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Cited by 1,826Statistical Methods and Bayesian InferenceAdvanced Statistical Methods and ModelsProbability and Statistical Research

Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance

Glass, Gene V, Peckham, Percy D., Sanders, James R.·1972·Review of Educational Research
DOI 10.3102/00346543042003237
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Abstract

The effects of violating the assumptions underlying the fixed-effects analyses of variance (ANOVA) and covariance (ANCOVA) on Type-I and Type-II error rates have been of great concern to researchers and statisticians. The major effects of violation of assumptions are now well known, after nearly four decades of research. Early summaries and reviews by Hey (1938), Garret and Zubin (1943), Grant (1944), and Gourlay (1955) and more recent reviews by Bradley (1963), Atiqullah (1967), Elashoff (1969) and Scheffe (1959, Ch. 10) can be extended and updated with recent research which provides closure to an area of active inquiry. (For a review of the effects of violation of the assumptions of the randomeffects ANOVA-a subject not reviewed here-the reader is directed to Scheffe, 1959, pp. 334-337 and Box & Anderson, 1962.) Asking whether ANOVA and ANCOVA assumptions are satisfied is not idle curiosity. The assumptions of most mathematical models are always false to a greater or lesser extent. The relevant question is not whether ANOVA assumptions are met exactly, but rather whether the plausible violations of the assumptions have serious consequences on the validity of probability statements based on the standard assumptions. Applied statistics in education and the social sciences experienced a largely unnecessary hegira to non-parametric statistics during the 1950s. Increasingly during the 1950s and early 1960s the fixed-effects, normal theory ANOVA was replaced by such comparable no…

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Crossref · 10.3102/00346543042003237

Cites

94 of 94 references verified0 citation errors · 0 not checkable

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  • Only little bias can be expected from minor violations of normality.

    “We focus on fairly drastic non-normality because only little bias can be expected from minor violations (Bishara & Hittner, 2012; Glass et al., 1972; Hack, 1958; Puth et al., 2014).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Glass et al., 1972

  • When applying a t test that assumes equal variances to data from substantially different variances (e.g., σ12/σ22 = 0.1), high rates of type I errors (e.g., 23%) may be obtained when sample sizes are unbalanced (N1 = 15, N2 = 5) and the small sample comes from the more variable group.

    “For instance, when applying a t test that assumes equal variances in both groups to data that come from substantially different variances (e.g., σ12/ σ22 = 0.1), then high rates of type I errors (e.g., 23%) may be obtained in a situation where sample sizes are unbalanced (N1 = 15, N2 = 5), namely when the small sample comes from the more variable group (Glass et al., 1972; Miller, 1986).”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Glass et al., 1972

  • Violating the homogeneity of variances assumption may result in more notable increases of type I errors (compared to what we examined here) at least when the violations are drastic.

    “Violating this assumption may result in more notable increases of type I errors (compared to what we examined here) at least when the violations are drastic.”

    From Violating the normality assumption may be the lesser of two evils (2021) · cites this paper as Glass et al., 1972

Cites

Flagged first, then by citations

1 of the 95 references couldn’t be matched to a known paper.

Research works printed but not linked: 16

  1. Atiqullah M, 1967, Bulletin of the Institute of Statistical Research and Training, 1, 77
  2. Behrens WU, 1929, Landweise Jahresbuch, 68, 807
  3. Gayen AK, 1949, Biometrika, 36, 353
  4. Glass GV, 1970, Statistical methods in education and psychology
  5. Horsnell G, 1953, Biometrika, 40, 28
  6. KohrRLA comparison of statistical procedures for testing μ 1 = μ 2 with unequal n ’s and variances1970Pennsylvania State UniversityDoctoral dissertation
  7. Lindquist EF, 1953, Design and analysis of experiments in education and psychology
  8. Lunney GH, 1969, Paper presented at the Annual Meeting of the American Educational Research Association
  9. Mandeville GK, 1969, A Monte Carlo investigation of the adequacy of standard analysis of variance test procedures for dependent binary variates
  10. Pitman EJG, 1937, Biometrika, 29, 322
  11. Porter AC, 1967, The effects of using fallible variables in the analysis of covariance, Ph.D
  12. Pratt JW, 1964, Journal of the American Statistical Association, 59, 665
  13. Quesnel CE, 1947, Skandanavian Aktuarietids, 30, 44
  14. van der Vaart HR, 1961, Quantative methods in pharmacology, 140
  15. Welch BL, 1947, Biometrika, 34, 28
  16. 10.2466/pms.1963.16.2.588 · DOI

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Authors
Glass, G. V., Peckham, P. D., & Sanders, J. R.
Affiliations
  • University of Colorado System (US)
  • University of Washington (US)
  • Indiana University (US)
ORCID
Glass, Gene V
Venue
Review of Educational Research
Publisher
American Educational Research Association (AERA)
Published
1972-09
Volume
42
Issue
3
Pages
237-288
ISSN
  • 0034-6543 (ISSN-L)
  • 1935-1046
DOI
10.3102/00346543042003237
OpenAlex
W2120106329
Semantic Scholar
96cd4ca99a137bf80e8c2dc5cb20ab6782df819e
Cited by
1,826
References
95
Citations by year
2026: 91 · 2025: 69 · 2024: 55 · 2023: 75 · 2022: 72 · 2021: 98 · 2020: 85 · 2019: 96 · 2018: 137 · 2017: 100 · 2016: 106 · 2015: 74 · 2014: 65 · 2013: 70 · 2012: 69
FWCI
10.37
Type
journal article
Language
en
Open access
closed
Licence
journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations
Review of Educational Research (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Keywords
covariance analysis, assumption violations, type I error, type II error, nonparametric statistics, Wilcoxon test, Mann-Whitney test, Kruskal-Wallis test, Friedman test, social science research

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