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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Retief, E., Lamprecht, S. C., & McLeod, A. (2023) · Journal of Plant Pathology · doi:10.1007/s42161-023-01446-6 · Cited by 9
“In cases where deviations from normality were due to kurtosis and not skewness, the data were accepted as reliable and the results were interpreted without transformation (Glass et al. 1972 ).”
Bârã, A., Oprea, S., Bucur, C., et al. (2023) · Journal of theoretical and applied electronic commerce research · doi:10.3390/jtaer18030075 · Cited by 9
“It is worth noting that ANOVA assumes homogeneity of variances and normally distributed data, assumptions that may not always hold in real-world analytics data [53].”
BackgroundImpact of packet error modeling in VANET simulations
Tripp-Barba, C., Urquiza-Aguiar, L. F., Estrada, J., et al. (2014) · IEEE International Conference on Adaptive Science & Technology · doi:10.1109/icastech.2014.7068133 · Cited by 9
“Since ANOVA assumes that the data come from normally distributed populations with homogeneous variance, we applied the Brown–Forsythe test [22] before running the Two-way ANOVA test, in order to verify the equality of variance in our data, although ANOVA is robust against the aforementioned assumptions [23], [24].”
MethodThe fatty acid composition of muscles and fat depots of ostriches as influenced by genotype
Hoffman, L. C., Brand, M., Cloete, S. W. P., et al. (2012) · South African Journal of Animal Science · doi:10.4314/sajas.v42i3.7 · Cited by 9
“Interpretation of results was thus continued as specified by Glass et al. (1972). Correlations were estimated using the Pearson product moment correlation coefficient.”
BackgroundMethodElementary Schoolers’ Attitudes toward Reading in English: How Boys Feel Relative to Girls
Asraf, R. M., & Abdullah, H. B. (2016) · English Language Teaching · doi:10.5539/elt.v9n6p134 · Cited by 9
RECRUITMENT OF WINTER TICKS (DERMACENTOR ALBIPICTUS) IN CONTRASTING FOREST HABITATS, ONTARIO, CANADA
Addison, E. M., McLaughlin, R. F., Addison, P. A., et al. (2016) · DOAJ (DOAJ: Directory of Open Access Journals) · Cited by 9
Shihab, M. R., & Rahardian, I. (2017) · International Journal of Business Information Systems · doi:10.1504/ijbis.2017.081449 · Cited by 9
Inferring power and dominance from dyadic nonverbal interactions in autism spectrum disorder
Kuschefski, M., Falter‐Wagner, C. M., Bente, G., Vogeley, K. T., & Georgescu, A. L. (2019) · Autism Research · doi:10.1002/aur.2069 · Cited by 9
Acute toxicity of copper to the larval stage of three species of ambystomatid salamanders
Weir, S. M., Yu, S., Scott, D. E., et al. (2019) · Ecotoxicology · doi:10.1007/s10646-019-02102-5 · Cited by 9
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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