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Analysis of Variance

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  • First Online:
Encyclopedia of Clinical Neuropsychology

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Synonyms

ANOVA, F-test

Definition

Analysis of variance (ANOVA) is a statistical test that identifies whether two or more group means are statistically different. ANOVA evaluates the null hypothesis that the means of each group are equal, and, by implication, that each group represents the same population. The alternative hypothesis is that at least one pair of group means is different, suggesting that these groups reflect different populations and that the independent variable (IV) has a significant effect on the dependent variable (DV). ANOVA uses a statistic referred to as F, which is defined as the ratio between the between-group (explained) variance and the within-group (unexplained) variance. A one-way ANOVA analyzes the difference between the means of multiple levels of one independent variable. A factorial ANOVA incorporates multiple independent variables (factors). For example, in a two-way ANOVA, the main effect of both IVs is examined. The interaction effect is also...

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Further Reading

  • Gueorguieva, R., & Krystal, J. H. (2004). Move over ANOVA: Progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry, 61, 310–317. https://doi.org/10.1001/archpsyc.61.3.310.

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  • Iverson, G. R., & Norpoth, H. (1987). Analysis of variance. Newbury Park: Sage.

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  • Watson, P. (2009). Review of analysis of variance and covariance: How to choose and construct models for the life sciences. Psychological Medicine, 39, 695–696.

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Author information

Authors and Affiliations

  1. Allegheny General Hospital, Pittsburgh, PA, USA

    Matthew J. L. Page

  2. Psychology, Allegheny Health Network, Pittsburgh, PA, USA

    Matthew J. L. Page

Authors
  1. Matthew J. L. Page
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Corresponding author

Correspondence to Matthew J. L. Page .

Editor information

Editors and Affiliations

  1. Department of Physical Medicine and Rehabilitation, Virginia Commonwealth University, Richmond, VA, USA

    Jeffrey S. Kreutzer

  2. Kessler Foundation, Pleasant Valley Way, West Orange, NJ, USA

    John DeLuca

  3. Independent Practice, Wynnewood, PA, USA

    Bruce Caplan

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Page, M.J.L. (2018). Analysis of Variance. In: Kreutzer, J.S., DeLuca, J., Caplan, B. (eds) Encyclopedia of Clinical Neuropsychology. Springer, Cham. https://doi.org/10.1007/978-3-319-57111-9_1172

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