Non-normally distributed data and non-parametric statistics

Different types of numerical data can be collected in a scientific investigation and the choice of statistical analysis will often depend on the distribution of the data. A basic distinction between variables is whether they are ‘parametric’ or ‘non-parametric’. When a variable is parametric, the data come from a symmetrically shaped distribution known as the ‘Gaussian’ or ‘normal distribution’ whereas non-parametric variables may have a distribution which deviates markedly in shape from normal. This article describes several aspects of the problem of non-normality including: (1) how to test for two common types of deviation from a normal distribution, viz., ‘skew’ and ‘kurtosis’, (2) how to fit the normal distribution to a sample of data, (3) the transformation of non-normally distributed data and scores, and (4) commonly used ‘non-parametric’ statistics which can be used in a variety of circumstances.

Has DRG payment influenced the technical efficiency and productivity of diagnostic technologies in Portuguese public hospitals? An empirical analysis using parametric and non‐parametric methods

The use of Diagnosis Related Groups (DRG) as a mechanism for hospital financing is a currently debated topic in Portugal. The DRG system was scheduled to be initiated by the Health Ministry of Portugal on January 1, 1990 as an instrument for the allocation of public hospital budgets funded by the National Health Service (NHS), and as a method of payment for other third party payers (e.g., Public Employees (ADSE), private insurers, etc.). Based on experience from other countries such as the United States, it was expected that implementation of this system would result in more efficient hospital resource utilisation and a more equitable distribution of hospital budgets. However, in order to minimise the potentially adverse financial impact on hospitals, the Portuguese Health Ministry decided to gradually phase in the use of the DRG system for budget allocation by using blended hospitalspecific and national DRG casemix rates. Since implementation in 1990, the percentage of each hospitals budget based on hospital specific costs was to decrease, while the percentage based on DRG casemix was to increase. This was scheduled to continue until 1995 when the plan called for allocating yearly budgets on a 50% national and 50% hospitalspecific cost basis. While all other nonNHS third party payers are currently paying based on DRGs, the adoption of DRG casemix as a National Health Service budget setting tool has been slower than anticipated. There is now some argument in both the political and academic communities as to the appropriateness of DRGs as a budget setting criterion as well as to their impact on hospital efficiency in Portugal. This paper uses a twostage procedure to assess the impact of actual DRG payment on the productivity (through its components, i.e., technological change and technical efficiency change) of diagnostic technology in Portuguese hospitals during the years 1992–1994, using both parametric and nonparametric frontier models. We find evidence that the DRG payment system does appear to have had a positive impact on productivity and technical efficiency of some commonly employed diagnostic technologies in Portugal during this time span.

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.

Discriminating antigen and non-antigen using proteome dissimilarity:bacterial antigens

It has been postulated that immunogenicity results from the overall dissimilarity of pathogenic proteins versus the host proteome. We have sought to use this concept to discriminate between antigens and non-antigens of bacterial origin. Sets of 100 known antigenic and nonantigenic peptide sequences from bacteria were compared to human and mouse proteomes. Both antigenic and non-antigenic sequences lacked human or mouse homologues. Observed distributions were compared using the non-parametric Mann-Whitney test. The statistical null hypothesis was accepted, indicating that antigen and non-antigens did not differ significantly. Likewise, we were unable to determine a threshold able to separate meaningfully antigen from non-antigen. Thus, antigens cannot be predicted from pathogen genomes based solely on their dissimilarity to the human genome.

Discriminating antigen and non-antigen using proteome dissimilarity II:viral and fungal antigens

Immunogenicity arises via many synergistic mechanisms, yet the overall dissimilarity of pathogenic proteins versus the host proteome has been proposed as a key arbiter. We have previously explored this concept in relation to Bacterial antigens; here we extend our analysis to antigens of viral and fungal origin. Sets of known viral and fungal antigenic and non-antigenic protein sequences were compared to human and mouse proteomes. Both antigenic and non-antigenic sequences lacked human or mouse homologues. Observed distributions were compared using the non-parametric Mann-Whitney test. The statistical null hypothesis was accepted, indicating that antigen and non-antigens did not differ significantly. Likewise, we could not determine a threshold able meaningfully to separate non-antigen from antigen. We conclude that viral and fungal antigens cannot be predicted from pathogen genomes based solely on their dissimilarity to mammalian genomes.

Changes in inositol lipids and phosphates after stimulation of the MAS-transfected NG115-401L-C3 cell line by mitogenic and non-mitogenic stimuli

A neuronal cell line (NG115-401L-C3) was stimulated by mitogenic (angiotensin) and non-mitogenic (bradykinin) peptides and examined for the time course of changes in the levels of radiolabelled inositol phosphates and phospholipids. Both peptides stimulated the time-dependent production of Ins(1,4,5)P3 and related metabolites. Bradykinin caused a much larger increase in Ins(1,4,5)P3 than did angiotensin. However, both peptides stimulated similar rises in the levels of Ins(1,3,4)P3 and InsP4. Bradykinin but not angiotensin, caused a rapid (within 2 s) fall in the levels of PtdIns(4,5)P2 and PtdIns(4)P. Serum pretreatment of the cells caused a 2-3-fold potentiation of both the responses to bradykinin and angiotensin. Although significant levels of PtdIns(3)P were detected in resting cells neither mitogenic (angiotensin, insulin-like growth factor I, transforming growth factor beta) nor non-mitogenic (bradykinin, nerve growth factor interleukin-1) receptor activation changed its levels, arguing against regulation of either PtdIns 3-kinase or PtdIns(3)P phosphatase. We conclude that, as judged by the levels of its product. PtdIns(3)P, the enzyme PtdIns 3-kinase is not activated. This questions the significance of this activity in the receptor-mediated initiation of DNA synthesis.

The fallacy of integration:work and non-work in professional services

Many organisations are encouraging their staff to integrate work and non-work, but a qualitative study of young professionals found that many crave greater segregation rather than more integration. Most wished to build boundaries to separate the two and simplify a complex world. Where working practices render traditional boundaries of time and space ineffective, this population seems to create new idiosyncratic boundaries to segregate work from non-work. These idiosyncratic boundaries depended on age, culture and life-stage though for most of this population there was no appreciable gender difference in attitudes to segregating work and non-work. Gender differences only became noticeable for parents. A matrix defining the dimensions to these boundaries is proposed that may advance understanding of how individuals separate their work and personal lives. In turn, this may facilitate the development of policies and practices to integrate work and non-work that meet individual as well as organisational needs.

Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Finding closest targets in non-oriented DEA models:the case of convex and non-convex technologies

This paper draws attention for the fact that traditional Data Envelopment Analysis (DEA) models do not provide the closest possible targets (or peers) to inefficient units, and presents a procedure to obtain such targets. It focuses on non-oriented efficiency measures (which assume that production units are able to control, and thus change, inputs and outputs simultaneously) both measured in relation to a Free Disposal Hull (FDH) technology and in relation to a convex technology. The approaches developed for finding close targets are applied to a sample of Portuguese bank branches.