Cited by 1,826Statistical Methods and Bayesian InferenceAdvanced Statistical Methods and ModelsProbability and Statistical Research

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

Glass, Gene V, Peckham, Percy D., Sanders, James R.·1972·Review of Educational Research

DOI 10.3102/00346543042003237

Open this paper in CoChat — free account

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…

Integrity signals

Registry

Crossref · 10.3102/00346543042003237

Cites

93 of 93 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Nonparametric Statistics for the Behavioral Sciences
Guitton, H., & Siegel, S. (1958) · Revue économique · doi:10.2307/3498751 · Cited by 35,279
Statistical principles in experimental design.
Winer, B. J. (1962) · McGraw-Hill Book Company · doi:10.1037/11774-000 · Cited by 27,137
Principles and Procedures of Statistics
Robinson, H. F. (1961) · Agronomy Journal · doi:10.2134/agronj1961.00021962005300050002x · Cited by 17,727
An Analysis of Transformations
Box, G. E. P., & Cox, D. R. (1964) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1964.tb00553.x · Cited by 15,287
Statistical Methods for Research Workers
Fisher, R. A. (1945) · American Journal of Clinical Pathology · doi:10.1093/ajcp/15.11.552b · Cited by 10,883
Nonparametric statistics for the behavioral sciences
McGinn, L. C. (1957) · Journal of the Franklin Institute · doi:10.1016/0016-0032(57)90766-4 · Cited by 7,284
Journal of The American Statistical Association
Fienberg, S. E. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess1317 · Cited by 6,289
The Analysis of Variance
Scheffé, H. (1960) · Soil Science · doi:10.1097/00010694-196006000-00016 · Cited by 5,625
On Methods in the Analysis of Profile Data
Greenhouse, S. W., & Geisser, S. (1959) · Psychometrika · doi:10.1007/bf02289823 · Cited by 4,946
THE GENERALIZATION OF ‘STUDENT'S’ PROBLEM WHEN SEVERAL DIFFERENT POPULATION VARLANCES ARE INVOLVED
WELCH, B. L. (1947) · Biometrika · doi:10.1093/biomet/34.1-2.28 · Cited by 4,135

Flagged first, then by citations

Show all 95 references

2 of the 95 references couldn’t be matched to a known paper.

Research works printed but not linked: 16

Atiqullah M, 1967, Bulletin of the Institute of Statistical Research and Training, 1, 77
Behrens WU, 1929, Landweise Jahresbuch, 68, 807
Gayen AK, 1949, Biometrika, 36, 353
Glass GV, 1970, Statistical methods in education and psychology
Horsnell G, 1953, Biometrika, 40, 28
KohrRLA comparison of statistical procedures for testing μ 1 = μ 2 with unequal n ’s and variances1970Pennsylvania State UniversityDoctoral dissertation
Lindquist EF, 1953, Design and analysis of experiments in education and psychology
Lunney GH, 1969, Paper presented at the Annual Meeting of the American Educational Research Association
Mandeville GK, 1969, A Monte Carlo investigation of the adequacy of standard analysis of variance test procedures for dependent binary variates
Pitman EJG, 1937, Biometrika, 29, 322
Porter AC, 1967, The effects of using fallible variables in the analysis of covariance, Ph.D
Pratt JW, 1964, Journal of the American Statistical Association, 59, 665
Quesnel CE, 1947, Skandanavian Aktuarietids, 30, 44
van der Vaart HR, 1961, Quantative methods in pharmacology, 140
Welch BL, 1947, Biometrika, 34, 28
10.2466/pms.1963.16.2.588 · DOI

Sorted by citations

Items 301–400 of 999

Multiparametric analysis of peripheral blood in the normal pediatric population by flow cytometry
Wiener, D. A., Rowlands, D. T., Lowell, N. E., et al. (1990) · Journal of Clinical Laboratory Analysis · doi:10.1002/jcla.1860040305 · Cited by 47
Response of Estuarine Fish to Large‐Scale Oyster Reef Restoration
Pierson, K. J., & Eggleston, D. B. (2014) · Transactions of the American Fisheries Society · doi:10.1080/00028487.2013.847863 · Cited by 47
“In some instances, transformed data remained non-normal-- in these circumstances, transformed data was still analyzed with ANOVA due to its robustness and insensitivity to skewness (Glass et al. 1972, Legendre and Borcard 2007).”
Background
Cyclooxygenases 1 and 2 Differentially Regulate Blood Pressure and Cerebrovascular Responses to Acute and Chronic Intermittent Hypoxia: Implications for Sleep Apnea
Beaudin, A. E., Pun, M., Yang, C., Nicholl, D. D. M., Steinback, C. D., Slater, D. M., Wynne‐Edwards, K. E., Hanly, P. J., Ahmed, S. B., & Poulin, M. J. (2014) · Journal of the American Heart Association · doi:10.1161/jaha.114.000875 · Cited by 45
Physical and sensory meat quality of South African Black ostriches (Struthio camelus var. domesticus), Zimbabwean Blue ostriches (Struthio camelus australis) and their hybrid
Hoffman, L. C., Müller, M., Cloete, S. W. P., et al. (2007) · Meat Science · doi:10.1016/j.meatsci.2007.10.022 · Cited by 47
Honey Bee Survival and Pathogen Prevalence: From the Perspective of Landscape and Exposure to Pesticides
Alburaki, M., Chen, D., Skinner, J. A., et al. (2018) · Insects · doi:10.3390/insects9020065 · Cited by 47
Differences in university students’ motivation between a required and an elective physical activity education policy
Kim, M. S., & Cardinal, B. J. (2018) · Journal of American College Health · doi:10.1080/07448481.2018.1469501 · Cited by 55
Developing a video‐based method to compare and adjust examiner effects in fully nested OSCEs
Yeates, P., Cope, N. A., Hawarden, A., Bradshaw, H., McCray, G., & Homer, M. (2018) · Medical Education · doi:10.1111/medu.13783 · Cited by 46
Computational explorations of the influence of structured knowledge on age-related cognitive decline.
Mireles, D. E., & Charness, N. H. (2002) · Psychology and Aging · doi:10.1037/0882-7974.17.2.245 · Cited by 47
Gut and sublingual microvascular effect of esmolol during septic shock in a porcine model
Jacquet‐Lagrèze, M., Allaouchiche, B., Restagno, D., et al. (2015) · Critical Care · doi:10.1186/s13054-015-0960-3 · Cited by 46
Gender, subject and context as determinants of approaches to studying in higher education
Hayes, K., & Richardson, J. T. E. (1995) · Studies in Higher Education · doi:10.1080/03075079512331381713 · Cited by 46
Do Common Systems Control Eye Movements and Motion Extrapolation?
Makin, A. D. J., & Poliakoff, E. (2011) · Quarterly Journal of Experimental Psychology · doi:10.1080/17470218.2010.548562 · Cited by 46
Robust Means Modeling
Fan, W., & Hancock, G. R. (2011) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998610396897 · Cited by 46
Agricultural Landscape and Pesticide Effects on Honey Bee (Hymenoptera: Apidae) Biological Traits
Alburaki, M., Steckel, S. J., Williams, M., et al. (2017) · Journal of Economic Entomology · doi:10.1093/jee/tox111 · Cited by 46
Assessing the validity of a video-based decision-making assessment for talent identification in youth soccer
Bennett, K. J. M., Novak, A. R., Pluss, M. A., et al. (2018) · Journal of science and medicine in sport · doi:10.1016/j.jsams.2018.12.011 · Cited by 46
Accurate or Assumed: Visual Learning in Children with ASD
Trembath, D. L., Vivanti, G., Iacono, T. A., & Dissanayake, C. (2015) · Journal of Autism and Developmental Disorders · doi:10.1007/s10803-015-2488-4 · Cited by 48
“Accordingly, ANOVAs—which are robust to violations of normality (Glass et al. 1972)—were used to test for group differences in performance as noted above; whereas within group associations between visual attention, receptive language, and performance were assessed using non-parametric correlations (Spearman’s Rho).”
Method
STRENGTHENING THE REFLECTIVE FUNCTIONING CAPACITIES OF PARENTS WHO HAVE A CHILD WITH A NEURODEVELOPMENTAL DISABILITY THROUGH A BRIEF, RELATIONSHIP-FOCUSED INTERVENTION
Sealy, J., & Glovinsky, I. (2016) · Infant Mental Health Journal · doi:10.1002/imhj.21557 · Cited by 45
Comparison of FDA-Reported Visual and Refractive Outcomes of the Toric ICL Lens, SMILE, and Topography-Guided LASIK for the Correction of Myopia and Myopic Astigmatism
Moshirfar, M., Somani, A. N., Motlagh, M. N., et al. (2019) · Journal of Refractive Surgery · doi:10.3928/1081597x-20190930-01 · Cited by 45
Neural and Endocrine Correlates of Sadness In Women: Implications for Neural Network Regulation of HPA Activity
Ottowitz, W. E., Dougherty, D. D., Sirota, A. D., NIAURA, R. S., Rauch, S. L., & Brown, W. A. (2004) · Journal of Neuropsychiatry · doi:10.1176/jnp.16.4.446 · Cited by 45
Designing Communication Strategies of Autonomous Vehicles with Pedestrians: An Intercultural Study
Lanzer, M., Babel, F., Yan, F., Zhang, B., You, F., Wang, J., & Baumann, M. (2020) · 12th International Conference on Automotive User Interfaces and Interactive Vehicular Applications · doi:10.1145/3409120.3410653 · Cited by 52
“Nevertheless, ANOVAs were conducted since they are relatively robust against not normally distributed variables [19] and the non-parametric Friedman-Test revealed the same result patterns in all cases.”
Result
Different types of redundancy and their effect on learning and cognitive load
Albers, F., Trypke, M., Stebner, F., Wirth, J., & Plass, J. L. (2023) · British Journal of Educational Psychology · doi:10.1111/bjep.12592 · Cited by 60
Passive restraint reduces visually induced motion sickness in older adults.
Keshavarz, B., Novak, A. C., Hettinger, L. J., Stoffregen, T. A., & Campos, J. L. (2017) · Journal of Experimental Psychology Applied · doi:10.1037/xap0000107 · Cited by 42
Comparison of nonparametric analysis of variance methods: A vote for van der Waerden
Lüpsen, H. (2017) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2017.1353613 · Cited by 45
“However Box (1954), Glass et al. (1972), and Dijkstra (1987) have shown that even in balanced designs unequal variances may lead to an increased type I error rate.”
Background
Dealing with Nonnormal Data: Parametric Analysis of Transformed Data vs Nonparametric Analysis
Rasmussen, J. L., & Dunlap, W. P. (1991) · Educational and Psychological Measurement · doi:10.1177/001316449105100402 · Cited by 44
Automatic and Intentional Number Processing Both Rely on Intact Right Parietal Cortex: A Combined fMRI and Neuronavigated TMS Study
Kadosh, R. C., Bien, N., & Sack, A. T. (2012) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2012.00002 · Cited by 49
“While some have suggested that violation of normality even with small sample can still lead to meaningful results (Glass et al., 1972), one might suggest to use non-parametric tests, which are less powerful, and those might lead to a type II error.”
Method
Tumor Necrosis Factor–Related Apoptosis-Inducing Ligand Alters Mitochondrial Membrane Lipids
Sandra, F., Esposti, M. D., Ndebele, K., et al. (2005) · Cancer Research · doi:10.1158/0008-5472.can-04-1913 · Cited by 44
Some Methodological and Statistical “Bugs” in Research on Children’s Learning
Levin, J. R. (1985) · Springer series in cognitive development · doi:10.1007/978-1-4613-9544-7_7 · Cited by 44
Second Language Processing of Subordinate Clauses and Anaphora—First Language and Universal Influences: A Review of Flynn's Research*
Bley‐Vroman, R., & Chaudron, C. (1990) · Language Learning · doi:10.1111/j.1467-1770.1990.tb01335.x · Cited by 44
Adaptive robust estimation and testing
Keselman, H. J., Wilcox, R. R., Lix, L. M., et al. (2006) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711005x63755 · Cited by 43
Influence of different test conditions on the emotional responses elicited by beers
Worch, T., Sinesio, F., Moneta, E., et al. (2020) · Food Quality and Preference · doi:10.1016/j.foodqual.2020.103895 · Cited by 43
Developmental activities and perceptions of challenge for National and Varsity women soccer players in Canada
Hendry, D. T., Williams, A. M., Ford, P. R., & Hodges, N. J. (2019) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2019.02.008 · Cited by 42
Stable reference genes for the measurement of transcript abundance during larval caste development in the honeybee
Cameron, R. C., Duncan, E. J., & Dearden, P. K. (2013) · Apidologie · doi:10.1007/s13592-012-0187-0 · Cited by 42
“Fortunately it has been shown that the false-positive rate is only mildly affected by violation of this assumption (Glass et al. 1972; Lix et al. 1996).”
Background
Applicability of Demirjian’s four methods and Willems method for age estimation in a sample of Turkish children
Akkaya, N., Yılancı, H. Ö., & Göksülük, D. (2015) · Legal Medicine · doi:10.1016/j.legalmed.2015.04.003 · Cited by 42
Relationship between oxytocin receptor genotype and recognition of facial emotion.
Melchers, M., Montag, C., Markett, S. A., & Reuter, M. (2013) · Behavioral Neuroscience · doi:10.1037/a0033748 · Cited by 42
Assessing the impacts of driving environment on driving behavior patterns
Faria, M. V., Baptista, P., Farias, T. L., et al. (2018) · Transportation · doi:10.1007/s11116-018-9965-5 · Cited by 42
How to Improve Performance in Bayesian Inference Tasks: A Comparison of Five Visualizations
Böcherer-Linder, K., & Eichler, A. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00267 · Cited by 42
“However, since the subgroups were large enough, we can assume robustness of the t-tests and of ANOVA with regard to nonnormality (Glass et al., 1972; Schmider et al., 2010).”
Play Preferences of Typically Developing Children and Children with Developmental Delays between Ages 3 and 7 Years
Case‐Smith, J., & Miller-Kuhaneck, H. (2008) · OTJR Occupational Therapy Journal of Research · doi:10.3928/15394492-20080101-01 · Cited by 42
Development and evaluation of cross-training policies for manufacturing teams
Bokhorst, J. A. C., Slomp, J., & Molleman, E. (2004) · IIE Transactions · doi:10.1080/07408170490496209 · Cited by 42
“The F-statistic, however, is robust against heterogeneous variances, as long as the group sizes are equal (Glass et al., 1972) or approximately equal (Stevens, 1996, p. 249).”
Background
Degradation of sodium monofluoroacetate (1080) in buried fox baits
Saunders, G., McLeod, S. R., & Kay, B. (2000) · Wildlife Research · doi:10.1071/wr99031 · Cited by 42
Impact of Hearing Aid Technology on Outcomes in Daily Life III: Localization
Johnson, J. A., Xu, J., & Cox, R. M. (2017) · Ear and Hearing · doi:10.1097/aud.0000000000000473 · Cited by 41
Testing for regression homogeneity under variance heterogeneity.
Dretzke, B. J., Levin, J. R., & Serlin, R. C. (1982) · Psychological Bulletin · doi:10.1037//0033-2909.91.2.376 · Cited by 41
Self-verbalization versus tutor verbalization in modifying impulsivity.
Bender, N. N. (1976) · Journal of Educational Psychology · doi:10.1037/0022-0663.68.3.347 · Cited by 41
Prevalence and structure of behavior symptoms among children in special education and regular classroom settings
Grieger, R. M., & Richards, H. C. (1976) · Journal of School Psychology · doi:10.1016/0022-4405(76)90059-5 · Cited by 41
Four principles for improved statistical ecology
Popovic, G. C., Mason, T. J., Drobniak, S. M., Marques, T. A., Potts, J., Joo, R., Altwegg, R., Burns, C. C. I., Mccarthy, M. A., Johnston, A., et al. (2024) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.14270 · Cited by 59
“For example, in a linear regression, the lack of normality is not as critical as constant vari - ance, the violation of which may increase Type I error rates (Glass et al., 1972 ).”
Background
Potential microbial drivers of biodegradation of polycyclic aromatic hydrocarbons in crude oil sludge using a composting technique
Obi, L. U., Atagana, H. I., Adeleke, R. A., et al. (2020) · Journal of Chemical Technology & Biotechnology · doi:10.1002/jctb.6352 · Cited by 40
Toward a Multiple-Method View of Mood Induction: The Appropriateness of a Modified Velten Mood Induction Technique and the Problems of Procedures With Group Assignment to Conditions
Sinclair, R. C., Mark, M. M., Enzle, M. E., Borkovec, T. D., & Cumbleton, A. G. (1994) · Basic and Applied Social Psychology · doi:10.1207/s15324834basp1504_1 · Cited by 40
Power of the independent samples t test under a prevalent psychometric measure distribution.
Sawilowsky, S. S., & Hillman, S. B. (1992) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.60.2.240 · Cited by 40
The Effect of Police and Mental Health Intervention on Juvenile Deviance: Specifying Contingencies in the Impact of Formal Reaction
Palamara, F., Cullen, F. T., & Gersten, J. C. (1986) · Journal of Health and Social Behavior · doi:10.2307/2136505 · Cited by 40
Misuse of statistical methods in arthritis and rheumatism
Felson, D. T., Cupples, L. A., & Meenan, R. F. (1984) · Arthritis & Rheumatism · doi:10.1002/art.1780270908 · Cited by 40
Significance Testing in Psychological Research: Some Persisting Issues
Estes, W. K. (1997) · Psychological Science · doi:10.1111/j.1467-9280.1997.tb00538.x · Cited by 40
Effects of plans for future meals on counterregulatory eating by restrained and unrestrained eaters.
Tomarken, A. J., & Kirschenbaum, D. S. (1984) · Journal of Abnormal Psychology · doi:10.1037//0021-843x.93.4.458 · Cited by 40
Reach out to one and you reach out to many: Social touch affects third‐party observers
Schirmer, A., Reece, C. E., Zhao, C., Ng, E. S. T., Wu, E., & Yen, S. (2014) · British Journal of Psychology · doi:10.1111/bjop.12068 · Cited by 39
Visual aesthetics and user experience: A multiple-session experiment
Sauer, J., & Sonderegger, A. (2022) · International Journal of Human-Computer Studies · doi:10.1016/j.ijhcs.2022.102837 · Cited by 39
Understanding the Impact of Time Pressure and Automation Support in a Visual Search Task
Rieger, T., & Manzey, D. (2024) · Human Factors: The Journal of the Human Factors and Ergonomics Society · doi:10.1177/00187208221111236 · Cited by 40
“First, the F -test is relatively robust towards deviations of variables from normal distribution and inhomogeneity of variances (Glass et al., 1972), particularly with equal group sizes (Blanca et al., 2018) as was the case in our research.”
Result
Playful handling by caretakers reduces fear of humans in the laboratory rat
Cloutier, S., Panksepp, J., & Newberry, R. C. (2012) · Applied Animal Behaviour Science · doi:10.1016/j.applanim.2012.06.001 · Cited by 38
Soil Morphologic Properties and Cattle Stocking Rate Affect Dynamic Soil Properties
Schmalz, H. J., Taylor, R. V., Johnson, T. N., et al. (2013) · Rangeland Ecology & Management · doi:10.2111/rem-d-12-00040.1 · Cited by 39
Dealing with the Unthinkable: a Study of the Cognitive and Emotional Stress of Adult and Child Homicide Investigations on Police Investigators
Roach, J. O., Cartwright, A., & Sharratt, K. (2016) · Journal of Police and Criminal Psychology · doi:10.1007/s11896-016-9218-5 · Cited by 47
“Parametric statistics were employed within this dataset despite the use of Likert scales due to the fact that research has evidenced that two-tailed parametric analyses are in fact robust enough to handle non-normally distributed data (Glass et al. 1972).”
Usability of Immunohistochemistry in Forensic Samples With Varying Decomposition
Lesnikova, I., Schreckenbach, M. N., Kristensen, M. P., et al. (2018) · American Journal of Forensic Medicine & Pathology · doi:10.1097/paf.0000000000000408 · Cited by 39
Neurophysiological Measures of the Perception of Antismoking Public Service Announcements Among Young Population
Cartocci, G., Modica, E., Rossi, D., Cherubino, P., Maglione, A. G., Colosimo, A., Trettel, A., Mancini, M., & Babiloni, F. (2018) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2018.00231 · Cited by 39
From classroom to career: the unique role of communal processes in predicting interest in STEM careers
Fuesting, M. A., Diekman, A. B., & Hudiburgh, L. M. (2017) · Social Psychology of Education · doi:10.1007/s11218-017-9398-6 · Cited by 42
“Further, the parametric tests we employ are robust to violations of assumptions of normality (Bohrnstedt and Carter 1971; Glass et al. 1972; Havlicek and Peterson 1976; see Norman 2010, for further review).”
Method
Attributions, cognitive processes and control systems
Shields, M. D., Birnberg, J. G., & Frieze, I. H. (1981) · Accounting Organizations and Society · doi:10.1016/0361-3682(81)90023-4 · Cited by 39
Accounting for Heteroskedasticity Resulting from Between-Group Differences in Multilevel Models
Huang, F. L., Wiedermann, W., & Zhang, B. (2022) · Multivariate Behavioral Research · doi:10.1080/00273171.2022.2077290 · Cited by 41
“When group sizes are balanced, the F-test tends to be robust to variance heterogeneity (Blanca et al., 2018; Glass et al., 1972; Kohr & Games, 1974) although some studies have suggested otherwise (Lix et al.”
BackgroundResultInfluential
Attitudes to teamwork and safety among Italian surgeons and operating room nurses
Prati, G., & Pietrantoni, L. (2014) · Work · doi:10.3233/wor-131702 · Cited by 38
Some properties of p-curves, with an application to gradual publication bias.
Ulrich, R., & Miller, J. O. (2017) · Psychological Methods · doi:10.1037/met0000125 · Cited by 36
Empirical validation of the Horowitz Multiple Systemic Infectious Disease Syndrome Questionnaire for suspected Lyme disease
Citera, M., Freeman, P. R., & Horowitz, R. I. (2017) · International Journal of General Medicine · doi:10.2147/ijgm.s140224 · Cited by 38
“60–62 To verify our results, however, we examined whether the same pattern of results would hold when tested with a nonparametric test of ranks, the Kruskal–Wallis test.”
Oyster (Crassostrea virginica) Aquaculture Shifts Sediment Nitrogen Processes toward Mineralization over Denitrification
Lunstrum, A. M., McGlathery, K. J., & Smyth, A. R. (2017) · Estuaries and Coasts · doi:10.1007/s12237-017-0327-x · Cited by 38
“Normality was assumed, as ANOVA is robust to deviations in normality and homogeneity of variance when sample sizes are equal or similar (n = 3 to 4 in this study), and the resulting effect on nominal significance values is usually conservative and/or small (Glass et al. 1972).”
Method
Summarizing Monte Carlo Results in Methodological Research: The Single-Factor, Fixed-Effects ANCOVA Case
Harwell, M. R. (2003) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986028001045 · Cited by 38
“Perhaps the best known of these is due to Glass, Peckham, and Sanders (1972), who narratively summarized the available MC and exact statistical theory results for the ANCOVA F test.”
Background
Interval estimates of weighted effect sizes in the one‐way heteroscedastic ANOVA
Kulinskaya, E., & Staudte, R. G. (2006) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711005x68174 · Cited by 38
The Distribution of Talker Variability Impacts Infants’ Word Learning
Quam, C., Knight, S., & Gerken, L. (2017) · Laboratory Phonology Journal of the Association for Laboratory Phonology · doi:10.5334/labphon.25 · Cited by 38
“We first conducted analyses of variance, which have been shown to be fairly robust to moderate non-normality (Glass et al., 1972; Harwell et al., 1992).”
Power comparison of ANOVA and Kruskal‒Wallis tests when error assumptions are violated
Nwobi, F. N., & Akanno, F. C. (2021) · Advances in Methodology and Statistics · doi:10.51936/ltgt2135 · Cited by 37
“The research carried out by Glass et al. (1972) focused on the powers of the F-test and KW test when the population of interest is skewed.”
Background
Transposon signatures of allopolyploid genome evolution
Session, A. M., & Rokhsar, D. S. (2023) · Nature Communications · doi:10.1038/s41467-023-38560-z · Cited by 39
“For each k-mer that meets the minimum count in each species, we provide a table that has the ANOVA and Tukey ’ s HSD statistics, including ANOVA F-statistic, Tukey p -values, effect sizes, and 95%Con ﬁ dence Intervals(Supplementary Data 4).”
Influential
The Effect of Requests for Positive Evaluations on Customer Satisfaction Ratings
Jones, M. A., Taylor, V. A., & Reynolds, K. E. (2014) · Psychology and Marketing · doi:10.1002/mar.20684 · Cited by 37
Bifurcation asymmetry of the porcine coronary vasculature and its implications on coronary flow heterogeneity
Kalsho, G., & Kassab, G. S. (2004) · American Journal of Physiology-Heart and Circulatory Physiology · doi:10.1152/ajpheart.00371.2004 · Cited by 37
Fourteen years of dreissenid presence in the rocky littoral zone of a large lake: effects on macroinvertebrate abundance and diversity
Ozersky, T., Barton, D. R., & Evans, D. O. (2011) · Journal of the North American Benthological Society · doi:10.1899/10-122.1 · Cited by 37
“The 2008 data could not be transformed to meet the assumption of equality of variance, but ANOVA was used because it is relatively robust against violation of this assumption, especially when the number of replicates in different treatments is equal or nearly equal (Glass et al. 1972).”
Method
Examining retaliatory responses to justice violations and recovery attempts in teams.
Christian, J. S., Christian, M. S., Garza, A. S., & Ellis, A. P. J. (2012) · Journal of Applied Psychology · doi:10.1037/a0029450 · Cited by 40
Memory quality modulates the effect of aging on memory consolidation during sleep: Reduced maintenance but intact gain
Muehlroth, B. E., Sander, M. C., Fandakova, Y., Grandy, T. H., Rasch, B., Shing, Y. L., & Werkle‐Bergner, M. (2019) · NeuroImage · doi:10.1016/j.neuroimage.2019.116490 · Cited by 43
Application of machine learning to mapping primary causal factors in self reported safety narratives
Robinson, S. D., Irwin, W. J., Kelly, T. K., & Wu, X. O. (2015) · Safety Science · doi:10.1016/j.ssci.2015.02.003 · Cited by 39
“…of the distributions for all reports is of limited concern given that the correlation values are generally robust to violations of the normality assumption and are likely to result in reduced power rather than inﬂated sig-niﬁcance (Glass et al., 1972; Edgell and Noon, 1984; Norman, 2010).”
Background
Evaluation of Spatial/3D Audio: Basic Audio Quality Versus Quality of Experience
Schoeffler, M., Silzle, A., & Herre, J. (2016) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2016.2639325 · Cited by 37
“Throughout the results analysis, effect sizes are reported along with the p-values of the statistical tests.”
Method
Tests for homogeneity of variance
Keselman, H. J., Gaines, P. A., & Clinch, J. (1979) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610917908812108 · Cited by 37
Effects of an introduced piscivorous fish on native benthic fishes in a coastal river
White, J. L., & Harvey, B. C. (2001) · Freshwater Biology · doi:10.1046/j.1365-2427.2001.00724.x · Cited by 37
Teaching earth sciences: Should we implement teacher-directed or student-controlled CAI in the secondary classroom?
Chang, C. (2003) · International Journal of Science Education · doi:10.1080/09500690210145701 · Cited by 38
Methodological considerations in corporate mail surveys: A research note
Kerin, R. A., & Harvey, M. G. (1976) · Journal of Business Research · doi:10.1016/0148-2963(76)90029-1 · Cited by 37
Chapter 11: Issues in Meta-Analysis
Hedges, L. (1986) · Review of Research in Education · doi:10.3102/0091732x013001353 · Cited by 85
POLYMORPHISM FOR BREEDING COLORS IN GASTEROSTEUS ACULEATUS II. REPRODUCTIVE SUCCESS AS A RESULT OF CONVERGENCE FOR THREAT DISPLAY
Hagen, D. W., Moodie, G. E. E., & Moodie, P. F. (1980) · Evolution · doi:10.1111/j.1558-5646.1980.tb04047.x · Cited by 37
Secondary traumatic stress among victim advocates: prevalence and correlates
Benuto, L., Newlands, R. T., Ruork, A., Hooft, S., & Ahrendt, A. (2018) · Journal of Evidence-Informed Social Work · doi:10.1080/23761407.2018.1474825 · Cited by 30
The potential of immersive virtual reality for representations in design education
Horvat, N., Martinec, T., Lukačević, F., Perišić, M. M., & Škec, S. (2022) · Virtual Reality · doi:10.1007/s10055-022-00630-w · Cited by 39
“ANOVA is robust to non-normal distributions (Blanca et al. 2017), as they have little effect on the Type I error probability (Glass et al. 1972).”
BackgroundMethod
Tests That are Robust against Variance Heterogeneity in k × 2 Designs with Unequal Cell Frequencies
Overall, J. E., Atlas, R. S., & Gibson, J. M. (1995) · Psychological Reports · doi:10.2466/pr0.1995.76.3.1011 · Cited by 36
A closer examination on some parametric alternatives to the ANOVA F-test
Beuckelaer, A. D. (1996) · Statistical Papers · doi:10.1007/bf02926110 · Cited by 36
A Mixed-Methods Comparison of Vocational and Identified-Gifted High School Students on the Overexcitability Questionnaire
Piirto, J., & Fraas, J. W. (2012) · journal for the education of the gifted · doi:10.1177/0162353211433792 · Cited by 36
An improved method for studying the condition of fish, with an example using Pacific sardine Sardinops sagax (Jenyns)
Patterson, K. R. (1992) · Journal of Fish Biology · doi:10.1111/j.1095-8649.1992.tb02629.x · Cited by 36
Soil and plant water relations in a crested wheatgrass pasture: response to spring grazing by cattle
Wraith, J. M., Johnson, D. A., Hanks, R. J., et al. (1987) · Oecologia · doi:10.1007/bf00379418 · Cited by 36
Colorful male guppies do not provide females with fecundity benefits
Pilastro, A., Gasparini, C., Boschetto, C., et al. (2008) · Behavioral Ecology · doi:10.1093/beheco/arm140 · Cited by 36
“Furthermore, when, as in the case of our dataset, there is an inverse relationship between sample size and variance (brood size, r ¼� 0.33; gestation r ¼� 0.49), alpha is inflated ( Glass et al. 1972 ).”
BackgroundInfluential
Motivational and Achievement Effects of Learner Control over Content Review within CAI
Kinzie, M. B., Sullivan, H. J., & Berdel, R. L. (1992) · Journal of Educational Computing Research · doi:10.2190/2ewh-j2f1-ck87-09nr · Cited by 36
“Glass, Peckham, and Sanders [31] recommended the F test as being sufficiently robust to handle analysis of variables expressed as proportions, even though they are not normally distributed.”
Background
A Review of Nonparametric Alternatives To Analysis of Covariance
Olejnik, S. F., & Algina, J. J. (1985) · Evaluation Review · doi:10.1177/0193841x8500900104 · Cited by 36
Calming children's television fears: Mr. Rogers vs. The incredible hulk
Cantor, J. R., Sparks, G. G., & Hoffner, C. A. (1988) · Journal of Broadcasting & Electronic Media · doi:10.1080/08838158809386702 · Cited by 36
Why Hedges’ g*s based on the non-pooled standard deviation should be reported with Welch’s t-testPreprint
Delacre, M., Lakens, D., Ley, C., Liu, L., & Leys, C. (2021) · doi:10.31234/osf.io/tu6mp · Cited by 36
Towards the design of user-centric strategy recommendation systems for collaborative Human–AI tasks
Dodeja, L., Tambwekar, P., Hedlund-Botti, E., & Gombolay, M. (2024) · International Journal of Human-Computer Studies · doi:10.1016/j.ijhcs.2023.103216 · Cited by 41
Sustainable Agriculture and Climate Change: Producing Potatoes (Solanum tuberosum L.) and Bush Beans (Phaseolus vulgaris L.) for Improved Food Security and Resilience in a Canadian Subarctic First Nations Community
Barbeau, C. D., Oelbermann, M., Karagatzides, J. D., et al. (2015) · Sustainability · doi:10.3390/su7055664 · Cited by 35
“Differences in the mean values of potato and bush bean yields between sites and between years were examined using two-way analysis of variance (ANOVA).”
BackgroundInfluential
Sympatric prey responses to lethal top-predator control: predator manipulation experiments
Allen, B. L., Allen, B. L., Engeman, R. M., & Leung, L. K. ‐. (2014) · Frontiers in Zoology · doi:10.1186/s12983-014-0056-y · Cited by 35
“However, repeated measures ANOVA is very robust to deviations from normality, with non-normal distributions seldom affecting the overall outcomes or interpretations [114-116].”
Efficacy of lecture‐based environmental education for biodiversity conservation: a robust controlled field experiment with recreational anglers engaged in self‐organized fish stocking
Fujitani, M. L., McFall, A., Randler, C., & Arlinghaus, R. (2015) · Journal of Applied Ecology · doi:10.1111/1365-2664.12560 · Cited by 39
Meta-analysis of the parasitic phase traits of Haemonchus contortus infection in sheep
Saccareau, M., Sallé, G., Robert-Granié, C., Duchemin, T., Jacquiet, P., Blanchard, A., Cabaret, J., & Moreno, C. R. (2017) · Parasites & Vectors · doi:10.1186/s13071-017-2131-7 · Cited by 35
“Fortunately, the ANOVA test 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 much affected by not adhering to this assumption [68].”
Background

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analyses of Variance and Covariance

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks