Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Exercício da sexualidade por adolescentes em ambientes de privação de liberdade

Este artigo apresenta os resultados de uma pesquisa cujo principal objetivo foi conhecer como se dá o exercício da sexualidade por parte de adolescentes privados de liberdade. Os dados foram coletados em três estados do nordeste brasileiro, que adotaram a política pública de oferecer visitas 'íntimas' aos jovens em conflito com a lei. Os resultados apresentam o perfil dos adolescentes, a vida sexual e os cuidados com a saúde antes da internação, o exercício da sexualidade no interior da instituição e, por fim, a visita íntima do ponto de vista dos entrevistados. Com base nesses dados e nos direitos dos adolescentes à autonomia; à participação; à igualdade e não discriminação, à integridade corporal e à saúde, essa política pública foi avaliada. Recomendações para aperfeiçoá-la foram tecidas, de modo a melhor atender aos direitos sexuais de jovens privados de liberdade.

Desistindo da denúncia ao agressor: relato de mulheres vítimas de violência doméstica

O objetivo do estudo é descrever a experiência de mulheres, vítimas da violência doméstica, que desistiram do processo contra seu agressor. As entrevistas foram orientadas pela questão: Como foi sua experiência de desistir da denúncia contra seu agressor? Das convergências dos depoimentos emergiram três temas: o tempo vivido da agressão até a denúncia e desistência; o companheiro, a família, a delegacia da mulher; refletindo sobre a experiência vivida, que descrevem o fenômeno estudado. As participantes expressam sentimentos ambíguos em relação ao agressor: afetividade, raiva, humilhação e medo. Reconhecem que são dominadas e humilhadas. Porém, noções de justiça e igualdade entre os cônjuges não aparecem nos depoimentos. A desistência do processo pode ser compreendida na concepção da reprodução da estrutura familiar, condicionada a fatores econômicos e sociais. Os resultados remetem à reflexão sobre o papel da Delegacia da Mulher e das instituições de saúde na assistência à mulher vítima da violência doméstica

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Exact nonequilibrium work generating function for a small classical system

We obtain the exact nonequilibrium work generating function (NEWGF) for a small system consisting of a massive Brownian particle connected to internal and external springs. The external work is provided to the system for a finite-time interval. The Jarzynski equality, obtained in this case directly from the NEWGF, is shown to be valid for the present model, in an exact way regardless of the rate of external work.

Impact of the Subprime Crisis in the Provision of Credit Risk of Major National Banks

Financial institutions are directly exposed to the credit risk, that is, the risk of the borrower not fulfill with their obligations, paying their debts in its stated periods established previously. The bank predict this type of risk, including them in their balance-sheets. In 2006/2007 there was the impact of a new financial crisis that spread around the world, known as the crisis of subprime. The objective of this study is to analyze if the provisions for credit risk or liquidation increased the sprouting of the crisis of subprime in ten major national banks, chosen accordant to their total assets. To answer this question, the balance-sheets of each one of these banks in the period of 2005 to 2007 were analyzed. This research is characterized, as for its objectives, as descriptive and as for the procedures as documentary research. It is also characterized as having a qualitative approach. The results show that the crisis of subprime has caused little impact in the credit risk provision of the analyzed institutions. It was noticed a slight increase in the provision indicators at the peak of the crisis in 2006. These percentages were reduced in, 2007, probably reflecting the economic stability of Brazil and the stagnation of the crisis Of subprime in that year, at least in relation to in our country.

Time flies with music whatever its emotional valence

The present study used a temporal bisection task to investigate whether music affects time estimation differently from a matched auditory neutral stimulus, and whether the emotional valence of the musical stimuli (i.e., sad vs. happy music) modulates this effect. The results showed that, compared to sine wave control music, music presented in a major (happy) or a minor (sad) key shifted the bisection function toward the right, thus increasing the bisection point value (point of subjective equality). This indicates that the duration of a melody is judged shorter than that of a non-melodic control stimulus, thus confirming that ""time flies"" when we listen to music. Nevertheless, sensitivity to time was similar for all the auditory stimuli. Furthermore, the temporal bisection functions did not differ as a function of musical mode. (C) 2010 Elsevier B.V. All rights reserved.