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

Glass, Gene V.; Peckham, Percy D.; Sanders, James R.

doi:10.3102/00346543042003237

Cited by 1,417 publications

(829 citation statements)

References 63 publications

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“…Importantly, statisticians have highlighted that it is less important whether ANOVA assumptions are exactly met, but more important to consider what the consequences of such violations might be (Glass et al, 1972). It is widely agreed that ANOVA is robust with respect to violations of the assumptions of normality and homoscedasticity, affecting type I and II errors only minimally (Glass et al, 1972; combined analysis of treatment and time effects, which is relevant in the present study). Moreover, transformations are also associated with problems and may confound data interpretation (Games, 1984;Osborne, 2002).…”

Section: Resultsmentioning

confidence: 92%

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Temporary inhibition of dorsal or ventral hippocampus by muscimol: Distinct effects on measures of innate anxiety on the elevated plus maze, but similar disruption of contextual fear conditioning

Zhang

Bast

et al. 2014

Behavioural Brain Research

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Section: Resultsmentioning

confidence: 92%

“…ANOVA is based on the assumptions of normality and homoscedasticity (equal variance); as has been pointed out by statisticians, most real data only meet these assumptions to some degree (Glass et al, 1972;Judd et al, 1995). Data transformations may help to improve compliance with these assumptions (Judd et al, 1995;Osborne, 2002).…”

Section: Resultsmentioning

confidence: 99%

Temporary inhibition of dorsal or ventral hippocampus by muscimol: Distinct effects on measures of innate anxiety on the elevated plus maze, but similar disruption of contextual fear conditioning

Zhang

Bast

et al. 2014

Behavioural Brain Research

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show abstract

“…However, more recent ROBUST ESTIMATION 10 investigations revealed that differences in skewness, non-normality and heteroscedasticity interact in complicated ways that impact power (Wilcox, 2017). For example, it was believed that as kurtosis increases, the Type I error rate decreases and quickly drops below its nominal .05 level, and consequently power decreases (Glass, et al, 1972). We now know that this conclusion is correct only if distributions have the same amount of skewness, because in this situation the difference between variables will have a symmetric distribution.…”

Section: Misconceptions About Robustnessmentioning

confidence: 93%

“…In experimental research, in which the predictors in the linear model represent groups of people in different treatment conditions, the 'overall fit of the model' becomes a test of whether group means differ. Early work suggested that F controls the Type I error rate under conditions of skew when group sizes are equal (Donaldson, 1968;Glass, Peckham, & Sanders, 1972). However, more recent investigations revealed that differences in skewness, non-normality and heteroscedasticity interact in complicated ways that impact power (Wilcox, 2017).…”

Section: Misconceptions About Robustnessmentioning

confidence: 99%

Robust statistical methods: A primer for clinical psychology and experimental psychopathology researchers

Field

Wilcox

2017

Behaviour Research and Therapy

348

227

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This paper reviews and offers tutorials on robust statistical methods relevant to clinical and experimental psychopathology researchers. We review the assumptions of one of the most commonly applied models in this journal (the general linear model, GLM) and the effects of violating them. We then present evidence that psychological data are more likely than not to violate these assumptions. Next, we overview some methods for correcting for violations of model assumptions. The final part of the paper presents 8 tutorials of robust statistical methods using R that cover a range of variants of the GLM (t-tests, ANOVA, multiple regression, multilevel models, latent growth models). We conclude with recommendations that set the expectations for what methods researchers submitting to the journal should apply and what they should report. Keywords Robust statistical methods, assumptions, bias ROBUST ESTIMATION 3 Robust statistical methods: a primer for clinical psychology and experimental psychopathology researchers OverviewThe general linear model (GLM), which is routinely used in clinical and experimental psychopathology research, was once thought to be robust to violations of its assumptions. However, based on hundreds of journal articles published during the last fifty years, it is well established that this view is incorrect. Moreover, modern methods for dealing with the violations of these assumptions can result in substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. We begin with an overview of the key assumptions underlying the GLM. We then review various misconceptions about how robust the GLM is to violations of those assumptions and look at the effects that violations can have. We end the first section by looking at the evidence that psychological data, in general, are likely to violate the assumptions of the GLM.In part 2 of the paper we overview a selection of ways to deal with violations of assumptions that fall under the headings of data transformation, adjustments to standard errors, and robust estimation. In the final part, we present 8 tutorials that use datasets relevant to this journal to show how to implement a selection of techniques (robust estimators for model parameters and standard errors) for designs common to this journal (comparing dependent and independent means, predicting continuous outcomes from continuous predictors and longitudinal designs). ROBUST ESTIMATION 4The assumptions of the general linear model Critical assumptionsPsychology researchers (generally) and those with interests in psychopathology (specifically) typically apply variants of the general linear model to their data. In this model, an outcome variable (Y) is predicted from a linear and additive combination of one or more predictor variables (X). For each predictor there is a parameter that is estimated from the data (!) that represents the relationship between the predictor and outcome variable if the effects of other predictors in the model are held constant. There ...

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“…Several authors from the fields of psychology and sociology assumed that these variables often originate scores that are treated as latent variables (interval type) (2,6) , which is justified conceptually and empirically by simulation studies (14)(15) .…”

Section: Variables and Measuresmentioning

confidence: 99%

Analysis of variables that are not directly observable: influence on decision-making during the research process

Curado

Teles²,

Marôco

2014

Rev. esc. enferm. USP

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A dimensão da amostra, o tipo de variá-veis, o seu formato de medida, a construção dos instrumentos de recolha de dados válidos e fiáveis, são aspectos a ter em consideração no processo de investigação. No âmbito das ciências sociais, da saúde e especificamente na área de enfermagem, os instrumentos de recolha de dados são muitas vezes compostos por variáveis componentes ou indicadores que dão origem a variáveis latentes ou não observáveis diretamente, daí a importância da decisão relativa à forma como são medidas (escala ordinal, Likert ou de tipo Likert). As escalas psicométricas são exemplos de instrumentos, pelo tipo de variáveis que as integram, que podem trazer problemas de medida e de análise estatística (testes paramétricos versus não paramétricos). Assim o investigador quando usa estas variáveis deve respeitar alguns pressupostos baseados em estudos de simulação ou em recomendações fundamentadas na evidência científica, de forma a tomar a melhor decisão.

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

Cited by 1,417 publications

References 63 publications

Temporary inhibition of dorsal or ventral hippocampus by muscimol: Distinct effects on measures of innate anxiety on the elevated plus maze, but similar disruption of contextual fear conditioning

Temporary inhibition of dorsal or ventral hippocampus by muscimol: Distinct effects on measures of innate anxiety on the elevated plus maze, but similar disruption of contextual fear conditioning

Robust statistical methods: A primer for clinical psychology and experimental psychopathology researchers

Analysis of variables that are not directly observable: influence on decision-making during the research process

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