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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“Although the dependent variable is binary, prior research has suggested that such violations of normality might be largely inconsequential (Glass et al., 1972).”
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MethodSimilar somatotopy for active and passive digit representation in primary somatosensory cortex
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“Moreover, despite all of the simulation studies that have been done, there does not seem to be a consensus about when heteroscedasticity is a big enough problem that alternatives to ANOVA should be used [36], [37].”
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BackgroundThe Effect of Reciprocity Norms on Moral Judgment and Causal Attribution
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“Because non-parametric tests are not suitable for analysing interactions between variables in a factorial design, and considering that analysis of variance is remarkably robust to moderate violation of the normality assumption (Glass et al., 1972), we analysed these variables using the mixed linear model on both untra…”
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“Additionally, the GLM two-way ANOVA test with type III sum of squares, which is considered robust to violations of normality (Glass et al., 1972), was performed to assess the interaction and main effects of ELS and ethanol.”
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“2:1, this violation was not a concern (Glass et al., 1972).”
InfluentialLearner interests, achievement, and continuing motivation in instruction
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“…we were not able to model the hetero - geneous variance directly; however, because the magnitude of the variance was positively correlated with the sample size (N. ostrina model: r = 0.58, p = 0.0002; all-species model r = 0.13, p = 0.36) we expect our analyses are conservative (Glass et al. 1972).”
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“normality assumption [17], we decided that this test is indeed applicable in our case.”
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“Analysis of single Likert-type scale items using the F test has also been shown to be robust when testing is on an a priori basis, items have at least 5 scale points and the underlying concept can be considered continuous (Glass et al., 1972).”
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“relatively robust towards deviations from normal distribution and inhomogeneity of variances [34], particularly with equal group sizes [35] as was the case in the current study, the analyses were conducted as planned.”
ResultDoes Breath Carbon Monoxide Measure Nicotine Dependence?
Kapusta, N. D., Pietschnig, J., Plener, P. L., Blüml, V., Lesch, O., & Walter, H. (2010) · Journal of Addictive Diseases · doi:10.1080/10550887.2010.509280 · Cited by 27
The effect of environmental factors and husbandry practices on stress in goats
Kruger, L. P., Nedambale, T. L., Scholtz, M. M., & Webb, E. C. (2016) · Small Ruminant Research · doi:10.1016/j.smallrumres.2016.06.004 · Cited by 27
“In cases where deviation from normality was because of skewness outliners were removed (Glass et al.,1972).”
MethodBehavioral effects following repeated exposure to hexachloronaphthalene in rats
Kilanowicz, A., Wiaderna, D., Lutz, P., et al. (2012) · NeuroToxicology · doi:10.1016/j.neuro.2012.02.011 · Cited by 27
Primary School Students' Attitudes towards Computer Based Testing and Assessment in Turkey.
Yurdabakan, İ., & Uzunkavak, C. (2012) · Turkish Online Journal of Distance Education · doi:10.17718/tojde.91607 · Cited by 27
The impact of domain knowledge on the effectiveness of requirements engineering activities
Niknafs, A., & Berry, D. M. (2016) · Empirical Software Engineering · doi:10.1007/s10664-015-9416-2 · Cited by 28
“However, it has been shown that the severity of the affects of non-normality on an ANOVA is amplified by kurtosis and skewness of the data (Glass et al. 1972), which need to be considered beside normality.”
BackgroundOrganizational citizenship behavior of IT professionals: lessons from Poland and Germany
Kowal, J., Keplinger, A., & Mäkiö, J. (2018) · Information Technology for Development · doi:10.1080/02681102.2018.1508402 · Cited by 32
Corenblum, B., & Wilson, A. E. (1982) · Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement · doi:10.1037/h0081232 · Cited by 27
A study measuring the impact of shared decision making in a human-robot team
Azhar, M. Q., & Sklar, E. I. (2017) · The International Journal of Robotics Research · doi:10.1177/0278364917710540 · Cited by 26
“Although a Likert response format was used in the survey and the data collected is ordinal in nature, there is evidence in the literature defending the robustness of ANOVA for analysing Likert response format data (Glass et al. 1972; Carifio and Perla 2007).”
MethodBodden, C., van den Hove, D., Lesch, K., & Sachser, N. (2017) · Scientific Reports · doi:10.1038/s41598-017-09292-0 · Cited by 26
Clinical characteristics of early onset anorexia nervosa
van Noort, B. M., Lohmar, S. K., Pfeiffer, E. F., Lehmkuhl, U., Winter, S., & Kappel, V. (2018) · European Eating Disorders Review · doi:10.1002/erv.2614 · Cited by 26
Hendry, D. T., Crocker, P. R. E., WILLIAMS, A. M., & Hodges, N. J. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00304 · Cited by 34
Döring, N. M., Mikhailova, V., Brandenburg, K., Broll, W., Groß, H., Werner, S., & Raake, A. (2022) · Universal Access in the Information Society · doi:10.1007/s10209-022-00957-w · Cited by 34
“Social media and email responses showed very low variability within the variables; therefore, the decision was made to exclude them from the inferential statistical analysis, as such extreme deviations from normality could affect the validity of the inferential statistic [61].”
BackgroundSpatiotemporal variations in land surface albedo across Canada from MODIS observations
Davidson, A., & Wang, S. (2005) · Canadian Journal of Remote Sensing · doi:10.5589/m05-021 · Cited by 26
“We did not transform our data prior to ANOVA because the F statistic is robust to violations of the assumptions of normality and homogeneous variance as long as sample sizes are equal and sufficiently large (Srivastava, 1959; Glass et al., 1972).”
MethodReports of the Death of Regression-Discontinuity Analysis are Greatly Exaggerated
Reichardt, C. S., Trochim, W. M. K., & Cappelleri, J. C. (1995) · Evaluation Review · doi:10.1177/0193841x9501900102 · Cited by 26
“The analysis of covariance, however, is more sensitive than the analysis of variance to violations of the assumption that the residuals are normally distributed (Atiqullah 1964; Elashoff 1969; Glass, Peckham, and Sanders 1972).”
BackgroundThe Relationship between Iranian EFL Students' Self-efficacy Beliefs and Critical Thinking Ability
Fahim, M., & Nasrollahi-Mouziraji, A. (2013) · Theory and Practice in Language Studies · doi:10.4304/tpls.3.3.538-543 · Cited by 26
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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