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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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Blair, R. C., & Higgins, J. J. (1985) · Psychological Bulletin · doi:10.1037//0033-2909.97.1.119 · Cited by 149
The Visual Analogue Scale for Anxiety: A Validation Study
Hornblow, A. R., & Kidson, M. A. (1976) · Australian & New Zealand Journal of Psychiatry · doi:10.3109/00048677609159523 · Cited by 149
Effects of alternating set for speed or accuracy on response time, accuracy and confidence in a unidimensional discrimination task
Vickers, D., & Packer, J. (1982) · Acta Psychologica · doi:10.1016/0001-6918(82)90006-3 · Cited by 139
An Examination of Implicitly Activated, Explicitly Activated, and Nullified Stereotypes on Mathematical Performance: It's Not Just a Woman's Issue
Smith, J. L., & White, P. H. (2002) · Sex Roles · doi:10.1023/a:1021051223441 · Cited by 156
Advances in statistical methods for meta‐analysis
Hedges, L. V. (1984) · New Directions for Program Evaluation · doi:10.1002/ev.1376 · Cited by 142
Response of South African indigenous grass species to drought stress induced by polyethylene glycol (PEG) 6000
van den Berg, L., & Zeng, Y. (2006) · South African Journal of Botany · doi:10.1016/j.sajb.2005.07.006 · Cited by 139
“Glass et al. (1972) indicated that the consequences on inference after ANOVA are not serious, as no transformation could be found to rectify the problem.”
Background
NONPARAMETRIC TESTS FOR TREND DETECTION IN WATER QUALITY TIME SERIES1
Berryman, D., Bobée, B., Cluis, D., et al. (1988) · JAWRA Journal of the American Water Resources Association · doi:10.1111/j.1752-1688.1988.tb00904.x · Cited by 137
READING COMPREHENSION OF EXPOSITORY SCIENCE MATERIAL AND STUDENTS WITH LEARNING DISABILITIES: A COMPARISON OF STRATEGIES
Bakken, J. P., Mastropieri, M. A., & Scruggs, T. E. (1997) · The Journal of Special Education · doi:10.1177/002246699703100302 · Cited by 137
The efficiency analysis of container port production using DEA panel data approaches
Cullinane, K., & Wang, T. (2010) · OR Spectrum · doi:10.1007/s00291-010-0202-7 · Cited by 135
“ANOVA, it is also the case that simulations of the outcomes from an ANOVA have proved not to be very sensitive to moderate violations of the normality assumption ( Glass et al. 1972; Harwell et al. 1992; Lix et al. 1996).”
Method
Some Issues in the Statistical Analysis of Completely Randomized and Repeated Measures Designs for Speech, Language, and Hearing Research
Max, L., & Onghena, P. (1999) · Journal of Speech Language and Hearing Research · doi:10.1044/jslhr.4202.261 · Cited by 135
Powerful and consistent analysis of likert-type rating scales
Kaptein, M. C., Nass, C., & Markopoulos, P. (2010) · ACM SIGCHI Conference on Human Factors in Computing Systems (CHI) · doi:10.1145/1753326.1753686 · Cited by 130
“While there is debate among statisticians over the invariability of parametric measures under violations of these assumptions [1, 8, 9, 16, 19] it is clear that parametric methods are not invariant to monotone transformations of the collected data.”
Background
The impact of sample non‐normality on ANOVA and alternative methods
Lantz, B. (2012) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.2012.02047.x · Cited by 129
In vitro determination of the anti-aging potential of four southern African medicinal plants
Ndlovu, G., Fouché, G., Tselanyane, M., Cordier, W., & Steenkamp, V. (2013) · BMC Complementary and Alternative Medicine · doi:10.1186/1472-6882-13-304 · Cited by 134
Music Listening Preferences of Elementary School Children
Greer, R. D., Dorow, L. G., & Randall, A. (1974) · Journal of Research in Music Education · doi:10.2307/3344766 · Cited by 123
Comparing Indirect Effects in Different Groups in Single-Group and Multi-Group Structural Equation Models
Ryu, E., & Cheong, J. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.00747 · Cited by 120
“It is well-known that the empirical Type I error rate can be different from the nominal level when the equal variance assumption is violated (e.g., Box, 1954; Glass et al., 1972; Dretzke et al., 1982; Aguinis and Pierce, 1998).”
Background
Examining the reliability, correlation, and validity of commonly used assessment tools to measure balance
Dawson, N., Dzurino, D., Karleskint, M., & Tucker, J. (2018) · Health Science Reports · doi:10.1002/hsr2.98 · Cited by 116
Participatory adaptive management leads to environmental learning outcomes extending beyond the sphere of science
Fujitani, M. L., McFall, A., Randler, C., & Arlinghaus, R. (2017) · Science Advances · doi:10.1126/sciadv.1602516 · Cited by 129
“Statistical analysis Constructs of each assessment domain (that is, knowledge and cognitions) were obtained from Likert scales constructed from batteries of Likert response format items and analyzed with parametric methods (74, 75).”
Method
Analysis of Likert scale data in disability and medical rehabilitation research.
Nanna, M. J., & Sawilowsky, S. S. (1998) · Psychological Methods · doi:10.1037/1082-989x.3.1.55 · Cited by 117

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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