# manova1

One-way multivariate analysis of variance (MANOVA)

## Description

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

`manova1`

determines `d`

by calculating a test
statistic for each possible value of `d`

. The formula for the test
statistic is

$$\left(n-1-\frac{l+r}{2}\right)\mathrm{log}(\lambda ),$$

where *n* is the number of observations,
*l* is the number of factor levels, *r* is the number
of response variables, and $$\lambda $$ is Wilks' lambda. For more information about Wilks' lambda, see Multivariate Analysis of Variance for Repeated Measures.

The largest possible value of `d`

is the minimum between the number of
response variables and one less than the number of factor levels. `d`

is
the largest value for which the *p*-value is less than the significance
level specified by `alpha`

.

## Alternative Functionality

Instead of using `manova1`

, you can create a
`manova`

object using the `manova`

function,
and then use the `barttest`

object
function to calculate the dimension of the space containing the group means. The advantages of
using the `manova`

function include:

Support for two-way and N-way MANOVA

Table support for factor and response data

Additional properties of the

`manova`

object, including those for the fitted MANOVA model coefficients, degrees of freedom for the error, and response covariance matrix

## References

[1] Krzanowski, Wojtek. J.
*Principles of Multivariate Analysis: A User's Perspective*. New York:
Oxford University Press, 1988.

[2] Morrison, Donald F.
*Multivariate Statistical Methods*. 2nd ed, McGraw-Hill,
1976.

## Version History

**Introduced before R2006a**