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  Encyclopedia of Keywords > Anova > Manova   Michael Charnine

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  1. MANOVA is a special case of CANONICAL ANALYSIS.
  2. MANOVA is a "gateway".
  3. MANOVA is an extension of analysis of variance (ANOVA) that covers cases where there is more than one dependent variable.
  4. MANOVA is a technique which determines the effects of independent categorical variables on multiple continuous dependent variables.
  5. MANOVA is a special case of CANONICAL ANALYSIS.


  1. Wilks's lambda: Wilks's lambda is used in conjunction with Bartlett's V, much as in MANOVA, to test the significance of the first canonical correlation.
  2. Two way MANOVA considers t wo different treatments simultaneously.
  3. Canonical correlation is a generalization of MANOVA, MANCOVA, and multivariate multiple regression.
  4. Multivariate Analysis of Variance (MANOVA) is an extension of the concepts and techniques of ANOVA to situations with multiple dependent variables.
  5. The method is closely related to multivariate analysis of variance (MANOVA), multiple discriminant analysis, and canonical correlation analysis.

Sample Sizes

  1. SPSS offers and adjustment for unequal sample sizes in MANOVA.
  2. Two special cases arise in MANOVA, the inclusion of within-subjects independent variables and unequal sample sizes in cells.
  3. SPSS also outputs Levene's test as part of Manova.
  4. Where ANOVA tests for differences among group means, MANOVA tests for differences among the multivariate centroids of groups.
  5. It is a special case of MANOVA used with two groups or levels of a treatment variable (Hair et al., 1995).

Dependent Variables

  1. However, the earlier method, of following a significant MANOVA with a series of ANOVAs on each of the dependent variables, is still used.
  2. MANOVA uses one or more categorical independents as predictors, like ANOVA, but unlike ANOVA, there is more than one dependent variable.


  1. Click here for syntax for other MANOVA commands for various designs.
  2. Explain the syntax for MANOVA in SPSS. Note: This has largely been replaced by GLM syntax.
  3. Pairwise comparisons (post-hoc): If the MANOVA shows significant overall difference between groups, the analysis can proceed by pairwise comparisons.
  4. Line 1: The MANOVA command word is followed by the three variables opinion1, opinion2, and opinion3.


  1. Box's M test tests the multivariate homogeneity of variances and covariances, as required by MANOVA and some other procedures.
  2. Canonical correlation is a generalization of MANOVA, MANCOVA, and multivariate multiple regression.
  3. A Multivariate analysis of variance MANOVA, is a measure that examines whether group differences occur on more than one dependent variable.
  4. Multivariate analysis of variance ( MANOVA) is used when there is more than one dependent variable.


  1. Box's M: Box's M tests MANOVA's assumption of homoscedasticity using the F distribution.
  2. MANOVA is robust in the face of most violations of this assumption if sample size is not small (ex., <20).
  3. When there is a violation of this assumption, the researcher must use MANOVA rather than multiple univariate ANOVA tests.
  4. MANOVA or Multiple ANOVA - A parametric statistical test that requires that the normality assumption s are met.
  5. One-way MANOVA (Multivariate ANalysis Of VAriance) is the multivariate version of the univariate ANOVA, testing whether several samples have the same mean.

Repeated Measures

  1. The WSFACTORS subcommand follows the MANOVA command when there is a within-subjects factor, which is to say when there is a repeated measures design.
  2. MANOVA does not have the compound symmetry requirement that the one-factor repeated measures ANOVA model requires.
  3. Sphericity is an assumption of repeated measures MANOVA, for instance.


  1. Factorial manova is the extension to designs with more than one independent variable.
  2. That's would be a one-way ANOVA or MANOVA.
  3. The design matrices from MANOVA will have numbers other than 0 and 1, including negative numbers, and sometimes very complicated decimal values.
  4. MANOVA and MANCOVA assume that for each group (each cell in the factor design matrix) the covariance matrix is similar.
  5. As in ANOVA, when cells in a factorial MANOVA have different sample sizes, the sum of squares for effect plus error does not equal the total sum of squares.


  1. The GCR (Greatest Characteristic Root) test on the MANOVA form can be used with the largest eigenvalue determined here, for example.
  2. The Fisher iris data iris.m and iris.g may be used to test the 1-Way MANOVA. Read the former into the u array, the latter into the Y vector.
  3. Box’s M test: In MANOVA, box’ M test is used to know the equality of covariance between the groups.
  4. A MANOVA procedure allows us to test our hypothesis for all three dependent variables at once.
  5. F-test. The omnibus or overall F test is the first of the two-step MANOVA process of analysis.

Interaction Effects

  1. Multiple analysis of variance (MANOVA) is used to see the main and interaction effects of categorical variables on multiple dependent interval variables.
  2. MANOVA won't give you the interaction effects between the main effect and the repeated factor.
  3. MANOVA, general linear model, principal components, exploratory factor analysis.
  4. Similar to the MANOVA results, interaction effects are not detected as significant for any of the responses, at any of the times considered.


  1. In MANOVA, there will be one set of MDA output for each main and interaction effect.
  2. Step-down MANOVA is recommended only when there is an à priori theoretical basis for ordering the dependent (criterion) variables.
  3. Pillai-Bartlett trace, V. Multiple discriminant analysis (MDA) is the part of MANOVA where canonical roots are calculated.


  1. In MANOVA, this is done on multiple bases, using the raw weights, standardized weights, and structure correlations.
  2. Advantages MANOVA means multiple ANOVA - multiple dependent variables to be analyzed simultaneously.
  3. Multivariate Analysis of Variance (MANOVA) is an extension of the concepts and techniques of ANOVA to situations with multiple dependent variables.


  1. MANOVA works well in situations where there are moderate correlations between DVs.
  2. Whereas SPSS limits you to 10 in ANOVA, the limit is 200 in MANOVA -- more than appropriate for nearly all research situations.
  3. MANOVA is useful in experimental situations where at least some of the independent variables are manipulated.


  1. Outliers - Like ANOVA, MANOVA is extremely sensitive to outliers.
  2. Tests for outliers should be run before performing a MANOVA, and outliers should be transformed or removed.


  1. Because in MANOVA there are multiple DVs, a column matrix (vector) of values for each DV is used.
  2. MANCOVA is an extension of ANCOVA. It is simply a MANOVA where the artificial DVs are initially adjusted for differences in one or more covariates.
  3. As we have learned, in order to account for multiple correlated DVs, MANOVA creates weighted linear combinations of the DVs called canonical variates.
  4. In our analysis there are 2 DVs and 3-1 = 2 df for the IV, so MANOVA creates two canonical variates (labeled Roots No.


  1. In this way, MANOVA essentially tests whether or not the independent grouping variable explains a significant amount of variance in the canonical variate.


  1. MANOVA and MANCOVA models are the most common uses of multivariate GLM and are the focus of the remainder of this section.

Manova-Based Scoring Method

  1. Motivated by this characteristic feature of MANOVA, we propose a MANOVA-based scoring method for identifying differentially expressed PPI subnetworks.

Significant Manova

  1. However, the earlier method, of following a significant MANOVA with a series of ANOVAs on each of the dependent variables, is still used.

Different Dependent Variables

  1. MANOVA treats these measures (a within-subject factor in ANOVA) as if there were different dependent variables.

One-Way Manova

  1. One-way MANOVA (Multivariate ANalysis Of VAriance) is the multivariate version of the univariate ANOVA, testing whether several samples have the same mean.
  2. In a one-way MANOVA, there is one categorical independent variable and two or more dependent variables.


  1. In this case, we will have only effects labeled "CONSTANT," since we don't have any WSFACTORS as far as MANOVA is concerned.


  1. However, there are some assumptions when using the MANOVA approach [ 21].


  1. You can specify the following options in the MANOVA statement as test-options in order to define which multivariate tests to perform.


  1. A summary method for class "manova".


  1. Specification of such effects in MANOVA is simple, following a logical algorithm applied to our model specifications on the DESIGN subcommand.
  2. Finally, the fourth MANOVA statement has the identical effect as the third, but it uses an alternative form of the M= specification.


  1. Discriminant function is a reasonable option and is equivalent to a one-way manova.


  1. Cases when the MANOVA approach cannot be used.


  1. Regarding the number of observations or cases in a MANOVA, the larger the better.


  1. The summary.manova method uses a multivariate test statistic for the summary table.


  1. This approach to follow-up tasting for a MANOVA is highly conservative since it holds a maximum alpha level for all possible comparisons of a given type.


  1. The default DEVIATION contrasts in MANOVA are designed to compare each level of a factor to the mean of all levels.
  2. After showing us the means, MANOVA next prints out the ONEWAY design or basis matrix for each factor.


  1. Here is an example, obtained by specifying a simple repeated measures MANOVA with four levels and no between subjects factors.


  1. Analogous to ANOVA, MANOVA is based on the product of model variance matrix and error variance matrix inverse.


  1. This is further illustrated by using the MANOVA results to predict the murder rates of the two groups.


  1. In the manova statement, we indicate that our hypothesized effect, represented in SAS as h, is group.


  1. Independent Random Sampling: MANOVA normally assumes that the observations are independent of one another.


  1. In general, MANOVA is conducted when it is expected that the resulting canonical variates reflect some construct differentiating the groups.

Special Case

  1. It is a special case of MANOVA used with two groups or levels of a treatment variable (Hair et al., 1995).


  1. This matrix can be displayed by PROC GLM if PRINTE is specified as a MANOVA option.


  1. Instead of specifying a set of equations, the fourth MANOVA statement specifies rows of a matrix of coefficients for the five dependent variables.


  1. Multi-way analysis of variance (MANOVA) is an extension of the one-way model that allows for the inclusion of additional independent nominal variables.


  1. Inaccurate measurement reduces the power of MANOVA and increases the likelihood of a Type II error, i.e., failing to find a difference when there is one.

Statistical Power

  1. The book is noted for its extensive applied coverage of MANOVA, its emphasis on statistical power, and numerous exercises including answers to half.


  1. Structure Correlations: As in MANOVA and LDFA, structure correlations are defined as the correlation between the original variable and the composite.

Further Details

  1. See summary.manova for further details.
  2. See the HTYPE= option in the specifications for the MANOVA statement for further details.


  1. Anova
  2. Multivariate Analysis
  3. Dependent Variables
  4. Information > Evaluation > Analysis > Variance
  5. Glossaries > Glossary of Statistics /

Related Keywords

    * Anova * Assumptions * Covariates * Dependent Variable * Factor Analysis * General Linear Model * Glm * Independent Variable * Independent Variables * Interaction Effect * Linear Models * Model * Multivariate Analysis * Probability * Spss * Tests * Test Statistic * Univariate * Variables * Variance
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  Originally created: August 16, 2007.
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