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Exact critical values for one-way fixed effects models with random sample sizes

Publication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.

Analysis of variance (ANOVA) is one of the most frequently used statistical analyses in several research areas, namely in medical research. Despite its wide use, it has been applied assuming that sample dimensions are known. In this work we aim to carry out ANOVA like analysis of one-way fixed effects models, to situations where the samples sizes may not be previously known. In these situations it is more appropriate to consider the sample sizes as realizations of independent random variables. This approach must be based on an adequate choice of the distributions of the samples sizes. We assume the Poisson distribution when the occurrence of observations corresponds to a counting process. The Binomial distribution is the proper choice if we have observations failures and there exist an upper bound for the sample sizes. We also show how to carry out our main goal by computing correct critical values. The applicability of the proposed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoided by applying our approach.

2019Journal article

Open access

The flowbox theorem for divergence-free Lipschitz vector fields

Publication . Bessa, Mario

In this note, we prove the flowbox theorem for divergence-free Lipschitz vector fields.

2017Journal article

Restricted access

Parents’ educational level and second-hand tobacco smoke exposure at home in a sample of Portuguese children

Publication . Vitória, Paulo; Nunes, Célia; Precioso, J.

Second-hand tobacco smoke (SHS) exposure is a major and entirely avoidable health risk for children's health, well-being and development. The main objective of the current study was to investigate the association between parents' educational level and children's SHS home exposure. A self-administered questionnaire was conducted within a sample of 949 students in 4th grade (mean age 9.56±0.75, 53.4% male). The sample was randomly selected from all schools located at Lisbon District, Portugal. The current study confirmed that Portuguese children are exposed to unacceptable high levels of SHS at home, mainly by their parents' smoke. Prevalence of smokers was higher amongst parents with low educational level. Children of parents with low educational level were more likely to suffer SHS exposure at home. These results confirmed the social inequalities associated with smoking, support the relevance of more research on this subject and stress the need for more interventions to control this problem. Some interventions should be specifically aimed at less educated parents, particularly at less educated mothers.

2017Journal article

Open access

Convertible Subspaces of Hessenberg-Type Matrices

Publication . Cruz, Henrique F. Da; Rodrigues, Ilda Inácio; Serôdio, Rogério; Simões, A. M.; Velhinho, Jose

We describe subspaces of generalized Hessenberg matrices where the determinant is convertible into the permanent by affixing ± signs. An explicit characterization of convertible Hessenberg-type matrices is presented. We conclude that convertible matrices with the maximum number of nonzero entries can be reduced to a basic set.

2017Journal article

Restricted access

Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations

Publication . Simões, A. M.; Castro, L. P.

The purpose of this paper is to study different kinds of stability for a class of Hammerstein integral equations. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of Hammerstein integral equations. The consequent different cases of a finite interval and an infinite interval are considered, and some concrete examples are included to illustrate the results.

2017Journal article

Restricted access