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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“As the F-test for analysis of variances is relatively robust against distributional violations (Glass and Peckham 1972), we performed analyses of variances (ANOVAs), while using epsilon corrections for heterogeneity of covariances (Huynh and Feldt 1976) throughout where appropriate.”
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“Deviations from normality were due to kurtosis and not skewness, Therefore, we continued with interpretation on the untransformed data (Glass et al., 1972) (Table 1).”
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“With the similar sizes of the conditions, ANCOVA is expected to be robust against violations of normality (Glass, Peckham, & Sanders, 1972).”
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“…survey or not relevant for the category (-) despite variables violating the assumption of normal distribution as no non-parametric alternative is currently widely accepted when the sample size is substantially larger than 30 [46, 47], and one-way ANOVA’s are robust to violations of normality [48].”
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“Fortunately, an ANOVA is not very sensitive to moderate deviations from normality; simulation studies, using a variety of non-normal distributions, have shown that the false positive rate is not affected very much by this violation of the assumption (Glass et al., 1972; Harwell et al., 1992).”
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“In fact, failing to meet the assumptions may lead to loss of test reliability, problems with Type I or II errors (Glass et al. 1972; Bradley 1978; Levine & Dunlap 1983; Rasmussen 1985) and with the level of significance of the test (Kempthorne 1952; Little & Hills 1978; Gomez & Gomez 1984).”
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“, due to the low sample size, ANOVA was still used due to robustness of ANOVA to violation of the normality assumption (Glass et al., 1972; Harwell et al., 1992; Lix et al., 1996).”
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“Subsequently, we did a quick research and we found that the simulation studies, applying a variety of non-normal distributions, show that the false positive rate is not affected very much by this violation of the assumption, as in reference [14-16].”
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“Importantly, simulation studies have shown that F-tests control well the false-positive rate under conditions of non-normality (Glass et al., 1972; Harwell et al., 1992; Lix et al., 1996), suggesting that F-tests remain robust under conditions of non-normality, especially when group sizes are equal…”
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“As Lubke and Muthen (2004) [83] and Glass, Peckham, and Sanders (1972) [84] indicated, parametric tests may use Likert scale item validly depending on contingencies.”
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“The skewness was almost zero and the data were therefore interpreted for the percentage incidence (Glass et al. 1972).”
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“However, Glass et al. (1972) suggest that ANOVAs are robust to such violations and therefore no adjustments were made.”
BackgroundEffects of Increased Step-Width on Knee Biomechanics During Inclined and Declined Walking
Sample, D. W., Thorsen, T. A., Weinhandl, J. T., et al. (2020) · Journal of Applied Biomechanics · doi:10.1123/jab.2019-0298 · Cited by 15
Which features make illustrations in multimedia learning interesting?
Magner, U., Glogger‐Frey, I., & Renkl, A. (2014) · Educational Psychology · doi:10.1080/01443410.2014.933177 · Cited by 15
Myers, L. (1998) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659808811888 · Cited by 15
McLeod, A., Masimba, T., Jensen, T., et al. (2017) · Crop Protection · doi:10.1016/j.cropro.2017.08.005 · Cited by 15
Şenduran, C., Güneş, K., Topaloğlu, D., et al. (2018) · Chemosphere · doi:10.1016/j.chemosphere.2018.03.201 · Cited by 15
Cousijn, J., & van Duijvenvoorde, A. C. K. (2018) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2018.00301 · Cited by 16
“This means that some deviation away from normality does not have a large influence on Type I error rates, particularly when group sizes are moderate to large and relatively equally sized (44).”
BackgroundGroup Climate and Development in Adventure Therapy: An Exploratory Study
Christian, D. D., Brown, C. L., & Portrie-Bethke, T. L. (2019) · The Journal for Specialists in Group Work · doi:10.1080/01933922.2018.1561776 · Cited by 17
Prevett, P., Black, L., Hernandez‐Martinez, P., Pampaka, M., & Williams, J. S. (2020) · International Journal of Research & Method in Education · doi:10.1080/1743727x.2020.1785416 · Cited by 17
“Previously the approach has been to reduce the themes to a simple binary, the presence or absence of the theme, e.g. as used in Guest and McLellan (2003).”
MethodInfluentialJacob, G., & Arun, S. P. (2020) · Journal of Vision · doi:10.1167/jov.20.10.20 · Cited by 15
Comparing factual recall of tapped vs. handwritten text
Lee, B. (2020) · Acta Psychologica · doi:10.1016/j.actpsy.2020.103221 · Cited by 17
Penney, C. M., Burness, G., Tabh, J. K. R., & Wilson, C. C. (2021) · Conservation Physiology · doi:10.1093/conphys/coab021 · Cited by 15
“…Shapiro-Wilk W tests), however, we still opted for parametric tests as our selected analytical approaches are not highly sensitive to non-normality (Glass et al., 1972; Harwell et al., 1992; Lix et al., 1996; Bodden et al., 2017; Senduran et al., 2018) and depend more on homogeneity of variance…”
MethodSystematic factors that affect ostrich egg incubation traits
Brand, Z., Cloete, S. W. P., Brown, C. R., et al. (2008) · UWA Profiles and Research Repository (UWA) · doi:10.4314/sajas.v38i4.4065 · Cited by 15
“Deviations from normality for WL21 and WL35 involved kurtosis rather than skewness, and the interpretation of the results was thus continued without attempting to transform the data to obtain a better distribution (Glass et al., 1972).”
Fokides, E., & Zampouli, C. (2016) · Education and Information Technologies · doi:10.1007/s10639-016-9503-z · Cited by 15
“On the other hand, the literature suggests that ANOVA is not very sensitive to moderate deviations from normality and the false positive rate is not affected very much by this violation (Glass et al. 1972; Lix et al. 1996).”
BackgroundOn the role of stiffness and synchronization in human–robot handshaking
Mura, D., Knoop, E., Catalano, M. G., et al. (2020) · The International Journal of Robotics Research · doi:10.1177/0278364920903792 · Cited by 15
“However, considering the large number of data points and the high robustness of the ANOVA test in this regard (see e.g. Carifio and Perla (2007) and Glass et al. (1972)) we deem the ANOVA results valid nonetheless.”
BackgroundBosompem, M. (2021) · Precision Agriculture · doi:10.1007/s11119-021-09801-2 · Cited by 15
A simulation laboratory for statistics
Bradley, D. R., Hemstreet, R. L., & Ziegenhagen, S. T. (1992) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03203496 · Cited by 15
“For a general overview of research on the effects of violating as sumptions, see Glass, Peckham, and Sanders (1972).”
Background
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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