Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test

Detalhes bibliográficos
Autor(a) principal: Zimmermann, Francisco José Pfeilsticker
Data de Publicação: 2014
Tipo de documento: Artigo
Idioma: por
Título da fonte: Pesquisa Agropecuária Brasileira (Online)
Texto Completo: https://seer.sct.embrapa.br/index.php/pab/article/view/14686
Resumo: The effect of the heterocedasticity of treatments and the distribution of probability over the size and power of the F test was studied, in two experimental designs: complete randomized blocks (with 3, 5, 7, 9 e 11 treatments) and latin square (from sizes 3 x 3 to 7 x 7). Data were generated from seven probability distributions, to wit, normal, uniform, logistic, Laplace, Weibull, exponential and Cauchy. In each case 10,000 experiments were generated and it was counted the number of times the F test was significant, for the null hipotheses either true or false. Based on this counting, it could be concluded that non-normality does not affect the size and the power of the F test, which were affected only when heterocedasticity of the treatments occurred. Transformation of the data is recommended only when there is heterogeneity of variance mainly when associated to normal distribution, in which case the F test was not efficient and had a very bad test-size.
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spelling Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F testEfeito de heterogeneidade de variância e distribuição de probabilidade dos dados sobre o poder e tamanho do teste Fmathematical statistics of treatments; heterocedasticity simulation; data transformationestatística matemática; heterocedasticidade; simulação; transformação de dadosThe effect of the heterocedasticity of treatments and the distribution of probability over the size and power of the F test was studied, in two experimental designs: complete randomized blocks (with 3, 5, 7, 9 e 11 treatments) and latin square (from sizes 3 x 3 to 7 x 7). Data were generated from seven probability distributions, to wit, normal, uniform, logistic, Laplace, Weibull, exponential and Cauchy. In each case 10,000 experiments were generated and it was counted the number of times the F test was significant, for the null hipotheses either true or false. Based on this counting, it could be concluded that non-normality does not affect the size and the power of the F test, which were affected only when heterocedasticity of the treatments occurred. Transformation of the data is recommended only when there is heterogeneity of variance mainly when associated to normal distribution, in which case the F test was not efficient and had a very bad test-size.Estudou-se o efeito da heterogeneidade de variância dos tratamentos e da distribuição de probabilidade dos dados sobre o tamanho e o poder do teste F, em dois delineamentos experimentais: blocos ao acaso (com 3, 5, 7, 9 e 11 tratamentos) e quadrado latino (tamanhos de 3 x 3 até 7 x 7). Os dados foram gerados a partir de sete distribuições probabilísticas (normal, uniforme, logística, Laplace, Weibull, exponencial e Cauchy). Para cada caso, geraram-se 10.000 experimentos e contou-se o número de vezes que o teste F foi significativo, tanto nos casos de hipótese nula falsa, quanto verdadeira. Com base nesta contagem, concluiu-se que a não-normalidade dos dados não influenciou o tamanho e o poder do teste F, que só foram afetados quando houve heterogeneidade de variância. Recomenda-se, então, a transformação dos dados somente em casos de heterocedasticidade, principalmente quando associada à distribuição normal, pois, aí, verificou-se que o teste F foi totalmente prejudicado no aspecto de tamanho do teste.Pesquisa Agropecuaria BrasileiraPesquisa Agropecuária BrasileiraZimmermann, Francisco José Pfeilsticker2014-04-17info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://seer.sct.embrapa.br/index.php/pab/article/view/14686Pesquisa Agropecuaria Brasileira; v.22, n.11/12, nov./dez. 1987; 1209-1213Pesquisa Agropecuária Brasileira; v.22, n.11/12, nov./dez. 1987; 1209-12131678-39210100-104xreponame:Pesquisa Agropecuária Brasileira (Online)instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)instacron:EMBRAPAporhttps://seer.sct.embrapa.br/index.php/pab/article/view/14686/8377info:eu-repo/semantics/openAccess2014-10-14T19:58:45Zoai:ojs.seer.sct.embrapa.br:article/14686Revistahttp://seer.sct.embrapa.br/index.php/pabPRIhttps://old.scielo.br/oai/scielo-oai.phppab@sct.embrapa.br || sct.pab@embrapa.br1678-39210100-204Xopendoar:2014-10-14T19:58:45Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)false
dc.title.none.fl_str_mv Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
Efeito de heterogeneidade de variância e distribuição de probabilidade dos dados sobre o poder e tamanho do teste F
title Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
spellingShingle Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
Zimmermann, Francisco José Pfeilsticker
mathematical statistics of treatments; heterocedasticity simulation; data transformation
estatística matemática; heterocedasticidade; simulação; transformação de dados
title_short Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
title_full Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
title_fullStr Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
title_full_unstemmed Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
title_sort Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test
author Zimmermann, Francisco José Pfeilsticker
author_facet Zimmermann, Francisco José Pfeilsticker
author_role author
dc.contributor.none.fl_str_mv

dc.contributor.author.fl_str_mv Zimmermann, Francisco José Pfeilsticker
dc.subject.por.fl_str_mv mathematical statistics of treatments; heterocedasticity simulation; data transformation
estatística matemática; heterocedasticidade; simulação; transformação de dados
topic mathematical statistics of treatments; heterocedasticity simulation; data transformation
estatística matemática; heterocedasticidade; simulação; transformação de dados
description The effect of the heterocedasticity of treatments and the distribution of probability over the size and power of the F test was studied, in two experimental designs: complete randomized blocks (with 3, 5, 7, 9 e 11 treatments) and latin square (from sizes 3 x 3 to 7 x 7). Data were generated from seven probability distributions, to wit, normal, uniform, logistic, Laplace, Weibull, exponential and Cauchy. In each case 10,000 experiments were generated and it was counted the number of times the F test was significant, for the null hipotheses either true or false. Based on this counting, it could be concluded that non-normality does not affect the size and the power of the F test, which were affected only when heterocedasticity of the treatments occurred. Transformation of the data is recommended only when there is heterogeneity of variance mainly when associated to normal distribution, in which case the F test was not efficient and had a very bad test-size.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-17
dc.type.none.fl_str_mv
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://seer.sct.embrapa.br/index.php/pab/article/view/14686
url https://seer.sct.embrapa.br/index.php/pab/article/view/14686
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://seer.sct.embrapa.br/index.php/pab/article/view/14686/8377
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Pesquisa Agropecuaria Brasileira
Pesquisa Agropecuária Brasileira
publisher.none.fl_str_mv Pesquisa Agropecuaria Brasileira
Pesquisa Agropecuária Brasileira
dc.source.none.fl_str_mv Pesquisa Agropecuaria Brasileira; v.22, n.11/12, nov./dez. 1987; 1209-1213
Pesquisa Agropecuária Brasileira; v.22, n.11/12, nov./dez. 1987; 1209-1213
1678-3921
0100-104x
reponame:Pesquisa Agropecuária Brasileira (Online)
instname:Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
instacron:EMBRAPA
instname_str Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
instacron_str EMBRAPA
institution EMBRAPA
reponame_str Pesquisa Agropecuária Brasileira (Online)
collection Pesquisa Agropecuária Brasileira (Online)
repository.name.fl_str_mv Pesquisa Agropecuária Brasileira (Online) - Empresa Brasileira de Pesquisa Agropecuária (Embrapa)
repository.mail.fl_str_mv pab@sct.embrapa.br || sct.pab@embrapa.br
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