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

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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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“A deviation from the normal distribution does not exert a significant influence on both the Type I error (Glass et al., 1972; Harwell et al., 1992; Tiku, 1971) and the F-test power (David & Johnson, 1951; Harwell et al., 1992; Srivastava, 1959; Tiku, 1971), but unequal variances can significantly…”
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“…that ANOVA is robust to moderate deviations from normality (the absolute values of the skewness and kurtosis for the data not to be more than double their respective standard errors) and the false positive rate is not affected very much by this violation (Glass et al. 1972; Lix et al. 1996).”
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“The normality assumption was not met in a few cases, however, the ANOVA tolerates moderate deviations from normality, as was shown in several studies [27–29] .”
Result

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

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