View in EDS

The Effects of Violation of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Procedures.

Saved in:
Bibliographic Details
Title: The Effects of Violation of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Procedures.
Language: English
Authors: Johnson, Colleen Cook
Peer Reviewed: N
Page Count: 15
Publication Date: 1993
Document Type: Reports - Evaluative
Speeches/Meeting Papers
Descriptors: Analysis of Covariance, Analysis of Variance, Comparative Analysis, Computer Simulation, Monte Carlo Methods, Reliability, Research Design, Sample Size, Sampling, Statistical Distributions
Abstract: The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects analysis of variance (ANOVA) and one concomitant analysis of covariance (ANCOVA) statistical procedure. Methodological and data set statistical assumptions that must be met for ANOVA and ANCOVA are discussed. Research results were obtained from an exploratory study of the effects of single and compound violations of the mathematical conditions (assumptions) underlying use of ANOVA and ANCOVA through Monte Carlo methods using randomly created data for a mathematical simulation (665 data set conditions). For all of the analyses, comparisons were made between the empirical F sampling distributions and the theoretical (i.e., nominal) F distributions expected when one uses normal theory. For balanced designs, the ANOVA and ANCOVA F tests were found to be remarkably robust when faced with most of the violations in the simulation. Research does reaffirm that ANOVA and ANCOVA should be avoided when group sizes are not equal. Specific recommendations are made for checking the ratio of largest to smallest group variances. (Contains 29 references.) (SLD)
Entry Date: 1994
Accession Number: ED365720
Database: ERIC
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED365720
    Name: ERIC Full Text
    Category: fullText
    Text: Full Text from ERIC
Header DbId: eric
DbLabel: ERIC
An: ED365720
AccessLevel: 3
PubType: Report
PubTypeId: report
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: The Effects of Violation of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Procedures.
– 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: 15
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 1993
– 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="%22Comparative+Analysis%22">Comparative Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Simulation%22">Computer Simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+Methods%22">Monte Carlo Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Reliability%22">Reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Research+Design%22">Research Design</searchLink><br /><searchLink fieldCode="DE" term="%22Sample+Size%22">Sample Size</searchLink><br /><searchLink fieldCode="DE" term="%22Sampling%22">Sampling</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Distributions%22">Statistical Distributions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The purpose of this study is to help define the precise nature and limits of the tolerable range in which a researcher may be relatively confident about the statistical validity of his or her research findings, focusing specifically on the statistical validity of results when violating the assumptions associated with the one-way, fixed-effects analysis of variance (ANOVA) and one concomitant analysis of covariance (ANCOVA) statistical procedure. Methodological and data set statistical assumptions that must be met for ANOVA and ANCOVA are discussed. Research results were obtained from an exploratory study of the effects of single and compound violations of the mathematical conditions (assumptions) underlying use of ANOVA and ANCOVA through Monte Carlo methods using randomly created data for a mathematical simulation (665 data set conditions). For all of the analyses, comparisons were made between the empirical F sampling distributions and the theoretical (i.e., nominal) F distributions expected when one uses normal theory. For balanced designs, the ANOVA and ANCOVA F tests were found to be remarkably robust when faced with most of the violations in the simulation. Research does reaffirm that ANOVA and ANCOVA should be avoided when group sizes are not equal. Specific recommendations are made for checking the ratio of largest to smallest group variances. (Contains 29 references.) (SLD)
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 1994
– Name: AN
  Label: Accession Number
  Group: ID
  Data: ED365720
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=ED365720
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 15
    Subjects:
      – SubjectFull: Analysis of Covariance
        Type: general
      – SubjectFull: Analysis of Variance
        Type: general
      – SubjectFull: Comparative Analysis
        Type: general
      – SubjectFull: Computer Simulation
        Type: general
      – SubjectFull: Monte Carlo Methods
        Type: general
      – SubjectFull: Reliability
        Type: general
      – SubjectFull: Research Design
        Type: general
      – SubjectFull: Sample Size
        Type: general
      – SubjectFull: Sampling
        Type: general
      – SubjectFull: Statistical Distributions
        Type: general
    Titles:
      – TitleFull: The Effects of Violation of Data Set Assumptions when Using the Oneway, Fixed Effects Analysis of Variance and the One Concomitant Analysis of Covariance Statistical Procedures.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Johnson, Colleen Cook
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 11
              Type: published
              Y: 1993
ResultId 1