The Effects of Single and Compound Violations of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Models.
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| Title: | The Effects of Single and Compound Violations of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Models. |
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| Language: | English |
| Authors: | Johnson, Colleen Cook |
| Peer Reviewed: | N |
| Page Count: | 31 |
| Publication Date: | 1993 |
| Document Type: | Reports - Research Speeches/Meeting Papers |
| Descriptors: | Analysis of Covariance, Analysis of Variance, Computer Simulation, Models, Monte Carlo Methods, Robustness (Statistics), Sample Size, Sampling |
| Abstract: | This study integrates into one comprehensive Monte Carlo simulation a vast array of previously defined and substantively interrelated research studies of the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) statistical procedures. Three sets of balanced ANOVA and ANCOVA designs (group sizes of 15, 30, and 45) and one set of unbalanced ANOVA and ANCOVA designs (groups of 15, 30, and 45) were simulated. Violations of normal shape and three degrees of heterogeneity of group variances were included. Each set of ANCOVA analyses included ANOVA violations as well. Each data set violation was simulated in isolation and in combination, resulting in 665 unique ANOVA or ANCOVA F sampling distributions. Unbalanced designs almost always produced statistically invalid F ratios in the presence of any data set assumption except those that only involved perturbation of shape. In balanced designs, a degree of robustness beyond that expected was found, even when heterogeneity of variance was coupled with heterogeneous regression slopes and a skewed covariate. Robustness was found even when the ratio of largest to smallest group variance was five. Implications of these findings for educational, social science, and behavioral research are discussed. Three tables are included. (Contains 29 references.) (Author/SLD) |
| Entry Date: | 1994 |
| Accession Number: | ED365730 |
| Database: | ERIC |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED365730 Name: ERIC Full Text Category: fullText Text: Full Text from ERIC |
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| Header | DbId: eric DbLabel: ERIC An: ED365730 AccessLevel: 3 PubType: Report PubTypeId: report PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The Effects of Single and Compound Violations of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Models. – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Johnson%2C+Colleen+Cook%22">Johnson, Colleen Cook</searchLink> – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: N – Name: Pages Label: Page Count Group: Src Data: 31 – Name: DatePubCY Label: Publication Date Group: Date Data: 1993 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Reports - Research<br />Speeches/Meeting Papers – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Analysis+of+Covariance%22">Analysis of Covariance</searchLink><br /><searchLink fieldCode="DE" term="%22Analysis+of+Variance%22">Analysis of Variance</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Simulation%22">Computer Simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+Methods%22">Monte Carlo Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Robustness+%28Statistics%29%22">Robustness (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Sample+Size%22">Sample Size</searchLink><br /><searchLink fieldCode="DE" term="%22Sampling%22">Sampling</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study integrates into one comprehensive Monte Carlo simulation a vast array of previously defined and substantively interrelated research studies of the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) statistical procedures. Three sets of balanced ANOVA and ANCOVA designs (group sizes of 15, 30, and 45) and one set of unbalanced ANOVA and ANCOVA designs (groups of 15, 30, and 45) were simulated. Violations of normal shape and three degrees of heterogeneity of group variances were included. Each set of ANCOVA analyses included ANOVA violations as well. Each data set violation was simulated in isolation and in combination, resulting in 665 unique ANOVA or ANCOVA F sampling distributions. Unbalanced designs almost always produced statistically invalid F ratios in the presence of any data set assumption except those that only involved perturbation of shape. In balanced designs, a degree of robustness beyond that expected was found, even when heterogeneity of variance was coupled with heterogeneous regression slopes and a skewed covariate. Robustness was found even when the ratio of largest to smallest group variance was five. Implications of these findings for educational, social science, and behavioral research are discussed. Three tables are included. (Contains 29 references.) (Author/SLD) – Name: DateEntry Label: Entry Date Group: Date Data: 1994 – Name: AN Label: Accession Number Group: ID Data: ED365730 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=ED365730 |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English PhysicalDescription: Pagination: PageCount: 31 Subjects: – SubjectFull: Analysis of Covariance Type: general – SubjectFull: Analysis of Variance Type: general – SubjectFull: Computer Simulation Type: general – SubjectFull: Models Type: general – SubjectFull: Monte Carlo Methods Type: general – SubjectFull: Robustness (Statistics) Type: general – SubjectFull: Sample Size Type: general – SubjectFull: Sampling Type: general Titles: – TitleFull: The Effects of Single and Compound Violations of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Models. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Johnson, Colleen Cook IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Type: published Y: 1993 |
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