International Encyclopedia of Statistical Science

2011 Edition
| Editors: Miodrag Lovric

Multivariate Analysis of Variance (MANOVA)

  • Barbara G. Tabachnick
  • Linda S. Fidell
Reference work entry

ANOVA (analysis of variance) tests whether mean differences among groups on a single DV (dependent variable) are likely to have occurred by chance. MANOVA (multivariate analysis of variance) tests whether mean differences among groups on a combinationof DVs are likely to have occurred by chance. For example, suppose a researcher is interested in the effect of different types of treatment (the IV; say, desensitization, relaxation training, and a waiting-list control) on anxiety. In ANOVA, the researcher chooses one measure of anxiety from among many. With MANOVA, the researcher can assess several types of anxiety (say, test anxiety, anxiety in reaction to minor life stresses, and so-called free-floating anxiety). After random assignment of participants to one of the three treatments and a subsequent period of treatment, participants are measured for test anxiety, stress anxiety, and free-floating anxiety. Scores on all three measures for each participant serve as DVs. MANOVA is used...

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References and Further Reading

  1. Bock RD, Haggard EA (1968) The use of multivariate analysis of variance in behavioral research. McGraw-Hill, New YorkGoogle Scholar
  2. Mardia KV (1971) The effect of nonnormality on some multivariate tests and robustness to nonnormality in the linear model. Biometrika 58(1):105–121zbMATHMathSciNetGoogle Scholar
  3. Maxwell S (2001) When to use MANOVA and significant MANOVAs and insignificant ANOVAs or vice versa. J Consum Psychol 10(1–2):29–30Google Scholar
  4. Olson CL (1976) On choosing a test statistic in multivariate analysis of variance. Psychol Bull 83(4):579–586MathSciNetGoogle Scholar
  5. Seo T, Kanda T, Fujikoshi Y (1995) The effects of nonnormality on tests for dimensionality in canonical correlation and MANOVA models. J Multivariate Anal 52:325–337zbMATHMathSciNetGoogle Scholar
  6. Tabachnick BG, Fidell LS (2007) Using multivariate statistics. Allyn & Bacon, BostonGoogle Scholar
  7. Woodward JA, Overall JE (1975) Multivariate analysis of variance by multiple regression methods. Psychol Bull 82(1):21–32Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Barbara G. Tabachnick
    • 1
  • Linda S. Fidell
    • 1
  1. 1.California State UniversityNorthridgeUSA