Multivariate Analysis of Variance

Multivariate analysis of variance, known as MANOVA, is the extension of analysis of variance techniques to multiple responses. The responses for an observation are considered as one multivariate observation, rather than as a collection of univariate responses.

If the responses are independent, then it is sensible to just perform univariate analyses. However, if the responses are correlated, then MANOVA can be more informative, as well as less repetitive, than the univariate analyses.

To perform multivariate analysis of variance

Choose Statistics __image\ebd_ebd79.gif Multivariate __image\ebd_ebd80.gif MANOVA. The dialog shown below appears.

Model page

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In the Multivariate Analysis of Variance dialog, the Model page has the following options:

Data

Data Set

Select a data set from the dropdown list or type the name of a data set. You can also type into the Data Set edit field any expression that evaluates to a data set.

Weights

Enter the column that specifies weights to be applied to all observations used in the analysis. To weight all rows equally, leave this blank.

Subset Rows

Enter an S-PLUS expression that identifies the rows to use in the analysis. To use all the rows in the data set, leave this field blank.

Omit Rows with Missing Values

Select this box to omit from the analysis any rows in the data set that contain missing values for any of the variables in the model.

Formula

MANOVA Formula

Enter a formula specifying the desired model. The response or independent variable must be a matrix. Click the Create Formula button to open the formula builder dialog. Select two or more variables by CTRL-clicking, and click Response.

Save Model Object

Save Model Object

In the Save As field, enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. The model object can be used in later functions such as plotting.

Options page

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In the Multivariate Analysis of Variance dialog, the Options page has the following options:

Contrasts

Assign Contrast Choose contrasts for the factors; by default, the Helmert contrasts are assigned to unordered factors and polynomial contrasts are assigned to ordered factors.

to Variable(s) Select one or more variables to which the selected contrast in Assign Contrast will be assigned.

Contrasts This field displays the selection and assignment chosen in Assign Contrast and to Variable(s).

Results page

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In the Multivariate Analysis of Variance dialog, the Results page has the following options:

Printed Results

Short Output for MANOVA

Display the call to the S-PLUS function maov, the sums of squares and degrees of freedom for factors and residuals, and the residual standard error.

ANOVA Table

Display an analysis of variance table. The sums-of-squares in the table are for the terms added sequentially (Type I sums-of-squares).

Testing with

Choose the type of test used in the ANOVA table. Choices include pillai, wilks, hotelling-lawley, and roy.

Estimated Coefficients

Select this to print the estimated coefficients. There are K-1 such coefficients for each K-level factor.

Estimated K Coef for K-Level Factor

Print K coefficients for each K-level factor.

Saved Results

Save In

Enter the name of a data set in which a part of the analysis, such as fitted values and residuals, predictions, confidence intervals, or standard errors, is saved. If an object with the name you enter does not already exist (in database 1), then it is created

Fitted Values

Save the fitted values from the model in the object specified in Save In.

Residuals

Save the residuals from the model in the object specified in Save In. These are the ordinary residuals (the response minus the fitted value).

Related S-Plus language functions

manova, summary.manova, coef, dummy.coef, aov, raov, lm