressure and high temperature

We would like to thank EPSRC for a Doctoral Training Grant (G.A.M) and the Erasmus programme for supporting the study visit to Turin (R.W). We would also like to thank Dr. Federico Cesano for SEM/EDX measurements and for fruitful discussion. Dr. Jo Duncan is thanked for his tremendous insight during XRD interpretation.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

A constraint to improve the reliability of stereo matching using the rank transform

The rank transform is a non-parametric technique which has been recently proposed for the stereo matching problem. The motivation behind its application to the matching problem is its invariance to certain types of image distortion and noise, as well as its amenability to real-time implementation. This paper derives an analytic expression for the process of matching using the rank transform, and then goes on to derive one constraint which must be satisfied for a correct match. This has been dubbed the rank order constraint or simply the rank constraint. Experimental work has shown that this constraint is capable of resolving ambiguous matches, thereby improving matching reliability. This constraint was incorporated into a new algorithm for matching using the rank transform. This modified algorithm resulted in an increased proportion of correct matches, for all test imagery used.

Permutation Tests for Classification

We introduce and explore an approach to estimating statistical significance of classification accuracy, which is particularly useful in scientific applications of machine learning where high dimensionality of the data and the small number of training examples render most standard convergence bounds too loose to yield a meaningful guarantee of the generalization ability of the classifier. Instead, we estimate statistical significance of the observed classification accuracy, or the likelihood of observing such accuracy by chance due to spurious correlations of the high-dimensional data patterns with the class labels in the given training set. We adopt permutation testing, a non-parametric technique previously developed in classical statistics for hypothesis testing in the generative setting (i.e., comparing two probability distributions). We demonstrate the method on real examples from neuroimaging studies and DNA microarray analysis and suggest a theoretical analysis of the procedure that relates the asymptotic behavior of the test to the existing convergence bounds.

Effects of Ownership on Hospital Efficiency in Germany

The objective of our study was to evaluate the efficiency of public, private for-profit, and private non-profit hospitals in Germany. First, bootstrapped data envelopment analysis (DEA) was used to evaluate the efficiency of a panel (n = 1,046) of public, private for-profit, and private non-profit hospitals between 2002 and 2006. This was followed by a second-step truncated linear regression model with bootstrapped DEA efficiency scores as dependent variable. The results show that public hospitals performed significantly better than their private for-profit and non-profit counterparts. In addition, we found a significant positive association between hospital size and efficiency, and that competitive pressure had a significant negative impact on hospital efficiency.

Programmatic efficiency comparisons between unequally sized groups of DMUs in DEA

Data envelopment analysis (DEA) is a popular non-parametric technique for determining the efficiency of a homogeneous set of decision-making units (DMUs). In many practical cases, there is some doubt if the all the DMUs form a single group with a common efficiency distribution. The Mann-Whitney rank statistic has been used in DEA both to test if two groups of DMUs come from a common efficiency distribution and also to test if the two groups have a common frontier, each of which are likely to have important but different policy implications for the management of the groups. In this paper it is demonstrated that where the Mann-Whitney rank statistic is used for the second of these it is likely to overestimate programmatic inefficiency, particularly of the smaller group. A new non-parametric statistic is proposed for the case of comparing the efficient frontiers of two groups, which overcomes the problems we identify in the use of the Mann-Whitney rank statistic for this purpose. © 2005 Operational Research Society Ltd. All rights reserved.

A framework for performance evaluation of employment offices:a case of Tunisia

This paper proposes a new framework for evaluating the performance of employment offices based on non-parametric technique of data envelopment analysis. This framework is explained using the assessment of technical efficiency of 82 employment offices in Tunisia which are under the direction of the National Agency for Employment and Independent Work. We further investigated the exogenous factors that may explain part of the variation in efficiency scores using a bootstrapping approach in period January 2006 to December 2008. Given the specialisation of employment offices, we used the proposed approach for the efficiency evaluation of graduate employment offices and multi-services employment offices, separately.