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 201–300 of 999

Early Childhood Experiences and Kindergarten Success: A Population-Based Study of a Large Urban Setting
Fantuzzo, J. W., Rouse, H. L., McDermott, P. A., Sekino, Y., Childs, S., & Weiss, A. (2005) · School Psychology Review · doi:10.1080/02796015.2005.12088018 · Cited by 66
“The analysis of covariance provides increased precision by statistically controlling the sources of variation not directly manipulated by the experimenter ( Glass, Peckham, & Saunders, 1972 ).”
Background
Comparisons of the Mann-Whitney, Student’st, and AlternatetTests for Means of Normal Distributions
Gibbons, J. D., & Chakraborti, S. (1991) · The Journal of Experimental Education · doi:10.1080/00220973.1991.10806565 · Cited by 66
Chronic and acute alcohol administration induced neurochemical changes in the brain: comparison of distinct zebrafish populations
Chatterjee, D., Shams, S., & Gerlai, R. T. (2013) · Amino Acids · doi:10.1007/s00726-013-1658-y · Cited by 66
“…ig n ifi ca n t re su lt s known to be fairly insensitive to the violation of the variance homogeneity and normal distribution criteria especially when sample sizes of the analyzed groups are similar, i.e., differ by a ratio less than two to one (Pagano 1990; May et al. 1989; Glass et al. 1972).”
Background
Multivariate Approaches in Ecology: The Assessment of Ecologic Similarity
Green, R. H. (1980) · Annual Review of Ecology and Systematics · doi:10.1146/annurev.es.11.110180.000245 · Cited by 66
Violating the normality assumption may be the lesser of two evilsPreprint
Knief, U., & Forstmeier, W. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/498931 · Cited by 67
Sleep, internalizing problems, and social withdrawal: unique associations in clinic-referred youth with elevated sluggish cognitive tempo symptoms
Rondon, A. T., Hilton, D. C., Jarrett, M. A., & Ollendick, T. H. (2020) · Journal of Attention Disorders · doi:10.1177/1087054718756197 · Cited by 66
Actually in the Cinema: A Field Study Comparing Real 3D and 2D Movie Patrons' Attention, Emotion, and Film Satisfaction
Rooney, B., & Hennessy, E. (2013) · Media Psychology · doi:10.1080/15213269.2013.838905 · Cited by 65
Impact of Hearing Aid Technology on Outcomes in Daily Life I: The Patients’ Perspective
Cox, R. M., Johnson, J. A., & Xu, J. (2016) · Ear and Hearing · doi:10.1097/aud.0000000000000277 · Cited by 67
“Some of the distributions deviated from normality; however, it has been shown that ANOVA is quite robust to violations of normality for groups of moderate size (Donaldson 1968; Glass et al. 1972).”
Parametric tests for Likert scale: For and against
Wadgave, U., & Khairnar, M. (2016) · Asian Journal of Psychiatry · doi:10.1016/j.ajp.2016.08.016 · Cited by 65
Robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials
SULLIVAN, L. M., & D’Agostino, R. B. (2003) · Statistics in Medicine · doi:10.1002/sim.1433 · Cited by 64
An examination of challenging behaviors in autistic disorder versus pervasive developmental disorder not otherwise specified: Significant differences and gender effects
Kozlowski, A. M., & Matson, J. L. (2011) · Research in Autism · doi:10.1016/j.rasd.2011.06.005 · Cited by 63
IQOSTM vs. e-Cigarette vs. Tobacco Cigarette: A Direct Comparison of Short-Term Effects after Overnight-Abstinence
Adriaens, K., Gucht, D. V., & Baeyens, F. (2018) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph15122902 · Cited by 64
“Normality was violated for some individual variables but due to the fact that group sizes were equal (within-subjects design), we decided to still conduct ANOVAs (because of the robustness of the statistic against violations of normality with equal sample sizes) [70].”
Method
Designing efficient order picking systems: The effect of real-life features on the relationship among planning problems
van Gils, T., Caris, A., Ramaekers, K. M., Braekers, K., & de Koster, R. B. M. (2019) · Transportation Research Part E Logistics and Transportation Review · doi:10.1016/j.tre.2019.02.010 · Cited by 64
A FURTHER CONSIDERATION IN THE APPLICATION OF AN ANALYSIS‐OF‐VARIANCE MODEL FOR THE INTRASUBJECT REPLICATION DESIGN
Kratochwill, T. R., Alden, K., Demuth, D., et al. (1974) · Journal of Applied Behavior Analysis · doi:10.1901/jaba.1974.7-629 · Cited by 64
Analysis of repeated measurements in physical therapy research
Atkinson, G. (2001) · Physical Therapy in Sport · doi:10.1054/ptsp.2001.0071 · Cited by 64
Choosing Between Parametric and Nonparametric Tests
Harwell, M. R. (1988) · Journal of Counseling & Development · doi:10.1002/j.1556-6676.1988.tb02007.x · Cited by 63
The Direct and Indirect Effects of Inadmissible Evidence1
Carretta, T. R., & Moreland, R. L. (1983) · Journal of Applied Social Psychology · doi:10.1111/j.1559-1816.1983.tb01741.x · Cited by 63
Does the host match the content? A taxonomical update on online consumption communities
Breitsohl, J., Kunz, W. H., & Dowell, D. J. (2015) · Journal of Marketing Management · doi:10.1080/0267257x.2015.1036102 · Cited by 65
Summarizing Monte Carlo Results in Methodological Research
Harwell, M. R. (1992) · Journal of Educational Statistics · doi:10.3102/10769986017004297 · Cited by 62
Biopriming with Seaweed Extract and Microbial-Based Commercial Biostimulants Influences Seed Germination of Five Abelmoschus esculentus Genotypes
Makhaye, G., Aremu, A. O., Gerrano, A. S., et al. (2021) · Plants · doi:10.3390/plants10071327 · Cited by 61
“[42] also indicated that the consequences on inference after ANOVA are not serious.”
Background
Teachers’ perceptions of factors affecting the educational use of ICT in technology-rich classrooms
Badia, A., Meneses, J., & Sigalés, C. (2013) · Electronic Journal of Research in Educational Psychology · doi:10.14204/ejrep.31.13053 · Cited by 66
Implementation of sustainable public procurement practices and policies: A sorting framework
Prier, E., Schwerin, E., & McCue, C. P. (2016) · Journal of Public Procurement · doi:10.1108/jopp-16-03-2016-b004 · Cited by 61
Automation in airport security X-ray screening of cabin baggage: Examining benefits and possible implementations of automated explosives detection.
Hattenschwiler, N., Sterchi, Y., Mendes, M., & Schwaninger, A. (2018) · Applied Ergonomics · doi:10.1016/j.apergo.2018.05.003 · Cited by 54
Comparison of sterol and fatty acid profiles of chytrids and their hosts reveals trophic upgrading of nutritionally inadequate phytoplankton by fungal parasites
Gerphagnon, M., Agha, R., Martin‐Creuzburg, D., Bec, A., Pérrière, F., Rad‐Menéndez, C., Gachon, C. M. M., & Wolinska, J. (2018) · Environmental Microbiology · doi:10.1111/1462-2920.14489 · Cited by 61
Phylogeny influences the relationships linking key ecological thermal metrics for North American freshwater fish species
Hasnain, S., Shuter, B. J., & Minns, C. K. (2013) · Canadian Journal of Fisheries and Aquatic Sciences · doi:10.1139/cjfas-2012-0217 · Cited by 60
The Agewell trial: a pilot randomised controlled trial of a behaviour change intervention to promote healthy ageing and reduce risk of dementia in later life
Clare, L., Nelis, S. M., Jones, I. R., Hindle, J. V., Thom, J. M., Nixon, J., Cooney, J., Jones, C. L., Edwards, R. T., & Whitaker, C. J. (2015) · BMC Psychiatry · doi:10.1186/s12888-015-0402-4 · Cited by 65
“ANCOVA analyses are generally robust to moderate violations of this assumption as long as the sample sizes in each group is approximately equal [56], as was the case for GSES and total cholesterol.”
Method
A comparison of the efficacy of an appearance-focused skin cancer intervention within indoor tanner subgroups identified by latent profile analysis
Stapleton, J. L., Turrisi, R., Hillhouse, J., Robinson, J. K., & Abar, B. W. (2010) · Journal of Behavioral Medicine · doi:10.1007/s10865-009-9246-z · Cited by 60
“…chose to use multiple comparisons over alternative approaches (e.g., ANOVA) because the subgroups found in an LPA often have unequal numbers of individuals and disproportionate variances between subgroups which can lead to unpredictable changes in type 1 error rates with ANOVA (Glass et al. 1972).”
MethodInfluential
The Unit of Analysis in Field Research: Issues and Approaches to Design and Data Analysis
Silverman, S., & Solmon, M. A. (1998) · Journal of Teaching in Physical Education · doi:10.1123/jtpe.17.3.270 · Cited by 60
Analysis of categorical moderators in mixed‐effects meta‐analysis: Consequences of using pooled versus separate estimates of the residual between‐studies variances
Rubio‐Aparicio, M., Sánchez‐Meca, J., López‐López, J. A., Botella, J., & Marín‐Martínez, F. (2017) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12092 · Cited by 56
“Note that the performance of the QB(P) test was similar to that expected for the F test in a typical ANOVA with unbalanced sample sizes, when the homoscedasticity assumption was not met (Glass et al., 1972; Hinkle et al., 2003).”
Result
Effect of non‐normality on test statistics for one‐way independent groups designs
Cribbie, R. A., Fıksenbaum, L., Keselman, H. J., & Wilcox, R. R. (2011) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.2011.02014.x · Cited by 59
Recognising the “forgotten man”: Fathers’ experiences in caring for a young child with autism spectrum disorder
Paynter, J. M., Davies, M., & Beamish, W. (2017) · Journal of Intellectual & Developmental Disability · doi:10.3109/13668250.2017.1293235 · Cited by 70
Understanding the Practical Advantages of Modern ANOVA Methods
Wilcox, R. R. (2002) · Journal of Clinical Child & Adolescent Psychology · doi:10.1207/s15374424jccp3103_12 · Cited by 59
“Glass, Peckham, and Sanders (1972) appear to be the first to realize that there are practical problems, and many articles have since confirmed that unequal variances can result in poor control over the probability of a Type I error.”
Background
Neuronal activity is not required for the initial formation and maturation of visual selectivity
Hagihara, K. M., Murakami, T., Yoshida, T., Tagawa, Y., & Ohki, K. (2015) · Nature Neuroscience · doi:10.1038/nn.4155 · Cited by 58
The quality of experimental designs in mobile learning research: A systemic review and self-improvement tool
Sung, Y., Lee, H.-Y., Yang, J.-M., & Chang, K.-E. (2019) · Educational Research Review · doi:10.1016/j.edurev.2019.05.001 · Cited by 64
The analysis of repeated measurements: A quantitative research synthesis
Keselman, J. C., Lix, L. M., & Keselman, H. J. (1996) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1996.tb01089.x · Cited by 58
Emotional Processing and Brain Activity in Youth at High Risk for Alcoholism
Cservenka, A., Fair, D. A., & Nagel, B. J. (2014) · Alcoholism Clinical and Experimental Research · doi:10.1111/acer.12435 · Cited by 67
“Since analysis of variance (ANOVA) is considered to be robust to violations of normality (Glass et al., 1972), a 2x7 mixed model 44 ANOVA was used to examine emotion recognition accuracy and reaction time on the ERT, in which family history status was the between-subjects factor, and emotional…”
Method
Public Cellphone Use Does Not Activate Negative Responses in Others…Unless They Hate Cellphones
Gonzales, A. L., & Wu, Y. (2016) · Journal of Computer-Mediated Communication · doi:10.1111/jcc4.12174 · Cited by 56
Flow and turbulence structure across the ripple–dune transition: an experiment under mobile bed conditions
Schindler, R. J., & Robert, A. (2005) · Sedimentology · doi:10.1111/j.1365-3091.2005.00706.x · Cited by 57
“…information was only used in subsequent post hoc analysis because: (i) anova is robust, operating well even with considerable heterogeneity of variances, assuming sample sizes are approximately equal (Glass et al., 1972); and (ii) no suitable non-parametric alternative exists (Zar, 1984, p. 231).”
Method
Ethical Context and Ethical Decision Making: Examination of an Alternative Statistical Approach for Identifying Variable Relationships
Valentine, S. R., Nam, S., Hollingworth, D., & Hall, C. (2013) · Journal of Business Ethics · doi:10.1007/s10551-013-1879-8 · Cited by 56
Perfunctory analysis of variance in agronomy, and its consequences in experimental results interpretation
Acutis, M., Scaglia, B., & Confalonieri, R. (2012) · European Journal of Agronomy · doi:10.1016/j.eja.2012.06.006 · Cited by 56
Impact of Hearing Aid Technology on Outcomes in Daily Life II: Speech Understanding and Listening Effort
Johnson, J. A., Xu, J., & Cox, R. M. (2016) · Ear and Hearing · doi:10.1097/aud.0000000000000327 · Cited by 58
“Furthermore, because ANOVA is robust against deviations from normality (e.g., Donaldson 1968; Glass et al. 1972), we felt that any transformation would have been minor in effect at best.”
Background
Sampling Errors of Variance Components in Small Sample Multifacet Generalizability Studies
Smith, P. L. (1978) · Journal of Educational Statistics · doi:10.3102/10769986003004319 · Cited by 56
The confounding influence of homogenising invasive species in a globally endangered and largely urban biome: Does habitat quality dominate avian biodiversity?
Dures, S. G., & Cumming, G. S. (2010) · Biological Conservation · doi:10.1016/j.biocon.2009.12.019 · Cited by 55
“In addition to the spatial aspects of fragmentation, the temporal aspect of relaxation must be considered (Gonzalez, 2000).”
Background
Data analysis techniques in service quality literature: Essentials and advances
Mohammed, K., & Adil, M. (2013) · Serbian Journal of Management · doi:10.5937/sjm8-3469 · Cited by 58
“The assumption of homogeneity of variances is essential when comparing two groups, because if variances are unequal, the validity of the results can get jeopardized i.e. increases Type I error leading to invalid inferences (Glass et al., 1972; Nordstokke et al., 2011).”
Background
The Efficacy of two Improvement-Over-Chance Effect Sizes for Two-Group Univariate Comparisons under Variance Heterogeneity and Nonnormality
Hess, B. J., Olejnik, S., & Huberty, C. J. (2001) · Educational and Psychological Measurement · doi:10.1177/00131640121971572 · Cited by 46
Career Patterns of Supply Chain Executives: An Optimal Matching Analysis
Flöthmann, C., & Hoberg, K. (2017) · Journal of Business Logistics · doi:10.1111/jbl.12150 · Cited by 55
Chemosensory sensitivity reflects reproductive status in the ant Harpegnathos saltator
Ghaninia, M., Haight, K. L., Berger, S. L., et al. (2017) · Scientific Reports · doi:10.1038/s41598-017-03964-7 · Cited by 55
Anxiety and depression among college students with attention-deficit/hyperactivity disorder (ADHD): Cross-informant, sex, and subtype differences
Nelson, J. M., & Liebel, S. W. (2017) · Journal of American College Health · doi:10.1080/07448481.2017.1382499 · Cited by 68
Early majority engagement pathway best defines transitions from youth to adult elite men's soccer in the UK: A three time-point retrospective and prospective study
Hendry, D. T., & Hodges, N. J. (2018) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2018.01.009 · Cited by 56
Data transformations, power, and skew: A rebuttal to Levine and Dunlap.
Games, P. A. (1984) · Psychological Bulletin · doi:10.1037/0033-2909.95.2.345 · Cited by 55
Sublethal effects of zinc and municipal effluents on larvae of the red abalone Haliotis rufescens
Hunt, J. W., & Anderson, B. S. (1989) · Marine Biology · doi:10.1007/bf00541657 · Cited by 55
The Impact of Context and Word Type on Students' Maze Task Accuracy
January, S. A., & Ardoin, S. P. (2012) · School Psychology Review · doi:10.1080/02796015.2012.12087508 · Cited by 54
Collisions and traffic violations of alcohol, cannabis and cocaine abuse clients before and after treatment
Macdonald, S., Mann, R. E., Chipman, M. L., et al. (2003) · Accident Analysis & Prevention · doi:10.1016/j.aap.2003.07.004 · Cited by 54
Effects of internal phosphorus loading on nutrient limitation in a eutrophic reservoir
Nikolai, S. J., & Dzialowski, A. R. (2014) · Limnologica · doi:10.1016/j.limno.2014.08.005 · Cited by 57
The Effects of Immersion and Real-World Distractions on Virtual Social Interactions
Oh, C. S., Herrera, F., & Bailenson, J. N. (2019) · Cyberpsychology Behavior and Social Networking · doi:10.1089/cyber.2018.0404 · Cited by 57
“Although there is an on-going debate regarding the robustness of analysis of variance in cases of normality assumption violations and Likert-type scales, 37–39 we report the results of the nonparametric aligned rank transform analyses of variance, as it is the more conservative method.”
A Guide to Nature Immersion: Psychological and Physiological Benefits
Lim, P. Y., Dillon, D., & Chew, P. K. H. (2020) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph17165989 · Cited by 66
“However, research has suggested that ANOVA is robust against violations of normality, and thus the analysis proceeded despite the violation [83,84].”
RepliCueAuth: Validating the Use of a Lab-Based Virtual Reality Setup for Evaluating Authentication Systems
Mathis, F., Vaniea, K. E., & Khamis, M. (2021) · CHI Conference on Human Factors in Computing Systems · doi:10.1145/3411764.3445478 · Cited by 53
“We applied ANOVAs to parametric and normal/near-normal distributed data as ANOVAs are robust to deviations from normality [32].”
Method
An Empirical Investigation of the Effects of Heterogeneous Regression Slopes in Analysis of Covariance
Hamilton, B. L. (1977) · Educational and Psychological Measurement · doi:10.1177/001316447703700313 · Cited by 54
“The generation of the slopes within each treatment group was accomplished by means of a procedure used by Knapp and Swoyer (1967), involving the following theorem: &dquo;Let X and W be two independent random normal variables with zero mean and unit variance.”
Body Site Variation of Cool Perception Thresholds, with Observations on Paradoxical Heat
Greenspan, J. D., Taylor, D. J., & McGillis, S. L. B. (1993) · Somatosensory & Motor Research · doi:10.3109/08990229309028851 · Cited by 54
Long‐range temporal correlations in the subthalamic nucleus of patients with Parkinson’s disease
Hohlefeld, F. U., Huebl, J., Huchzermeyer, C., Schneider, G., Schönecker, T., Kühn, A. A., Curio, G., & Nikulin, V. V. (2012) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2012.08198.x · Cited by 54
“These prerequisites justified parametric testing in the case of the scaling exponents, together with the observed robustness of the F-test to slight deviations from basic assumptions (e.g. normal distribution; Glass et al., 1972; Lindman, 1974).”
Coach ratings of skills and their relations to practice, play and successful transitions from youth-elite to adult-professional status in soccer
Hendry, D. T., WILLIAMS, A. M., & Hodges, N. J. (2018) · Journal of Sports Sciences · doi:10.1080/02640414.2018.1432236 · Cited by 53
Comparing oral health in patients with different levels of dental anxiety
Zinke, A., Hannig, C., & Berth, H. (2018) · Head & Face Medicine · doi:10.1186/s13005-018-0182-4 · Cited by 53
Impact of concurrent task performance on transcranial direct current stimulation (tDCS)-Induced changes in cortical physiology and working memory
Hill, A. T., Rogasch, N. C., Fitzgerald, P. B., & Hoy, K. E. (2018) · Cortex · doi:10.1016/j.cortex.2018.11.022 · Cited by 51
Investigating Smartphone-based Pan and Zoom in 3D Data Spaces in Augmented Reality
Büschel, W., Mitschick, A., Meyer, T. A., et al. (2019) · International Conference on Human-Computer Interaction with Mobile Devices and Services (MobileHCI) · doi:10.1145/3338286.3340113 · Cited by 53
“, [23]) and because ANOVAs on log-transformed data showed the same general trends.”
Background
Measurement and statistics: An examination of construct validity.
Maxwell, S. E., & Delaney, H. D. (1985) · Psychological Bulletin · doi:10.1037/0033-2909.97.1.85 · Cited by 53
The Role of Relational and Instructional Classroom Supports in the Language Development of At-Risk Preschoolers
Gosse, C. S., McGinty, A. S., Mashburn, A. J., Hoffman, L. M., & Pianta, R. C. (2013) · Early Education and Development · doi:10.1080/10409289.2013.778567 · Cited by 59
“However, linear regression is robust to assumptions of normality (Glass et al., 1972; Ito, 1980).”
Background
The Role of Trust in Proactive Conversational Assistants
Kraus, M., Wagner, N., Callejas, Z., & Minker, W. (2021) · IEEE Access · doi:10.1109/access.2021.3103893 · Cited by 56
“However, the F-statistic of an ANOVA can be robust to violations of assumptions, as long as the group sizes are equal [74].”
Method
Leisure attitudes: A comparison between Chinese in Canada and Anglo‐Canadians
Deng, J., Walker, G. J., & Swinnerton, G. S. (2005) · Leisure/Loisir · doi:10.1080/14927713.2005.9651331 · Cited by 52
Service-Learning as a Catalyst for Community Development
Geller, J. D., Zuckerman, N., & Seidel, A. (2014) · Education and Urban Society · doi:10.1177/0013124513514773 · Cited by 52
Dental microwear texture analysis of Homo sapiens sapiens: Foragers, farmers, and pastoralists
Schmidt, C. W., Remy, A., Sessen, R. V., Willman, J. C., Krueger, K. L., Scott, R. M., Mahoney, P., Beach, J. J., McKinley, J. I., D’Anastasio, R., et al. (2019) · American Journal of Physical Anthropology · doi:10.1002/ajpa.23815 · Cited by 52
Parametric Alternatives to the Student T Test under Violation of Normality and Homogeneity of Variance
Zimmerman, D. W., & Zumbo, B. D. (1992) · Perceptual and Motor Skills · doi:10.2466/pms.1992.74.3.835 · Cited by 51
The Problem of Multiple Inference in Psychiatric Research
Hall, W., & Bird, K. D. (1985) · Australian & New Zealand Journal of Psychiatry · doi:10.3109/00048678509158831 · Cited by 52
Concerning Trends in Likert Scale Usage in Human-robot Interaction: Towards Improving Best Practices
Schrum, M., Ghuy, M., Hedlund-Botti, E., Natarajan, M., Johnson, M., & Gombolay, M. (2022) · ACM Transactions on Human-Robot Interaction · doi:10.1145/3572784 · Cited by 51
ISSUES IN BIOMEDICAL STATISTICS: STATISTICAL INFERENCE
Ludbrook, J., & Dudley, H. A. F. (1994) · Australian and New Zealand Journal of Surgery · doi:10.1111/j.1445-2197.1994.tb02308.x · Cited by 51
Intraspecific differences in thermal tolerance of the diamondback watersnake (Nerodia rhombifer): effects of ontogeny, latitude, and sex
Winne, C. T., & Keck, M. B. (2004) · Comparative Biochemistry and Physiology Part A Molecular & Integrative Physiology · doi:10.1016/j.cbpb.2004.11.009 · Cited by 51
Effect of Exposure to Good vs Poor Medical Trainee Performance on Attending Physician Ratings of Subsequent Performances
Yeates, P., O'Neill, P. A., Mann, K. V., & Eva, K. W. (2012) · JAMA · doi:10.1001/jama.2012.36515 · Cited by 51
The role of process information in narrations while learning with animations and static pictures
Stebner, F., Kühl, T., Höffler, T. N., Wirth, J., & Ayres, P. (2016) · Computers & Education · doi:10.1016/j.compedu.2016.11.001 · Cited by 51
“However, ANOVAs are considered as fairly robust against violations of normality (Glass et al., 1972).”
Background
Exergaming in VR: The Impact of Immersive Embodiment on Motivation, Performance, and Perceived Exertion
Born, F., Abramowski, S., & Masuch, M. (2019) · International Conference on Virtual Worlds and Games for Serious Applications (VS-Games) · doi:10.1109/vs-games.2019.8864579 · Cited by 55
Processing Social Information in Messages
Slater, M. D. (1990) · Communication Research · doi:10.1177/009365090017003003 · Cited by 51
Power-Cost Efficiency of Eight Macrobenthic Sampling Schemes in Puget Sound, Washington, USA
Ferraro, S. P., Cole, F. A., Deben, W. A., et al. (1989) · Canadian Journal of Fisheries and Aquatic Sciences · doi:10.1139/f89-267 · Cited by 51
Statistical treatment of endogonaceous spore counts
John, T. V. S., & Koske, R. E. (1988) · Transactions of the British Mycological Society · doi:10.1016/s0007-1536(88)80012-3 · Cited by 51
Power shift and connectivity changes in healthy aging during resting-state EEG
Perinelli, A., Assecondi, S., Tagliabue, C. F., & Mazza, V. (2022) · NeuroImage · doi:10.1016/j.neuroimage.2022.119247 · Cited by 54
Variance Stabilizing Transformations and the Power of the F Test
Budescu, D. V., & Appelbaum, M. I. (1981) · Journal of Educational Statistics · doi:10.3102/10769986006001055 · Cited by 50
An experimental manipulation of metacognition: A test of the metacognitive model of obsessive-compulsive symptoms
Myers, S. G., & Adrian Wells, A. (2013) · Behaviour Research and Therapy · doi:10.1016/j.brat.2013.01.007 · Cited by 50
Imazalil residue loading and green mould control in citrus packhouses
Erasmus, A., Lennox, C. L., Jordaan, H., Smilanick, J. L., Lesar, K., & Fourie, P. H. (2011) · Postharvest Biology and Technology · doi:10.1016/j.postharvbio.2011.05.006 · Cited by 50
“In cases where non-normalitywas due to high kurtosis, analysiswas conducted on percentages (Glass et al., 1972).”
Method
Light Stress Responses by the Eelgrass, Zostera marina (L)
Bertelli, C. M., & Unsworth, R. K. F. (2018) · Frontiers in Environmental Science · doi:10.3389/fenvs.2018.00039 · Cited by 50
“ANOVA was still performed due to the robust nature of the test and the relative insensitivity of the F test to departures from normality (Glass et al., 1972; Lix et al., 1996; McDonald, 2014).”
Method
Hyaluronic acid as a macromolecular crowding agent for production of cell-derived matrices
Shendi, D., Marzi, J., Linthicum, W., Rickards, A. J., Dolivo, D., Keller, S., Kauss, M. A., Wen, Q., McDevitt, T. C., Dominko, T., et al. (2019) · Acta Biomaterialia · doi:10.1016/j.actbio.2019.09.042 · Cited by 50
Salivary cortisol, stress and mood in healthy older adults: The Zenith study
Simpson, E. E. A., McConville, C. F., Rae, G., O’Connor, J. M., Stewart-Knox, B. J., Coudray, C., & Strain, J. (2008) · Biological Psychology · doi:10.1016/j.biopsycho.2007.12.001 · Cited by 50
Inbreeding depression in fecundity and inbred line extinction in the bulb mite, Rhizoglyphus robini
Radwan, J. (2003) · Heredity · doi:10.1038/sj.hdy.6800254 · Cited by 50
“This was analysed using standard ANOVA, as it is robust against moderate departures from heteroscedasticity (Glass et al, 1972), and Bartlett’s test did not detect significant heterogeneity of variances in the data (P¼ 0.84).”
Influential
Practice mode and learner control in computer-based instruction
Pollock, J., & Sullivan, H. J. (1990) · Contemporary Educational Psychology · doi:10.1016/0361-476x(90)90022-s · Cited by 50
TARP γ-2 and γ-8 Differentially Control AMPAR Density Across Schaffer Collateral/Commissural Synapses in the Hippocampal CA1 Area
Yamasaki, M., Fukaya, M., Yamazaki, M., Azechi, H., Natsume, R., Abe, M., Sakimura, K., & Watanabe, M. (2016) · The Journal of Neuroscience · doi:10.1523/jneurosci.4178-15.2016 · Cited by 43
“For further assessment of the relationship among synapse type, PSD size, and AMPAR, labeling density was performed with a twoway ANOVA, which is generally robust to moderate deviations from normality (Glass et al., 1972).”
Method
The formation of group norms in computer-mediated communication
Postmes, T., Spears, R., & Lea, M. (2000) · Human Communication Research · doi:10.1093/hcr/26.3.341 · Cited by 557
On the Use of Likert-Type Scales in Multilevel Data
Beal, D. J., & Dawson, J. (2007) · Organizational Research Methods · doi:10.1177/1094428106295492 · Cited by 49
Enhanced Locomotion Efficiency of a Bio-inspired Walking Robot using Contact Surfaces with Frictional Anisotropy
Manoonpong, P., Petersen, D. S., Kovalev, A. E., Wörgötter, F., Gorb, S. N., Spinner, M., & Heepe, L. (2016) · Scientific Reports · doi:10.1038/srep39455 · Cited by 49
Cortisol concentration in scales is a valid indicator for the assessment of chronic stress in European sea bass, Dicentrarchus labrax L
Σαμαράς, Α., Dimitroglou, A., Kollias, S., Skouradakis, G., Papadakis, I. E., & Pavlidis, M. A. (2021) · Aquaculture · doi:10.1016/j.aquaculture.2021.737257 · Cited by 49
Characterization of Rhizoctonia spp. Recovered from Crop Plants Used in Rotational Cropping Systems in the Western Cape Province of South Africa
Tewoldemedhin, Y. T., Lamprecht, S. C., McLeod, A., et al. (2006) · Plant Disease · doi:10.1094/pd-90-1399 · Cited by 49
A Reaction to "Consequences of Failure to Meet Assumptions Underlying the Fixed Effects Analysis of Variance and Covariance"
Blair, R. C. (1981) · Review of Educational Research · doi:10.2307/1170363 · Cited by 49
Relationships of mercury concentrations across tissue types, muscle regions and fins for two shark species
O’Bryhim, J. R., Adams, D. H., Spaet, J. L. Y., et al. (2017) · Environmental Pollution · doi:10.1016/j.envpol.2017.01.029 · Cited by 48
“However, ANOVA is fairly robust to violations of a single assumption, especially if sample sizes are relatively large (Glass et al., 1972).”
Background
The Effect of Visual, Spatial and Temporal Manipulations on Embodiment and Action
Ratcliffe, N., & Newport, R. (2017) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2017.00227 · Cited by 49
“Furthermore, a number of stimulation studies have concluded that ANOVA is ‘‘robust’’ to deviations from normality, particularly when sample size and variance is equal across groups (Glass et al., 1972; Harwell, 1992; Norman, 2010; Schmider et al., 2010).”
Background
Effects of age of retirement, reason for retirement, and pre-retirement training on psychological and physical health during retirement
Sharpley, C. F., & Layton, R. (1998) · Australian Psychologist · doi:10.1080/00050069808257392 · Cited by 48

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