Comparison of ANOVA-F and ANOM tests with regard to type I error rate and test power

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dc.contributor.authorMendes, Mehmet
dc.contributor.authorYigit, Soner
dc.date.accessioned2025-01-27T21:04:09Z
dc.date.available2025-01-27T21:04:09Z
dc.date.issued2013
dc.departmentÇanakkale Onsekiz Mart Üniversitesi
dc.description.abstractA Monte Carlo simulation was conducted to compare the type I error rate and test power of the analysis of means (ANOM) test to the one-way analysis of variance F-test (ANOVA-F). Simulation results showed that as long as the homogeneity of the variance assumption was satisfied, regardless of the shape of the distribution, number of group and the combination of observations, both ANOVA-F and ANOM test have displayed similar type I error rates. However, both tests have been negatively affected from the heterogeneity of the variances. This case became more obvious when the variance ratios increased. The test power values of both tests changed with respect to the effect size (), variance ratio and sample size combinations. As long as the variances are homogeneous, ANOVA-F and ANOM test have similar powers except unbalanced cases. Under unbalanced conditions, the ANOVA-F was observed to be powerful than the ANOM-test. On the other hand, an increase in total number of observations caused the power values of ANOVA-F and ANOM test approach to each other. The relations between effect size () and the variance ratios affected the test power, especially when the sample sizes are not equal. As ANOVA-F has become to be superior in some of the experimental conditions being considered, ANOM is superior in the others. However, generally, when the populations with large mean have larger variances as well, ANOM test has been seen to be superior. On the other hand, when the populations with large mean have small variances, generally, ANOVA-F has observed to be superior. The situation became clearer when the number of the groups is 4 or 5.
dc.identifier.doi10.1080/00949655.2012.679942
dc.identifier.endpage2104
dc.identifier.issn0094-9655
dc.identifier.issn1563-5163
dc.identifier.issue11
dc.identifier.scopus2-s2.0-84886926860
dc.identifier.scopusqualityQ2
dc.identifier.startpage2093
dc.identifier.urihttps://doi.org/10.1080/00949655.2012.679942
dc.identifier.urihttps://hdl.handle.net/20.500.12428/27565
dc.identifier.volume83
dc.identifier.wosWOS:000325451100007
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherTaylor & Francis Ltd
dc.relation.ispartofJournal of Statistical Computation and Simulation
dc.relation.publicationcategoryinfo:eu-repo/semantics/openAccess
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20250125
dc.subjectanalysis of variance
dc.subjectANOM
dc.subjecttype I error
dc.subjecttest power
dc.subjectsimulation
dc.titleComparison of ANOVA-F and ANOM tests with regard to type I error rate and test power
dc.typeArticle

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