Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments

Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments

ABSTRACT: This research evaluated the importance of a preliminary general analysis of variance (ANOVA) in the interpretation of data from factorial experiments under total nullity. For this, we evaluated the familywise type I error rate (accumulated FWER) of the F test for the unfolding of factorial ANOVA and factorial ANOVA on ranks, which were compared with the FWER for the global effect of treatments. In addition, we evaluated the FWER of the Tukey’s test under total nullity for factorial experiments in the presence or absence of preliminary ANOVA protection (omnibus F test). The study was conducted by simulating data from 2,000 experiments, which were separated into four representative agricultural research scenarios. For both the parametric factorial ANOVA and the non-parametric factorial ANOVA, the FWER significantly exceeded the nominal level of 5%, even under total nullity. While the tests that control the total FWER in the factorials are not being used, the factorial ANOVA should not be performed without the preliminary ANOVA F test showing a significant effect. This, of course, does not apply to tests that are not multiple comparisons, such as Bonferroni, Dunn-Sidak and others, which do not need ANOVA protection. The same recommendation applies to the factorial ANOVA on ranks.

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Main Authors: Carvalho,André Mundstock Xavier de, Souza,Matheus Romano de, Marques,Tadeu Bernardes, Souza,Davi Leite de, Souza,Emanuel Fernando Maia de
Format: Digital revista
Language:English
Published: Universidade Federal de Santa Maria 2023
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-84782023000700201
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spelling oai:scielo:S0103-847820230007002012022-10-19Familywise type I error of ANOVA and ANOVA on ranks in factorial experimentsCarvalho,André Mundstock Xavier deSouza,Matheus Romano deMarques,Tadeu BernardesSouza,Davi Leite deSouza,Emanuel Fernando Maia de omnibus F-test aligned rank transformation multiplicity in multiway ANOVA ABSTRACT: This research evaluated the importance of a preliminary general analysis of variance (ANOVA) in the interpretation of data from factorial experiments under total nullity. For this, we evaluated the familywise type I error rate (accumulated FWER) of the F test for the unfolding of factorial ANOVA and factorial ANOVA on ranks, which were compared with the FWER for the global effect of treatments. In addition, we evaluated the FWER of the Tukey’s test under total nullity for factorial experiments in the presence or absence of preliminary ANOVA protection (omnibus F test). The study was conducted by simulating data from 2,000 experiments, which were separated into four representative agricultural research scenarios. For both the parametric factorial ANOVA and the non-parametric factorial ANOVA, the FWER significantly exceeded the nominal level of 5%, even under total nullity. While the tests that control the total FWER in the factorials are not being used, the factorial ANOVA should not be performed without the preliminary ANOVA F test showing a significant effect. This, of course, does not apply to tests that are not multiple comparisons, such as Bonferroni, Dunn-Sidak and others, which do not need ANOVA protection. The same recommendation applies to the factorial ANOVA on ranks.info:eu-repo/semantics/openAccessUniversidade Federal de Santa MariaCiência Rural v.53 n.7 20232023-01-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-84782023000700201en10.1590/0103-8478cr20220146
institution SCIELO
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country Brasil
countrycode BR
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databasecode rev-scielo-br
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region America del Sur
libraryname SciELO
language English
format Digital
author Carvalho,André Mundstock Xavier de
Souza,Matheus Romano de
Marques,Tadeu Bernardes
Souza,Davi Leite de
Souza,Emanuel Fernando Maia de
spellingShingle Carvalho,André Mundstock Xavier de
Souza,Matheus Romano de
Marques,Tadeu Bernardes
Souza,Davi Leite de
Souza,Emanuel Fernando Maia de
Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
author_facet Carvalho,André Mundstock Xavier de
Souza,Matheus Romano de
Marques,Tadeu Bernardes
Souza,Davi Leite de
Souza,Emanuel Fernando Maia de
author_sort Carvalho,André Mundstock Xavier de
title Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
title_short Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
title_full Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
title_fullStr Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
title_full_unstemmed Familywise type I error of ANOVA and ANOVA on ranks in factorial experiments
title_sort familywise type i error of anova and anova on ranks in factorial experiments
description ABSTRACT: This research evaluated the importance of a preliminary general analysis of variance (ANOVA) in the interpretation of data from factorial experiments under total nullity. For this, we evaluated the familywise type I error rate (accumulated FWER) of the F test for the unfolding of factorial ANOVA and factorial ANOVA on ranks, which were compared with the FWER for the global effect of treatments. In addition, we evaluated the FWER of the Tukey’s test under total nullity for factorial experiments in the presence or absence of preliminary ANOVA protection (omnibus F test). The study was conducted by simulating data from 2,000 experiments, which were separated into four representative agricultural research scenarios. For both the parametric factorial ANOVA and the non-parametric factorial ANOVA, the FWER significantly exceeded the nominal level of 5%, even under total nullity. While the tests that control the total FWER in the factorials are not being used, the factorial ANOVA should not be performed without the preliminary ANOVA F test showing a significant effect. This, of course, does not apply to tests that are not multiple comparisons, such as Bonferroni, Dunn-Sidak and others, which do not need ANOVA protection. The same recommendation applies to the factorial ANOVA on ranks.
publisher Universidade Federal de Santa Maria
publishDate 2023
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-84782023000700201
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