Conditional Frequentist Test on Normal Mean Parameter and its application in entomological data

Conditional Frequentist Test on Normal Mean Parameter and its application in entomological data

Authors

  • Carla Guimarães Brighenti Universidade Federal de São João del Rei
  • Thelmo Souza Oliveira Universidade Federal de São João Del Rei
  • Deodoro Magno Brighenti Universidade Federal de São João Del Rei

DOI:

https://doi.org/10.5433/1679-0375.2014v35n2p139

Keywords:

Likelihood Ratio, Partitioning Function, Conditional Error Probability, Africanized bees

Abstract

In the traditional tests the value of type I error (?) is fixed, on the other hand, in the conditional frequentist test we propose a partition of the region of rejection and acceptance so that the probability of error presented is dependent on the distance of observed data in relation to the border of the critical region. This error probability is the Conditional Error Probability (CEP), which may be of type I or II. The objective of this study was to evaluate the behavior of the conditional frequentist test under the Normal Mean parameter and apply it to entomological data. The test was evaluated via simulation, from developed routine in R software. In each simulated case obtained the likelihood ratio, the critical value and the PEC’s for the Normal distribution. It was concluded that the highest values of PEC were obtained with the more the sample mean value approaching the critical point of the test. This occurs regardless of the decision of the test to accept or reject the null hypothesis. The increase of the sample size causes the reduction of the conditional probability of error. In the application to real data from the average lifetime of bees exposed to different temperatures, it was found that the average lifetime of bees maintained at a temperature of 20°C was found to be similar at a temperature of 15°C with conditional error very small (CEP II equal to 0.54%). For temperatures of 30°C and 35°C the hypothesis was rejected with PEC I equal to 28.35% and 47.53%, respectively. Thus the conditional errors in decision making were very high.

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Author Biography

Carla Guimarães Brighenti, Universidade Federal de São João del Rei

Possui graduação em Ciências pela Universidade Federal de São João del-Rei (1997), licenciatura em Matemática pela Universidade Tricordiana de Educação (1996) , mestrado em Agroquímica pela Universidade Federal de Viçosa (2000), especialização em Matemática pela Universidade Federal de Viçosa (2001), mestrado em Estatística e Experimentação Agropecuária pela Universidade Federal de Lavras (2002) e doutorado em Estatística e Experimentação Agropecuária na Universidade Federal de Lavras(2007). Foi professora efetiva da EPCAr- Escola Preparatória de Cadetes do Ar de 1997 a 2008 e atualmente é professora adjunto III da Universidade Federal de São João del Rei no Departamento de Zootecnia e tem experiência na área de Estatística Aplicada atuando principalmente nos seguintes temas: testes frequentistas condicionais, análise sequencial, análise de sobrevivência, estatística aplicada a dados zootecnicos

Published

2014-10-30

How to Cite

Brighenti, C. G., Oliveira, T. S., & Brighenti, D. M. (2014). Conditional Frequentist Test on Normal Mean Parameter and its application in entomological data. Semina: Ciências Exatas E Tecnológicas, 35(2), 139–148. https://doi.org/10.5433/1679-0375.2014v35n2p139

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