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# ANOVA with random sample sizes

Seminário de Estatística e Gestão do Risco

Data: 16 de maio de 2018

Hora: 14h30

Local: Sala 1.3 Edifício VII.

Resumo:

Analysis of variance (ANOVA) is one of the most frequently used statistical analysis in practical applications. It is routinely used in several research areas, namely in medical research. Despite its wide use, it has been applied assuming that sample dimensions are known. The aim of this work is to extend the theory of one-way fixed effects ANOVA to situations where the samples sizes may not be previously known. An illustrative example of this, is the collection of observations during a fixed time period in a study comparing, for example, several pathologies of patients arriving at a hospital. In these cases it is more appropriate to consider the sample sizes as realizations of independent random variables. We will assume that the occurrences of observations correspond to counting processes, leading us to consider the sample sizes as Poisson distributed. The applicability of the proposed approach is illustrated considering a real data example on cancer registries. We also show how to compute correct critical values, which may be important to avoid working with incorrect test levels. Finally, we carry out with a simulation study, to compare and relate the performance of our approach with the common ANOVA.

Keywords: ANOVA, random sample sizes, fixed effects models, correct critical values, cancer registries.

References:

[1] Mexia, J.T., Nunes, C., Ferreira, D., Ferreira, S.S. and Moreira, E. (2011). Orthogonal fixed effects ANOVA with random sample sizes. Proceedings of the 5th International Conference on Applied Mathematics, Simulation, Modelling (ASM'11), Corfu, Greece, 2011, 84-90. Best paper Award.

[2] Nunes, C., Ferreira, D., Ferreira, S. and Mexia, J. T. (2012). F-tests with a rare pathology. Journal of Applied Statistics. Vol. 39(3), pp. 551-561.

[3] Nunes, C., Capistrano, G., Ferreira, D. and Ferreira, S.S. (2013). ANOVA with Random Sample Sizes: An Application to a Brazilian Database on Cancer Registries. 11th International Conference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. Vol. 1558, 825-828.

[4] Nunes, C., Ferreira, D., Ferreira, S.S. and Mexia, J. T. (2014). Fixed effects ANOVA: An extension to samples with random size. Journal of Statistical Computation and Simulation. Vol. 84(11), pp 2316-2328.