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- Random sample sizes in one-way fixed effects modelsPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.Analysis of variance (ANOVA) is one of the most frequently used statistical analysis 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. Assuming that the samples were generated by Pois- son counting processes we obtain the unconditional distribution of the test statistic, under the assumption that we have random sample sizes. The applicability of the pro- posed approach is illustrated considering a real data example on cancer registries. The results obtained suggested that false rejections may be avoid by applying our approach.
- Exact critical values for one-way fixed effects models with random sample sizesPublication . 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.
- Fixed effects ANOVA: an extension to samples with random sizePublication . Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.In many relevant situations, such as in medical research, sample sizes may not be previously known. The aim of this paper is to extend one and more than one-way analysis of variance to those situations and show how to compute correct critical values. The interest of this approach lies in avoiding false rejections obtained when using the classical fixed size F-tests. Sample sizes are assumed as random and we then proceed with the application of this approach to a database on cancer.
- Random sample sizes in orthogonal mixed models with stabilityPublication . Nunes, Célia; Mário, Anacleto César Xavier; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.In this work, we presente a new approach that considers orthogonal mixed models, under situations of stability, when the sample dimensions are not known in advande. In this case, samples are considered realizations of independente rendom variables. We apply this methodology to the case where there is na upper bound for the sample dimensions, which may not be attained since failures may occur. Based on this, we assume that sample sizes are binomially distributed. We consider na application on the incidence of unemployed persons in the European Union to illustrate the proposed methodology. A simulation study is also conduced. The obtained results show the relevance of the proposed approach in avoiding false rejections.
- ANOVA with random sample sizes: An application to a Brazilian database on cancer registriesPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.
- One-way random effects ANOVA with random sample sizes: An application to a Brazilian database on cancer registriesPublication . Capistrano, Gilberto; Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.
- Orthogonal fixed effects ANOVA with random sample sizesPublication . Mexia, J. T.; Nunes, Célia; Ferreira, Dário; Ferreira, Sandra S.; Moreira, ElsaIn many relevant situations, such as in medical research, sample sizes may not be previously known. We extend ANOVA to those situations starting with one-way and then the general orthogonal situation. Sample sizes will be assumed to be random.
- One-way fixed effects ANOVA with missing observationsPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.; Mexia, João T.The aim of this paper is to extend the theory of F-tests with random sample sizes to situations when missing observations may occur. We consider the one-way ANOVA with fixed effects. This approach is illustrated through an application to patients affected by melanoma skin cancer, from three different states of Brazil.
- Considering the sample sizes as truncated Poisson random variables in mixed effects modelsPublication . Nunes, Célia; Moreira, Elsa E.; Ferreira, Sandra S.; Ferreira, Dário; Mexia, João T.When applying analysis of variance, the sample sizes may not be previously known, so it is more appropriate to consider them as realizations of random variables. A motivating example is the collection of observations during a fixed time span in a study comparing, for example, several pathologies of patients arriving at a hospital. This paper extends the theory of analysis of variance to those situations considering mixed effects models. We will assume that the occurrences of observations correspond to a counting process and the sample dimensions have Poisson distribution. The proposed approach is applied to a study of cancer patients.