summary.manova {stats} | R Documentation |

A `summary`

method for class `"manova"`

.

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

`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. |

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.

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. |

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.

## 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, len=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 2.5.0 Index]