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

Célia Nunes, Gilberto Capistrano, Dário Ferreira, Sandra S. Ferreira, João Tiago Mexia

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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.

Original languageEnglish
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - Jul 2019


  • Cancer registries
  • Correct critical values
  • Fixed effects models
  • Random sample sizes


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