# R: Summary Method for Multivariate Analysis of Variance

summary.manova {stats} | R Documentation

## Summary Method for Multivariate Analysis of Variance

### Description

A `summary` method for class `"manova"`.

### Usage

    ## S3 method for class 'manova':
    summary(object,
            test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
            intercept = FALSE, ...)

### Arguments

`object` | An object of class `"manova"` or an `aov` object with multiple responses.
`test` | The name of the test statistic to be used. Partial matching is used so the name can be abbreviated.
`intercept` | logical. If `TRUE`, the intercept term is included in the table.
`...` | further arguments passed to or from other methods.

### Details

The `summary.manova` method uses a multivariate test statistic for the summary table. Wilks' statistic is most popular in the literature, but the default Pillai–Bartlett statistic is recommended by Hand and Taylor (1987).

The table gives a transformation of the test statistic which has approximately an F distribution. The approximations used follow S-PLUS and SAS (the latter apart from some cases of the Hotelling–Lawley statistic), but many other distributional approximations exist: see Anderson (1984) and Krzanowski and Marriott (1994) for further references. All four approximate F statistics are the same when the term being tested has one degree of freedom, but in other cases that for the Roy statistic is an upper bound.

### Value

A list with components

`SS` | A named list of sums of squares and product matrices.
`Eigenvalues` | A matrix of eigenvalues.
`stats` | A matrix of the statistics, approximate F value, degrees of freedom and P value.

### References

Anderson, T. W. (1994) An Introduction to Multivariate Statistical Analysis. Wiley.

Hand, D. J. and Taylor, C. C. (1987) Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall.

Krzanowski, W. J. (1988) Principles of Multivariate Analysis. A User's Perspective. Oxford.

Krzanowski, W. J. and Marriott, F. H. C. (1994) Multivariate Analysis. Part I: Distributions, Ordination and Inference. Edward Arnold.

### See Also

`manova`, `aov`

### Examples

    ## Example on producing plastic film from Krzanowski (1998, p. 381)
    tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
              6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
    gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
               9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
    opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
                 2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
    Y <- cbind(tear, gloss, opacity)
    rate <- factor(gl(2,10), labels=c("Low", "High"))
    additive <- factor(gl(2, 5, length=20), labels=c("Low", "High"))

    fit <- manova(Y ~ rate * additive)
    summary.aov(fit)           # univariate ANOVA tables
    summary(fit, test="Wilks") # ANOVA table of Wilks' lambda
    summary(fit)               # same F statistics as single-df terms

[Package stats version 2.6.0 Index]