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 15,356
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 901–999 of 999

Effect of Maxillary Osteotomy on Speech in Cleft Lip and Palate: Instrumental Outcomes of Velopharyngeal Function
Pereira, V. J., Tuomainen, J., Hay, N., Mars, M., Suchak, A., & Sell, D. (2020) · The Cleft Palate-Craniofacial Journal · doi:10.1177/1055665620947626 · Cited by 9
“In the case of our cohort, this would also result in unequal sample sizes of N¼ 7 (bimaxillary) and N ¼ 13 (maxillary osteotomy only), where the risk, potentially, is in committing a type I error (Glass et al., 1972).”
Background
Infants' discrimination of consonant contrasts in the presence and absence of talker variability
Quam, C., Clough, L. T., Knight, S., & Gerken, L. (2020) · Infancy · doi:10.1111/infa.12371 · Cited by 8
“We first conducted ANOVAs, which are fairly robust to moderate non-normality (Glass et al., 1972; Harwell et al., 1992).”
Method
Estimation of Age-at-Death Using Cortical Bone Histomorphometry of the Rib and Femur: A Validation Study on a British Population
Karydi, C., García-Donas, J. G., Tsiminikaki, K., Bonicelli, A., Moraitis, K., & Kranioti, E. F. (2022) · Biology · doi:10.3390/biology11111615 · Cited by 9
“Each statistical test was used after the sample was tested for meeting the required assumptions [43].”
Method
Does It Affect You? Social and Learning Implications of Using Cognitive-Affective State Recognition for Proactive Human-Robot Tutoring
Kraus, M., Betancourt, D., & Minker, W. (2023) · IEEE RO-MAN · doi:10.1109/ro-man57019.2023.10309574 · Cited by 9
“The F-statistic of an ANOVA can be robust to violations of assumptions [46].”
Method
Determinants of variability in motor performance in middle childhood: a cross-sectional study of balance and motor co-ordination skills
Kitsao-Wekulo, P., Holding, P., Taylor, H. G., Kvalsvig, J. D., & Connolly, K. (2013) · BMC Psychology · doi:10.1186/2050-7283-1-29 · Cited by 10
“It should be noted that a much wider (and significant) variance in the mean scores of three tests for rural children in the current study possibly affected the significance levels recorded and may have jeopardized the validity of the obtained results (Glass et al. 1972).”
Result
Averaging auditory evoked magnetoencephalographic and electroencephalographic responses: a critical discussion
König, R., Matysiak, A., Kordecki, W., Sielużycki, C., Zacharias, N., & Heil, P. F. (2015) · European Journal of Neuroscience · doi:10.1111/ejn.12833 · Cited by 9
“…presence of heterosce-dasticity (heterogeneity of variance) is not only important for statistical evaluation (Cochran, 1947; Eisenhart, 1947; Glass et al. , 1972; Erceg-Hurn & Mirosevich, 2008; Kipi (cid:2) nski et al. , 2011), but may also prevent misinterpretations (Bryk & Raudenbush,…”
BackgroundMethod
Canopy position and cold storage duration affects mealiness incidence and consumer preference for the appearance and eating quality of ‘Forelle’ pears
Cronje, A., Crouch, E. M., Müller, M., et al. (2015) · Scientia Horticulturae · doi:10.1016/j.scienta.2015.08.033 · Cited by 9
Relational Satisfaction from Providing and Receiving Support is Associated with Reduced Post-Disaster Depression: Data From Within One Year of the 2011 Japan Triple Disaster
Lebowitz, A. (2016) · Community Mental Health Journal · doi:10.1007/s10597-016-9995-4 · Cited by 9
Mapping changes in support: a longitudinal analysis of networks of pre-service mathematics and science teachers
Bokhove, C., & Downey, C. (2018) · Oxford Review of Education · doi:10.1080/03054985.2017.1400427 · Cited by 9
Nocturnal insect availability in bottomland hardwood forests managed for wildlife in the Mississippi Alluvial Valley
Ketzler, L. P., Comer, C. E., & Twedt, D. J. (2017) · Forest Ecology and Management · doi:10.1016/j.foreco.2017.02.009 · Cited by 9
Behavioural and physiological assessments of dimethyl trisulfide treatment for acute oral sodium cyanide poisoning
Rice, N. C., Rauscher, N. A., Wilkins, W. L., et al. (2019) · Basic & Clinical Pharmacology & Toxicology · doi:10.1111/bcpt.13220 · Cited by 9
Acute Administration of Bioavailable Curcumin Alongside Ferrous Sulphate Supplements Does Not Impair Iron Absorption in Healthy Adults in a Randomised Trial
Lorinczova, H. T., Begum, G., Renshaw, D. W., & Zariwala, M. G. (2021) · Nutrients · doi:10.3390/nu13072300 · Cited by 9
Testing for seasonal means in time series data
Liu, G., Shao, Q., Lund, R., et al. (2016) · Environmetrics · doi:10.1002/env.2383 · Cited by 9
“While this distributional claim is reasonably robust against moderate departures from normality, it degrades quickly when f t g is correlated (Glass et al. 1972; this will become apparent later).”
BackgroundMethod
Continuing Motivation of Boys and Girls Under Differing Evaluation Conditions and Achievement Levels
Hughes, B. J., Sullivan, H. J., & Beaird, J. H. (1986) · American Educational Research Journal · doi:10.3102/00028312023004660 · Cited by 9
Complex Trait-Treatment-Interaction analysis: A powerful approach for analysing individual differences in experimental designs
Leutner, D., & Rammsayer, T. H. (1995) · Personality and Individual Differences · doi:10.1016/0191-8869(95)00062-b · Cited by 9
Hypothesis-Testing Procedures in Repeated-Measures Designs: On the Road Map Not Taken
Romaniuk, J. G., Levin, J. R., & Hubert, L. J. (1977) · Child Development · doi:10.1111/j.1467-8624.1977.tb04000.x · Cited by 9
Reproduction criteria and meat quality of South African Black (Struthio Camelus var. Domesticus), Zimbabwean Blue (Struthio Camelus Australis) and South African Black X Zimbabwean Blue ostriches
Brand, M. (2006) · SUNScholar (Stellenbosch University) · Cited by 9
Effectiveness of a digital weight management program on diet quality: a randomized controlled trial
Palacios, A. M., Lee, A. M., Parker, C., Watts, C. Q., Dickinson, S. L., Henschel, B., Anderson, G., Kersey, J. X., Allison, D. B., Foster, G. D., et al. (2025) · The American Journal of Clinical Nutrition · doi:10.1016/j.ajcnut.2025.06.024 · Cited by 8
Measuring user experience in automated driving
Himmels, C., Omozik, K., Jarosch, O., & Buchner, A. (2021) · International Conference on Automotive User Interfaces and Interactive Vehicular Applications (AutomotiveUI) · doi:10.1145/3409118.3475135 · Cited by 8
“Repeated-measures MANOVAs [30] were calculated which are known to be robust against violations of assumptions such as that of normality with large sample sizes and balanced designs [6, 17, 32].”
Method
Shifting thermal regimes influence competitive feeding and aggression dynamics of brook trout ( Salvelinus fontinalis ) and creek chub ( Semotilus atromaculatus )
Colby, B., Niles, J., Persons, M. H., & Wilson, M. J. (2022) · Ecology and Evolution · doi:10.1002/ece3.9056 · Cited by 8
“This is because the false- positive rate is affected little despite violations of normality, even with modest sample sizes (Ghasemi & Zahediasl, 2012; Glass et al., 1972; Harwell et al., 1992; Lix et al., 1996).”
Background
Evaluating the effectiveness of sonification in science education using Edukoi
Fovino, L. G. N., Zanella, A., Mascolo, L. D., Ginolfi, M., Carpita, N., Manuncola, F. T., & Grassi, M. (2024) · Personal and Ubiquitous Computing · doi:10.1007/s00779-024-01809-5 · Cited by 9
“Over each plot, we also represented the individual performances of the students 5 Note that although our data were not normally distributed with homogeneous variance, both t -test and ANOVA are robust even when distributions of the data violate the distribution assumed by the test [36–38].”
Method
Experimental Designs and Statistical Analyses for Rootstock Trials
Marini, R. P. (2024) · Agronomy · doi:10.3390/agronomy14102312 · Cited by 9
Robust statistical methods and the credibility movement of psychological science
Sladekova, M., & Field, A. P. (2025) · PeerJ · doi:10.7717/peerj.20043 · Cited by 12
“False positives will, however, be inflated in the presence of heteroscedasticity ( Glass, Peckham & Sanders, 1972 ; Rogan & Keselman, 1977 ; Harwell et al., 1992 ; Hsiung & Olejnik, 1996 ; Moder, 2010 ; Blanca et al., 2018 ; Nguyen et al., 2019 ; Yang, Tu & Chen, 2019 ) and the effects on the…”
Influential
Chi-square and F Ratio: Which should be used when?
Lehmann, C. S. (2018) · Journal of Methods and Measurement in the Social Sciences · doi:10.2458/v8i2.22990 · Cited by 8
Does the Information about Classroom Norms Change the Individual Injunctive Norms about Cyberbullying? – A Minimal Intervention Study
Pfetsch, J. S., Schultze‐Krumbholz, A., & Füllgraf, F. (2018) · International Journal of Developmental Science · doi:10.3233/dev-180250 · Cited by 8
“The assumptions for the repeated ANOVA were testedaccordingtostandardprocedures(Field,2013), which did not yield substantial violations, taking the big sample size and the equal group sizes into account (Glass, Peckham, & Sanders, 1972; Wilcox, 2012).”
Altered cutaneous reflexes to non-noxious stimuli in the triceps surae of people with chronic incomplete spinal cord injury
Phipps, A. M., & Thompson, A. K. (2023) · Journal of Neurophysiology · doi:10.1152/jn.00266.2022 · Cited by 8
Exploring Urban Challenges: Understanding Advanced Driver Assistance Systems in Different Situational Contexts
Buchner, C., Himmels, C., Schmitz, J., Stoll, T., & Baumann, M. (2024) · International Conference on Automotive User Interfaces and Interactive Vehicular Applications (AutomotiveUI) · doi:10.1145/3640792.3675709 · Cited by 8
“Parametric ANOVAs were performed, which are robust against violations of the assumptions of normality and homogeneous variances with large samples and balanced designs [13, 34].”
The value of a datum – how little data do we need for a quantitative risk analysis?
Leung, B., & Steele, R. J. (2013) · Diversity and Distributions · doi:10.1111/ddi.12062 · Cited by 8
“This is often carried out in statistics to test the behaviour of statistical models (e.g. Glass et al., 1972; Berkof et al., 2003; Lambert et al., 2005).”
Background
Physical and Chemical Characteristics of Warthog (Phacochoerus africanus) Meat
Swanepoel, M., Leslie, A. J., van der Rijst, M., et al. (2016) · African Journal of Wildlife Research · doi:10.3957/056.046.0103 · Cited by 8
Evaluating the effect of sample type on American alligator (Alligator mississippiensis) analyte values in a point-of-care blood analyser
Hamilton, M. T., Finger, J. W., Winzeler, M. E., & Tuberville, T. D. (2016) · Conservation Physiology · doi:10.1093/conphys/cov065 · Cited by 8
“Given that ANOVA is fairly robust to violations of normality when sample sizes are large (Glass et al., 1972; Schmider et al., 2010), we proceeded with a repeated-measures ANOVA followed by a pairwise t-test with Bonferroni correction.”
Method
Validity and reliability of single-item self-report measures of meaning in life and satisfaction with life
Atroszko, P. A., Krzyżaniak, P., Sendal, L., & Atroszko, B. (2015) · CeON Repository (Centre for Evaluation in Education and Science) · Cited by 8
Appraisal of Statistical Practices in HRI vis-a-vis the T-Test for Likert Items/Scales.
Gombolay, M., & Shah, A. (2016) · National Conference on Artificial Intelligence · Cited by 8
Reconsidering the Role of Design Standards in Developing Effective Safety Labeling: Monolithic Recipes or Collections of Separable Features?
Kalsher, M. J., Obenauer, W. G., & Weiss, C. F. (2019) · Human Factors The Journal of the Human Factors and Ergonomics Society · doi:10.1177/0018720818820413 · Cited by 8
Komplexitätsreduktion in Lehr-Lern-Laboren
Kürten, R., Greefrath, G., Hammann, M., & Verlag, W. (2020) · Waxmann Verlag GmbH eBooks · doi:10.31244/9783830989905 · Cited by 9
Good Boy Here or Bad Boy Far Away?
Schrills, T., Zoubir, M., Stahl, J., et al. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-49183-3_31 · Cited by 8
Effects of two types of dynamic office workstations (DOWs) used at two intensities on cognitive performance and office work in tasks with various complexity
Schellewald, V., Kleinert, J., & Ellegast, R. P. (2020) · Ergonomics · doi:10.1080/00140139.2020.1862308 · Cited by 8
Definitions of Meaningful Work for Generation X and Millennial Cuspers
Hyatt, B. V. (2021) · Journal of Human Resource Management · doi:10.11648/j.jhrm.20210901.11 · Cited by 8
“Moreover, “the relevant question is not whether ANOVA assumptions are met, but rather whether the plausible violations of assumptions have consequences on validity of probability statements based on standard assumptions” [81].”
Background
Factors That Affect Drivers’ Perception of Closing and an Immediate Hazard
Weaver, B. W., DeLucia, P. R., & Jupe, J. (2021) · Human Factors The Journal of the Human Factors and Ergonomics Society · doi:10.1177/00187208211009028 · Cited by 8
“In other words, prior research has indicated departures from normal- cance or power of an ANOVA (Cochran, 1947; Glass et al., 1972).”
Background
Tool-Use profiles in Undergraduate Mathematics
Anastasakis, M., & Lerman, S. (2021) · International Journal of Science and Mathematics Education · doi:10.1007/s10763-021-10196-9 · Cited by 8
All devices are not created equal: Simultaneous data collection of three triaxial accelerometers sampling at different frequencies
Gruber, A. H., Marotta, L., McDonnell, J., et al. (2022) · Proceedings of the Institution of Mechanical Engineers Part P Journal of Sports Engineering and Technology · doi:10.1177/17543371221140517 · Cited by 8
“…peak acceleration between the original signals from each device (i.e. sampling frequencies) and across timepoints ( a = 0.050; IBM SPSS Statistics 26): where X is the matrix of sampling frequency, timepoint, and its interaction; Z is the identifier for participant; e is the error; and b is the…”
Influential
Effectiveness of lactation cookies on human milk production rates: a randomized controlled trial
Palacios, A. M., Cardel, M. I., Parker, E. S., Dickinson, S., Houin, V. R., Young, B. E., & Allison, D. B. (2023) · American Journal of Clinical Nutrition · doi:10.1016/j.ajcnut.2023.03.010 · Cited by 8
Nonparametric alternatives to the f statistic in analysis of variance
Kelley, D. L., & Sawilowsky, S. S. (1997) · Journal of Statistical Computation and Simulation · doi:10.1080/00949659708811839 · Cited by 8
Experimental evidence on financial incentives, information and decision-making
Dobbs, I. M., & Miller, A. D. (2008) · The British Accounting Review · doi:10.1016/j.bar.2008.10.002 · Cited by 8
“Although some writers claim standard tests are robust to departures from Normality, see for instance Clinch & Keselman (1982) and Tan (1982), others have opposing views; see Bradley (1978), Glass et al (1972), Wilcox (1995) and Wilcox (1998).”
The Effects of Four Decades of Recession on Higher Education Enrollments in the United States
Wright, D. A., Ramdin, G., & Vásquez-Colina, M. D. (2013) · Universal Journal of Educational Research · doi:10.13189/ujer.2013.010303 · Cited by 8
The Basis of the Syllable Hierarchy: Articulatory Pressures or Universal Phonological Constraints?
Zhao, X., & Berent, I. (2017) · Journal of Psycholinguistic Research · doi:10.1007/s10936-017-9510-2 · Cited by 8
“2 The ANOVA was conducted because of its resilience to moderate deviations from normality (Glass et al. 1972; Martin and Games 1977; Harwell et al. 1992; Lix et al. 1996).”
Method
The role of READ1 and KIAA0319 genetic variations in developmental dyslexia: testing main and interactive effects
Trezzi, V., Forni, D., Giorda, R., Villa, M., Molteni, M., Marino, C., & Mascheretti, S. (2017) · Journal of Human Genetics · doi:10.1038/jhg.2017.80 · Cited by 10
Suicidal Ideation and Sense of Community in Faith Communities
Mason, K. E., Martin, W. B., & Kim, E. (2018) · Religions · doi:10.3390/rel9020040 · Cited by 9
“KW results were confirmed by ANOVAs, because of ANOVA’s robustness despite the violation of normality (Glass et al. 1972).”
Result
The role of noninitial clusters in the Children's Test of Nonword Repetition: Evidence from children with language impairment and typically developing children
Cilibrasi, L., Stojanovik, V., Loucas, T., & RIDDELL, P. M. (2018) · Dyslexia · doi:10.1002/dys.1599 · Cited by 8
Who's in Control of the Ark? A Study of Internal Controls in Operating and Auditing A Small Preschool
Grace, E. V., & Davis, A. (2019) · Issues in Accounting Education · doi:10.2308/iace-52375 · Cited by 8
Addiction is a brain disease, and it doesn’t matter: Prior choice in drug use blocks leniency in criminal punishment.
Sinclair-House, N., Child, J. J., & Crombag, H. S. (2019) · Psychology Public Policy and Law · doi:10.1037/law0000217 · Cited by 11
IDENTIFYING THE EFFECT OF REVIEWERS’ EXPERTISE ON DESIGN REVIEW USING VIRTUAL REALITY AND DESKTOP INTERFACE
Horvat, N., Škec, S., Martinec, T., et al. (2020) · Proceedings of the Design Society DESIGN Conference · doi:10.1017/dsd.2020.304 · Cited by 8
“As the violation of this assumption has a high effect on the Type I error (Glass et al., 1972), the obtained p -values need further clarification.”
BackgroundResultInfluential
Replacement of Sodium Tripolyphosphate with Iota Carrageenan in the Formulation of Restructured Ostrich Ham
Schutte, S., Marais, J., Müller, M., et al. (2021) · Foods · doi:10.3390/foods10030535 · Cited by 8
“In some cases, deviations from normality were the cause of one or two outliners, which were removed before the final analysis [43].”
Background
The Effects of Continuous vs. Intermittent Prism Adaptation Protocols for Treating Visuospatial Neglect: A Randomized Controlled Trial
Scheffels, J. F., Korabova, S., Eling, P., et al. (2021) · Frontiers in Neurology · doi:10.3389/fneur.2021.742727 · Cited by 8
“Statistical evaluation of possible carry-over effects for the primary and secondary outcome measures included analyses of variance (ANOVAs) for repeated measurements (43).”
Method
Depression Is Associated With the Absence of Sex Differences in the 2D:4D Ratio of the Right Hand
Sanwald, S., Widenhorn‐Müller, K., Wernicke, J., Sindermann, C., Kiefer, M., & Montag, C. (2019) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2019.00483 · Cited by 8
Assessing Web interaction with recollection: Age-related and task-related differences
Etcheverry, I., Terrier, P., & Marquié, J.-C. (2011) · Computers in Human Behavior · doi:10.1016/j.chb.2011.08.004 · Cited by 8
An expert system predevelopment test for assessment of sales territory difficulty
Claxton, J. D., Vandenbosch, M., & Weinberg, C. B. (1990) · International Journal of Research in Marketing · doi:10.1016/0167-8116(90)90022-f · Cited by 8
Case-Based Instruction in Early Childhood Teacher Preparation: Does It Work?
Florez, I. R. (2011) · Journal of Early Childhood Teacher Education · doi:10.1080/10901027.2011.572227 · Cited by 8
Can the activity budget hypothesis explain sexual segregation in western grey kangaroos?
MacFarlane, A. M. (2006) · Behaviour · doi:10.1163/156853906778607390 · Cited by 8
Johnson's transformation two-sample trimmed t and its bootstrap method for heterogeneity and non-normality
Luh, W., & Guo, J. (2000) · Journal of Applied Statistics · doi:10.1080/02664760050173292 · Cited by 8
“For the twosample case, Yuen & Dixon (1973) used a trimmed t against the contaminated normal distribution.”
BackgroundMethodInfluential
Evaluation of the Early Years Programme of the Childhood Development Initiative
Hayes, N., Siraj, I., Keegan, S., & Goulding, E. (2020) · Lenus, The Irish Health Repository (Dr Steevens Hospital Library) · doi:10.7486/dri.j960fn70n · Cited by 8
Enhancing Training Outcomes in the Context of e-Learning: The Impact of Objective Learner Control, Training Content Complexity, Cognitive Load, Learning Goal Orientation, and Metacognitive Strategies
Granger, B. (2012) · Digital Commons - University of South Florida (University of South Florida) · Cited by 8
Analysis of variance methods for the design and analysis of Monte Carlo statistical studies
Wire, E. L., & Church, J. D. (1977) · Bulletin of the Psychonomic Society · doi:10.3758/bf03329302 · Cited by 8
Analysis of variance: univariate and multivariate approaches
Rosopa, P. J., & King, B. M. (2022) · Elsevier eBooks · doi:10.1016/b978-0-12-818630-5.10065-x · Cited by 8
The normal distribution is not normal in psychological data: Moving beyond parametric dogma
Ferr, H. (2025) · PLOS Mental Health · doi:10.1371/journal.pmen.0000403 · Cited by 7
“When assumptions are not met, the probability statements based on standard parametric tests may not be valid, leading to potentially misleading interpretations of data [11,12].”
Refinement of the stress-enhanced fear learning model of post-traumatic stress disorder: a behavioral and molecular analysis
Assche, I. A. V., Padilla, M. S., Stupart, O., & Milton, A. L. (2022) · Lab Animal · doi:10.1038/s41684-022-01054-4 · Cited by 7
Stakeholder acceptance of a robot-assisted social training scenario for autistic children compared to a tablet-computer-based approach
Frenkel, J., Kirst, S., Naumann, S., Simon, M., Seßner, J., Roesler, E., Onnasch, L., & Dziobek, I. (2025) · Scientific Reports · doi:10.1038/s41598-025-93970-x · Cited by 12
Synergizing AI and collaborative learning: a new approach to Chinese character acquisition in lower elementary education
Ye, J., Yu, Y. B., Zhang, M., & Long, S. (2025) · Interactive Learning Environments · doi:10.1080/10494820.2025.2528096 · Cited by 7
“Our experimental design ensured balanced group sizes which mitigated the impact of skewed distributions (Glass et al., 1972); (2) according to Central Limit Theorem, it can be assumed that the mean of samples follow normal distribution as the sample size is sufficiently large (n = 68); (3) the…”
Viable bacterial population and persistence of foodborne pathogens on the pear carpoplane
Duvenage, F. J., Duvenage, S., du Plessis, E. M., et al. (2016) · Journal of the Science of Food and Agriculture · doi:10.1002/jsfa.7847 · Cited by 7
Butyrate and Metformin Affect Energy Metabolism Independently of the Metabolic Phenotype in the Tumor Therapy Model
Meyer, F. B., Marx, C., Spangel, S. B., & Thierbach, R. (2021) · Biomolecules · doi:10.3390/biom11121831 · Cited by 7
“The results were tested for homogeneity of variances in each case, and as described elsewhere [26,27], the normal distribution was neglected.”
Method
The influence of the order and congruency of correct and erroneous worked examples on learning and (meta-)cognitive load
Wesenberg, L., Krieglstein, F., Jansen, S., Rey, G. D., Beege, M., & Schneider, S. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.1032003 · Cited by 9
Effectiveness of Digital and Analog Stress Management Interventions within Occupational Health Management in the Public Sector
Fasthoff, R. M., Nolte, L., & Kortsch, T. (2023) · Merits · doi:10.3390/merits3040037 · Cited by 11
“…the regression model of baseline stress and motivation at work at T2 and T3, ISocJR at T1 in the WLC, and ICJD at T3 in the online course), multiple regression models and mixed ANOVA were used because these procedures have been shown to be robust to violations of the normal distribution [98–100].”
Method
Logistics digitalization and the third-party logistics blue-collar employees performance: the role of paradoxical leader behavior
Ashraf, M. H., Triki, A., & Yalcin, M. G. (2024) · The International Journal of Logistics Management · doi:10.1108/ijlm-03-2024-0194 · Cited by 7
Judged and Remembered Trustworthiness of Faces Is Enhanced by Experiencing Multisensory Synchrony and Asynchrony in the Right Order
Toscano, H., & Schubert, T. W. (2015) · PLoS ONE · doi:10.1371/journal.pone.0145664 · Cited by 7
“Given that the statistical power of a GLM is not greatly affected by non-normality [35] and that type-I errors are well controlled in a GLM under these conditions [36], we concluded that our data analysis should be analyzed with GLM.”
Method
The persistence of short‐term cold acclimation in D rosophila melanogaster ( D iptera: D rosophilidae)
Everman, E. R., Ledbetter, N. M., & Morgan, T. J. (2017) · Physiological Entomology · doi:10.1111/phen.12191 · Cited by 7
“We proceeded with a parametric analysis of RCH score because parametric tests have been shown to be largely robust to deviations from normality (Glass et al., 1972) and datasets with a large number of observations can lead to significant deviations from normality as a result of the increased power in these datasets to…”
Method
Experimental Treatment with a Hypomethylating Agent Alters Life History Traits and Fitness in Brassica rapa
Kottler, E. J., VanWallendael, A., & Franks, S. J. (2018) · Journal of Botany · doi:10.1155/2018/7836845 · Cited by 7
Sidestepping spatial confounds in object-based correspondence effects: The Bimanual Affordance Task (BMAT)
Azaad, S., & Laham, S. M. (2019) · Quarterly Journal of Experimental Psychology · doi:10.1177/1747021819852216 · Cited by 7
Losing control: sleep deprivation impairs the suppression of unwanted thoughts
Harrington, M. O., Ashton, J. E., Sankarasubramanian, S., Anderson, M. C., & Cairney, S. A. (2019) · Sleep Medicine · doi:10.1101/813121 · Cited by 7
Estimating the tactical impact of robot swarms using a semi-automated forces system and design of experiments methods
Foster, K., & Petty, M. D. (2021) · The Journal of Defense Modeling and Simulation Applications Methodology Technology · doi:10.1177/15485129211008532 · Cited by 7
“the model that would otherwise be excluded if the correct P-values were available.(38) The plot of the reduced model fitted values versus the standardized residuals for the response variable (Blue destroyed) demonstrates increasing variance in the standardized residual as the fitted values of Blue destroyed increase (…”
BackgroundMethod
Effects of hypotension and hypertension on source memory and working memory
Cansino, S., Torres-Trejo, F., Estrada-Manilla, C., Mercado-Canales, A., Medina-Velázquez, D., Esquivel-Garcia, R., & Ruiz‐Velasco, S. (2021) · Aging & Mental Health · doi:10.1080/13607863.2021.1942435 · Cited by 8
“Because analysis of variance (ANOVA) is nearly unaffected when data moderately deviate from normality according to simulation studies (Glass et al., 1972), we employed ANOVA with data from the working memory task, which were the only relevant dependent variables that slightly deviated from…”
Method
DNA methylation of Vesicular Glutamate Transporters in the mesocorticolimbic brain following early-life stress and adult ethanol exposure—an explorative study
Vrettou, M., Yan, L., Nilsson, K. W., Wallén‐Mackenzie, Å., Nylander, I., & Comasco, E. (2021) · Scientific Reports · doi:10.1038/s41598-021-94739-8 · Cited by 8
Revisiting multi‐stage models for upstream technology adoption: Evidence from rapid generation advance in rice breeding
Lenaerts, B., de Mey, Y., & Demont, M. (2021) · Journal of Agricultural Economics · doi:10.1111/1477-9552.12450 · Cited by 7
THE IMPACT OF THE USE OF GEOGEBRA ON STUDENT’S MATHEMATICAL REPRESENTATION SKILLS AND ATTITUDE
Rabi, F., Ma, F., Aziz, M., et al. (2021) · European Journal of Education Studies · doi:10.46827/ejes.v8i12.4007 · Cited by 7
“When finding the difference in mean value of pretest is significant or not, a normality test was performed to know whether population's distribution is normal or not (Hopkins et al., 1990; Lilliefors, H. W., 1967; Septian et al., 2020; Glass et al., 1972).”
BackgroundMethod
Generalized Worry in Patients With Chronic Fatigue Syndrome Following Cognitive Behavioral Therapy: A Prospective Cohort Study in Secondary Care
Kalfas, M., Smakowski, A., Hirsch, C. R., Simiao, F., & Chalder, T. (2022) · Behavior Therapy · doi:10.1016/j.beth.2022.01.004 · Cited by 7
Differential Effects of Fundamental and Longitudinal Life History Trade-Offs on Delay Discounting: An Evolutionary Framework
Lu, J., Lu, Q., & Lu, L. (2022) · Behavioral Sciences · doi:10.3390/bs12030063 · Cited by 7
“Second, nonnormality, typically exhibited in Likert scales and behavioral measures, poses a serious problem for classical statistics [57,58].”
Background
Squalene-Rich Amaranth Oil Pickering Emulsions Stabilized by Native α-Lactalbumin Nanoparticles
Cuevas‐Gómez, A. P., González-Magallanes, B., Arroyo-Maya, I. J., Gutiérrez‐López, G. F., Cornejo‐Mazón, M., & Hernández‐Sánchez, H. (2022) · Foods · doi:10.3390/foods11141998 · Cited by 7
“Foods 2022, 11, x FOR PEER REVIEW 8 of 12 Statistically, it is difficult to work with small samples which come from populations with large standard deviations since, in these cases, the false positive rate is considerable when evaluating significant differences using One-way ANOVA [44].”
MethodInfluential
Propagation of measurement error in opinion dynamics models: The case of the Deffuant model
Carpentras, D., & Quayle, M. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.127993 · Cited by 8
Spatial Upsampling of Sparse Spherical Microphone Array Signals
Lübeck, T., Arend, J. M., & Pörschmann, C. (2023) · IEEE/ACM Transactions on Audio Speech and Language Processing · doi:10.1109/taslp.2023.3250841 · Cited by 7
Entrepreneurial competency in agriculture: is it a panacea for the problem of farmers' welfare?
Esubalew, A. A. (2023) · Journal of Agribusiness in Developing and Emerging Economies · doi:10.1108/jadee-01-2022-0006 · Cited by 11
“Name Three Good Things About Yourself in Mathematics” – An Intervention to Reduce Pre-Service Teachers’ Shame in Mathematics
Jenßen, L. (2023) · International Journal of Applied Positive Psychology · doi:10.1007/s41042-023-00120-7 · Cited by 12
“Because the mixed ANOVA is robust against violations of the assumption of normally distributed dependent variables for each combination of the within-and between-subjects factor, no consequences were drawn for the main analyses (Glass et al., 1972).”
Tolerance against exposure to solution of magnesium perchlorate in microinvertebrates
Kayastha, P., Rzymski, P., Gołdyn, B., Nagwani, A. K., Fiałkowska, E., Pajdak‐Stós, A., Sobkowiak, R., Robotnikowski, G., & Kaczmarek, Ł. (2023) · Zoological Journal of the Linnean Society · doi:10.1093/zoolinnean/zlad060 · Cited by 8
Initial Development of a Second Language Discussion Task-Specific Self-Efficacy Instrument: An Illustration for Frontline Researchers
Vitta, J. P., Leeming, P., McLean, S., & Nicklin, C. (2023) · RELC Journal · doi:10.1177/00336882231195102 · Cited by 7
“Therefore, the distributional characteristics of the data collected via the instrument were also assessed, since normal distributions tend to result in satisfying the residual assumptions of the general linear model (Field, 2018; Glass et al., 1972).”
Reassessing the Impact of Fear Appeals in Sustainable Consumption Communication: An Investigation into Message Types and Message Foci
Yu, C.-C., & Lu, C. (2023) · Sustainability · doi:10.3390/su152316442 · Cited by 9
Variance stabilization for computing and comparing grand mean waveforms in MEG and EEG
Matysiak, A., Kordecki, W., Sielużycki, C., Zacharias, N., Heil, P. F., & König, R. (2013) · Psychophysiology · doi:10.1111/psyp.12047 · Cited by 7
Statistical Modeling of Hydrogeologic Data ‐ Part I: Regression and ANOVA Models
Kufs, C. T. (1992) · Groundwater Monitoring & Remediation · doi:10.1111/j.1745-6592.1992.tb00042.x · Cited by 7
“Some authors believe that it is justified (e.g., Montgomery et al. 1987, U.S. EPA 1989), and others do not (Glass et al. 1972).”
Background
Teachers’ Attitudes About Using Curriculum-Based Measurement in Reading (CBM-R) for Universal Screening and Progress Monitoring
Rowe, S. S., Witmer, S. E., Cook, E. L., & daCruz, K. (2014) · Journal of Applied School Psychology · doi:10.1080/15377903.2014.938793 · Cited by 7
Intertidal habitat utilization patterns of birds in a Northeast Pacific estuary
Frazier, M. R., Lamberson, J. O., & Nelson, W. G. (2014) · Wetlands Ecology and Management · doi:10.1007/s11273-014-9346-6 · Cited by 7
“Simulations have demonstrated that the false positive rate is not strongly affected by non-normal distributions for ANOVA analyses (e.g., Glass et al. 1972; Harwell et al. 1992), however, the P values from this analysis should still be interpreted cautiously.”
Background
Effect of cropping system on composition of the Rhizoctonia populations recovered from canola and lupin in a winter rainfall region of South Africa
Lamprecht, S. C., Tewoldemedhin, Y. T., Hardy, M., et al. (2011) · European Journal of Plant Pathology · doi:10.1007/s10658-011-9809-z · Cited by 7
“In cases where deviations from normality were due to kurtosis and not skewness, data were accepted as reliable and the results were interpreted without transformation (Glass et al. 1972).”
Background
Auditory Learning Using a Portable Real-Time Vocoder: Preliminary Findings
Casserly, E. D., & Pisoni, D. B. (2015) · Journal of Speech Language and Hearing Research · doi:10.1044/2015_jslhr-h-13-0216 · Cited by 7
Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon (Addendum added October 2012)
de Winter, J. F. C., & Dodou, D. (2010) · University of Massachusetts Amherst · doi:10.7275/bj1p-ts64 · Cited by 231

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