The DOI matches its Crossref record; 93 of the 95 references it cites were found in a registry or an index.
Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance
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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“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
In the citing paper
“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
In the citing paper
“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
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“…these violations, such as averaging, can result in the loss of otherwise meaningful data (Bland and Altman, 1995), and conducting analyses despite violations can result in misleading or uninterpretable results (Glass et al., 1972; Hubbard, 1978; Kenny and Judd, 1986; Scariano and Davenport, 1987).”
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“The likely nonnormality of the 35 W results may have influenced the ANOVA, but this is unlikely [74].”
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“Also, the false positive rate is not affected notably by violations of the normality assumptions [27].”
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Arend, J. M., Liesefeld, H. R., & Pörschmann, C. (2021) · Acta Acustica · doi:10.1051/aacus/2021001 · Cited by 12
External Collaboration Results in Student Learning Gains and Positive STEM Attitudes in CUREs
Callahan, K. P., Peterson, C. N., Martínez-Vaz, B. M., Huisinga, K. L., Galport, N., Koletar, C., Eddy, R. M., Provost, J. J., Bell, J. K., & Bell, E. (2022) · CBE—Life Sciences Education · doi:10.1187/cbe.21-06-0167 · Cited by 12
“This may have slightly reduced the power of the corresponding F-tests (Glass et al., 1972) Similarly, six items had heterogenous variances.”
BackgroundMethodUnderstanding and acceptance of the theory of evolution in high school students in Mexico
Salazar-Enriquez, G., Guzman-Sepulveda, J. R., & Peñaloza, G. (2023) · PLoS ONE · doi:10.1371/journal.pone.0278555 · Cited by 12
Six Modifications Of The Aligned Rank Transform Test For Interaction
Peterson, K. (2002) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1020255240 · Cited by 12
Thymidylate synthase gene polymorphisms and markers of DNA methylation capacity
Ho, V., Massey, T. E., & King, W. D. (2011) · Molecular Genetics and Metabolism · doi:10.1016/j.ymgme.2010.12.015 · Cited by 12
“However, it has often been reported that violation of the normality assumption should be of little concern; specifically, little effect of non-normality has been reported on the F-tests, given a sufficiently large sample size [32,33].”
Tewoldemedhin, Y. T., Lamprecht, S. C., & Mazzola, M. (2015) · Plant Disease · doi:10.1094/pdis-11-14-1211-re · Cited by 12
Feifel, D., Shilling, P. D., Fazlinejad, A., & Melendez, G. (2016) · Journal of Psychopharmacology · doi:10.1177/0269881115625360 · Cited by 12
“86:1), the impact of the variance homogeneity is considered minimal (Box, 1954; Glass et al., 1972; Kohr and Games, 1974; Moder, 2007), and we therefore reported the F-statistic.”
BackgroundInfluentialVirtual Museums in Arts Education. Results of a Pilot Project in Primary School Settings
Fokides, E., & Sfakianou, M. (2017) · Asian Research Journal of Arts & Social Sciences · doi:10.9734/arjass/2017/33601 · Cited by 12
“On the other hand, the literature suggests 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 [37,38].”
BackgroundMapping the diversity of spectral shapes discriminates between adjacent benthic biophonies
Lossent, J., Iorio, L. D., Valentini‐Poirier, C., Boissery, P., & Gervaise, C. (2017) · Marine Ecology Progress Series · doi:10.3354/meps12370 · Cited by 12
“…strictly equal, the standard deviation of D1, D2 are of the same order across the regions Q1, Q2, Q3 and Q4, and ANOVA is known to be robust to deviations of the assumption of a strict homogeneity of variance for equal group sizes, which is the case for our bootstrapping method (Glass et al. 1972).”
MethodA Protective Mechanism against Illusory Perceptions Is Amygdala-Dependent
Spengler, F. B., Scheele, D., Kaiser, S., Heinrichs, M., & Hurlemann, R. (2019) · Journal of Neuroscience · doi:10.1523/jneurosci.2577-18.2019 · Cited by 13
“ANOVA is known to be rather insensitive to moderate violations of the normality assumption (Glass et al., 1972; Harwell et al., 1992; Lix et al., 1996).”
BackgroundTraining chemistry students to ask research questions
Hartford, F., & Good, R. (1982) · Journal of Research in Science Teaching · doi:10.1002/tea.3660190705 · Cited by 12
Effect of different maize meal diets on growth and vitamin A: Case-study on chickens
Pretorius, B., & Schönfeldt, H. C. (2012) · Food Chemistry · doi:10.1016/j.foodchem.2012.06.066 · Cited by 12
Boe, S. G., Cassidy, R. J., McIlroy, W. E., & Graham, S. J. (2012) · Journal of Neuroscience Methods · doi:10.1016/j.jneumeth.2012.06.016 · Cited by 12
“…distribution was sufficiently negligible, and considering the robustness of parametric statistics to violations of their underlying assumptions (Glass et al., 1972; Zimmerman, 1998), it was determined that parametric statistics could be appropriately applied to assess training-related changes…”
BackgroundThe impact of the Weibull distribution on the performance of the single-factor ANOVA model
Black, G., Ard, D., Smith, J., et al. (2010) · International Journal of Industrial Engineering Computations · doi:10.5267/j.ijiec.2010.02.007 · Cited by 12
Kuusipalo, J. (1987) · Vegetatio · doi:10.1007/bf00039330 · Cited by 12
“However, the relevant question is not whether mathematical assumptions are met exactly, but rather whether the violations of assumptions have serious consequences on the validity of probability statements ( Glass et al., 1972 ).”
BackgroundBarnard, A., & Calitz, F. J. (2011) · South African Journal of Plant and Soil · doi:10.1080/02571862.2011.10640009 · Cited by 12
“In cases where deviation from normality was caused by kurtosis and not skewness, the data was regarded as reliable (Glass et al., 1972).”
Examining the Impact of Training in the Unified Theory of Acceptance and Use of Technology
Harris, M. E., Mills, R. J., Fawson, C., & Johnson, J. J. (2016) · Journal of Computer Information Systems · doi:10.1080/08874417.2016.1230725 · Cited by 16
“Means and standard deviations While the individual Likert items in the strictest sense are ordinal, many statisticians argue that composite scores can be classified as continuous (interval/ratio data) [11, 21, 29].”
BackgroundAge- and Expertise-Related Differences of Sensorimotor Network Dynamics during Force Control
Vieluf, S., Mora, K., Gölz, C., Reuter, E., Godde, B., Dellnitz, M., Reinsberger, C., & Voelcker‐Rehage, C. (2018) · Neuroscience · doi:10.1016/j.neuroscience.2018.07.025 · Cited by 12
Bergstrom, B. J., Sensenig, R. L., Augustine, D. J., & Young, T. P. (2018) · Ecosphere · doi:10.1002/ecs2.2519 · Cited by 14
“…and two-factor ANOVA (F test, or general linear model— Minitab 2016) when group sample sizes were roughly equal, because this test is robust to ❖ www.esajournals.org 6 November 2018 ❖ Volume 9(11) ❖ Article e02519 deviations from normality or homoscedasticity in such cases (Glass et al. 1972).”
Method
Metadata
- 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
- Published
- 1972-09
- Volume
- 42
- Issue
- 3
- Pages
- 237-288
- ISSN
- 0034-6543 (ISSN-L)
- 1935-1046
- 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
- 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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