12,872 research outputs found
Some Notes on Indicator Variable Reduction
No full textMarozzi presented a simple method to reduce the dimension of indicator variables, compared it to PCA and showed that is markedly simpler to be used and requires milder assumptions. An application to university student satisfaction was discussed. In this paper we present further research about this method. Firstly, we propose two alternative ways for reducing the dimension of indicator variables of which one resembles regression forward selection, and apply them to the data considered in Marozzi (2008). General indications on which method choose are given. Secondly, we evaluate how the choice of the correlation coefficient influences the results
Multivariate Tri-Aspect Non-Parametric Testing
No full textPermutation tests are prized for their lack of assumptions concerning distribution of underlying populations. The (usual) permutation test for the two-sample location problem based on comparison of sample means is generally effective with regular, roughly symmetric, unimodal, and light-tailed distributions, whereas it might not be so with highly asymmetric and/or heavy-tailed distributions. Another drawback is that it is not consistent for distributions for which first and second moments do not exist. Marozzi [Marozzi, M., 2004, A bi-aspect nonparametric test for the two-sample location problem. Computational Statistics and Data Analysis, 44, 639–648.] proposed a bi-aspect non-parametric test for comparing two populations obtained by non-parametric combining the usual permutation test (which addresses the numerical aspect Xi ) and a test based on comparison of frequencies over the pooled median (which addresses the categorical aspect related to the comparison of sample units with the pooled sample median). Unlike the usual permutation test, the bi-aspect test is consistent for every distribution and is very powerful with highly-skewed and/or heavy-tailed distributions. In the paper, the bi-aspect testing idea is extended by also considering the aspect based on ranks, with the role of third aspect. A simulation study with many sample size and distribution settings shows that the triaspect test is more powerful than the bi-aspect one. Moreover, the multivariate problem is addressed and formal proofs of exactness, unbiasedness, and consistency are given
A Tri-Aspect Distribution Free Test for the Multivariate Location Problem
No full textThe paper refers to an extension of Marozzi (2004) Tab test by including as a third aspect in the combination the rank aspect. Tc test is very useful for distributions that have an intermediate outlier production behavior with respect to that of the normal (for which Ta is a good test) and Cauchy (for which Tb is a good test) distributions. The nonparametric combination of Ta, Tb and Tc tests is effective because it agrees with the idea of considering something close to the best of the combined tests, and this by taking account nonparametrically of their mutual dependence
Bi-Aspect Nonparametric Testing
No full textFacendo riferimento alla teoria della Combinazione Nonparametrica (Pesarin 2001), Marozzi (2002 & 2003) ha proposto due metodi nonparametrici bi-aspetto per il controllo di ipotesi sulla locazione. Esperimenti di simulazione rivelano come questi test siano marcatamente più potenti dei tradizionali test parametrici e di permutazione (tipicamente test uni-aspetto) quando la distribuzione generatrice è a coda pesante o notevolmente asimmetrica. In questo lavoro si fornisce una presentazione dettagliata e unificata della teoria e dell’idea alla base dei metodi. Vengono inoltre discusse alcune applicazioni a dati reali che mostrano come i test bi-aspetto permettano di condurre un’inferenza maggiormente informativa di quella ottenibile con strumenti tradizionali
Applications in Business, Medical and Industrial Statistics of Bi-Aspect Nonparametric Tests for Location Problems
No full textStarting from the theory of the Nonparametric Combination of Dependent Permutation Tests (Pesarin, 1992 & 2001), Marozzi (2002a & 2002b) proposed two bi-aspect nonparametric tests for the two-sample and the multi-sample location problems. These tests are shown by simulation to be remarkably more powerful than the traditional parametric and permutation competitors (which can be seen as uni-aspect tests) under heavy-tailed and skewed distributions. After a brief presentation of the bi-aspect idea to location testing problems, three actual applications are discussed. The first one is a problem of business statistics and deals with the analysis of time for service calls. The second one is in medical statistics and deals with the analysis of the effect of cigarette smoking on maternal airway function during pregnancy. The third one is in industrial statistics and deals with the analysis of the setting of machines that produce steel ball bearings. The bi-aspect testing allows us to draw deeper and more informative inference than that allowed by traditional competitors
Multivariate Bi-Aspect Testing for the Two-Sample Location Problem
No full textThe multivariate extension of the bi-aspect nonparametric testing procedure for the two-sample location problem presented in Marozzi (2004) is discussed. Two solutions are presented: the former is focused on each variable, the latter is focused on each of the two aspects involved in the bi-aspect (the categorical and the numerical one). Formal proofs of exactness, unbiasedness, and consistency of the multivariate tests are given. Such properties hold even when population first and second moments do not exist
A Bi-Aspect Nonparametric Test for the Multi-Sample Location Problem
No full textA bi-aspect nonparametric test for testing hypotheses of location shifts of two populations was proposed in literature. The test is based on the nonparametric combination of dependent tests theory and is obtained by combining the traditional permutation test for the two-sample location problem with a test that takes into account whether a sample observation is or is not greater than the pooled sample median. A natural multi-sample extension of the test is proposed. The extension is shown by simulation to behave very similarly to the bi-aspect test for the two-sample problem. In fact, it is shown that the proposed test is remarkably more powerful than the traditional permutation test for the multi-sample location problem under heavy-tailed distributions like the Cauchy, the half-Cauchy, the 10% and the 30% outlier distributions. When sampling from the double-exponential and the exponential distributions, the proposed test appears to be better on the whole than the traditional permutation test. Under the considered t2 distributions, the bi-aspect test is practically as powerful as the traditional permutation test. Whereas under normal, uniform and bimodal distributions it is slightly less powerful. Moreover, the proposed test maintained the type-one error rate close to the nominal significance level and was generally slightly conservative
A composite indicator dimension reduction procedure with application to university student satisfaction
No full textUniversities play a central role within society and should provide high quality services to students. Therefore, a careful evaluation of university services is necessary. This evaluation is complex because involves many partial aspects and can be assessed through a composite indicator. In the paper we propose a simple method for reducing the number of partial aspects underlying a composite indicator. A practical application to data from a sample survey conducted on last year students of the University of Padova is discussed. This survey considered the quality of many services, lecture rooms, library services, computer classrooms, reading rooms in libraries, study rooms, structure of exams, student socialization, reached skills and so forth. The method has been compared with principal component analysis. The results show that our method is worth of consideration since is markedly simpler to be applied than other dimension reduction methods and requires milder assumptions
Does bad inference drive out good?
No full textThe (mis)use of statistics in practice is widely debated, and a field where the debate is particularly active is medicine. Many scholars emphasize that a large proportion of published medical research contains statistical errors. It has been noted that top class journals like Nature Medicine and The New England Journal of Medicine publish a considerable proportion of papers that contain statistical errors and poorly document the application of statistical methods. This paper joins the debate on the (mis)use of statistics in the medical literature. Even though the validation process of a statistical result may be quite elusive, a careful assessment of underlying assumptions is central in medicine as well as in other fields where a statistical method is applied. Unfortunately, a careful assessment of underlying assumptions is missing in many papers, including those published in top class journals. In this paper, we show that nonparametric methods are good alternatives to parametric methods when the assumptions for the latter ones are not satisfied. A key point to solve the problem of the misuse of statistics in the medical literature is that all journals have their own statisticians to review the statistical method/analysis section in each submitted paper
Composite Indicators: a Sectorial Perspective
No full textFinancial analysts, managers, lenders and academic researchers widely use financial ratios. For example, financial analysts use them to predict how well the securities of one company will perform relative to that of another one, and lenders use them to predict if the borrower will be able to sustain interests and pay the principal. Ratios measuring profitability, activity, efficiency and liquidity are considered. Since most financial ratios by themselves may not be highly meaningful, they should be viewed as indicators, with some of them combined to get a more complete picture of the company. [9] addressed this question by using composite financial indicators, and proposed a simple method for reducing the dimension of a composite indicator. The liquidity issue has been considered. In this paper we extend [9] results by following a sectorial perspective. Financial ratio industry averages may differ markedly and therefore it is of interest to explicitly take into account company sector when computing a composite financial indicator. The results indicate that both the short-term and the long-term liquidity point of view are important in ranking the companies irrespective of the sector they belong to. However, it is suggested to group the companies according to the industry sector they belong to before applying the dimension reduction procedure because the importance of the ratios differ between sector and sector. The comparison with principal component analysis is addressed
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