An extremal property of normal distributions is that they have the smallest Fisher Information for location among all distributions with the same variance. A new test of normality proposed by Terrell (1995) utilizes the above property by finding that density of maximum likelihood constrained on having the expected Fisher Information under normality based on the sample variance. The test statistic is then constructed as a ratio of the resulting likelihood against that of normality. Since the asymptotic distribution of this test statistic is not available, the critical values for n = 3 to 200 have been obtained by simulation and smoothed using polynomials. An extensive power study shows that the test has superior power against distributions that are symmetric and leptokurtic (long-tailed). Another advantage of the test over existing ones is the direct depiction of any deviation from normality in the form of a density estimate. This is evident when the test is applied to several real data sets. Testing of normality in residuals is also investigated. Various approaches in dealing with residuals being possibly heteroscedastic and correlated suffer from a loss of power. The approach with the fewest undesirable features is to use the Ordinary Least Squares (OLS) residuals in place of independent observations. From simulations, it is shown that one has to be careful about the levels of the normality tests and also in generalizing the results. / Ph. D.

Notre progiciel PoweR vise à faciliter l'obtention ou la vérification des études empiriques de puissance pour les tests d'ajustement. En tant que tel, il peut être considéré comme un outil de calcul de recherche reproductible, car il devient très facile à reproduire (ou détecter les erreurs) des résultats de simulation déjà publiés dans la littérature. En utilisant notre progiciel, il devient facile de concevoir de nouvelles études de simulation. Les valeurs critiques et puissances de nombreuses statistiques de tests sous une grande variété de distributions alternatives sont obtenues très rapidement et avec précision en utilisant un C/C++ et R environnement. On peut même compter sur le progiciel snow de R pour le calcul parallèle, en utilisant un processeur multicœur. Les résultats peuvent être affichés en utilisant des tables latex ou des graphiques spécialisés, qui peuvent être incorporés directement dans vos publications. Ce document donne un aperçu des principaux objectifs et les principes de conception ainsi que les stratégies d'adaptation et d'extension. / Package PoweR aims at facilitating the obtainment or verification of empirical power studies for goodness-of-fit tests. As such, it can be seen as a reproducible research computational tool because it becomes very easy to reproduce (or detect errors in) simulation results already published in the literature. Using our package, it becomes easy to design new simulation studies. The empirical levels and powers for many statistical test statistics under a wide variety of alternative distributions are obtained fastly and accurately using a C/C++ and R environment. One can even rely on package snow to parallelize their computations, using a multicore processor. The results can be displayed using LaTeX tables or specialized graphs, which can be directly incorporated into your publications. This paper gives an overview of the main design aims and principles as well as strategies for adaptation and extension. Hand-on illustrations are presented to get new users started easily.

Notre progiciel PoweR vise à faciliter l'obtention ou la vérification des études empiriques de puissance pour les tests d'ajustement. En tant que tel, il peut être considéré comme un outil de calcul de recherche reproductible, car il devient très facile à reproduire (ou détecter les erreurs) des résultats de simulation déjà publiés dans la littérature. En utilisant notre progiciel, il devient facile de concevoir de nouvelles études de simulation. Les valeurs critiques et puissances de nombreuses statistiques de tests sous une grande variété de distributions alternatives sont obtenues très rapidement et avec précision en utilisant un C/C++ et R environnement. On peut même compter sur le progiciel snow de R pour le calcul parallèle, en utilisant un processeur multicœur. Les résultats peuvent être affichés en utilisant des tables latex ou des graphiques spécialisés, qui peuvent être incorporés directement dans vos publications. Ce document donne un aperçu des principaux objectifs et les principes de conception ainsi que les stratégies d'adaptation et d'extension. / Package PoweR aims at facilitating the obtainment or verification of empirical power studies for goodness-of-fit tests. As such, it can be seen as a reproducible research computational tool because it becomes very easy to reproduce (or detect errors in) simulation results already published in the literature. Using our package, it becomes easy to design new simulation studies. The empirical levels and powers for many statistical test statistics under a wide variety of alternative distributions are obtained fastly and accurately using a C/C++ and R environment. One can even rely on package snow to parallelize their computations, using a multicore processor. The results can be displayed using LaTeX tables or specialized graphs, which can be directly incorporated into your publications. This paper gives an overview of the main design aims and principles as well as strategies for adaptation and extension. Hand-on illustrations are presented to get new users started easily.