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Effects of Violations of Data Set Assumptions When Using the Analysis of Variance and Covariance with Unequal Group Sizes.

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Title: Effects of Violations of Data Set Assumptions When Using the Analysis of Variance and Covariance with Unequal Group Sizes.
Language: English
Authors: Johnson, Colleen Cook, Rakow, Ernest A.
Peer Reviewed: N
Page Count: 27
Publication Date: 1994
Document Type: Reports - Evaluative
Speeches/Meeting Papers
Descriptors: Analysis of Covariance, Analysis of Variance, Educational Research, Monte Carlo Methods, Research Methodology, Robustness (Statistics), Simulation, Statistical Significance
Abstract: This research explored the degree to which group sizes can differ before the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are jeopardized. Monte Carlo methodology was used, allowing for the experimental investigation of potential threats to robustness under conditions common to researchers in education. The effects of unequal group sizes were explored under the following data set conditions: (1) heterogeneity of group variances; (2) skew; (3) kurtosis; and (4) in ANCOVA, heterogeneity of regression slopes. Two independent sets of simulations were conducted, one using a total group of 90 and the other a total of 60. Experimentation was limited to simulations using three groups, with the total number divided in a systematic fashion. Results of these studies produced results consistent with previous research. In the analyses having homogeneity of group variances, the only simulations that emerged as statistically significant from the theoretical F test were those that had a large degree of difference in group numbers and unequal regression slopes. No significant differences emerged in simulations with near equal numbers. Tables in this paper document the simulation results, but also offer the research practitioner some idea of the true risk of Type I error in such situations. (Contains 7 tables and 24 references.) (SLD)
Entry Date: 1996
Accession Number: ED389729
Database: ERIC
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Effects of Violations of Data Set Assumptions When Using the Analysis of Variance and Covariance with Unequal Group Sizes.
– Name: Language
  Label: Language
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  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Johnson%2C+Colleen+Cook%22">Johnson, Colleen Cook</searchLink><br /><searchLink fieldCode="AR" term="%22Rakow%2C+Ernest+A%2E%22">Rakow, Ernest A.</searchLink>
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: N
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 27
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 1994
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Reports - Evaluative<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="%22Educational+Research%22">Educational Research</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+Methods%22">Monte Carlo Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Research+Methodology%22">Research Methodology</searchLink><br /><searchLink fieldCode="DE" term="%22Robustness+%28Statistics%29%22">Robustness (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Simulation%22">Simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Significance%22">Statistical Significance</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This research explored the degree to which group sizes can differ before the robustness of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are jeopardized. Monte Carlo methodology was used, allowing for the experimental investigation of potential threats to robustness under conditions common to researchers in education. The effects of unequal group sizes were explored under the following data set conditions: (1) heterogeneity of group variances; (2) skew; (3) kurtosis; and (4) in ANCOVA, heterogeneity of regression slopes. Two independent sets of simulations were conducted, one using a total group of 90 and the other a total of 60. Experimentation was limited to simulations using three groups, with the total number divided in a systematic fashion. Results of these studies produced results consistent with previous research. In the analyses having homogeneity of group variances, the only simulations that emerged as statistically significant from the theoretical F test were those that had a large degree of difference in group numbers and unequal regression slopes. No significant differences emerged in simulations with near equal numbers. Tables in this paper document the simulation results, but also offer the research practitioner some idea of the true risk of Type I error in such situations. (Contains 7 tables and 24 references.) (SLD)
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 1996
– Name: AN
  Label: Accession Number
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  Data: ED389729
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 27
    Subjects:
      – SubjectFull: Analysis of Covariance
        Type: general
      – SubjectFull: Analysis of Variance
        Type: general
      – SubjectFull: Educational Research
        Type: general
      – SubjectFull: Monte Carlo Methods
        Type: general
      – SubjectFull: Research Methodology
        Type: general
      – SubjectFull: Robustness (Statistics)
        Type: general
      – SubjectFull: Simulation
        Type: general
      – SubjectFull: Statistical Significance
        Type: general
    Titles:
      – TitleFull: Effects of Violations of Data Set Assumptions When Using the Analysis of Variance and Covariance with Unequal Group Sizes.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Johnson, Colleen Cook
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          Name:
            NameFull: Rakow, Ernest A.
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          Dates:
            – D: 11
              M: 11
              Type: published
              Y: 1994
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