mauchly.test {stats} | R Documentation |

## Mauchly's Test of Sphericity

### Description

Tests whether a Wishart-distributed covariance matrix (or
transformation thereof) is proportional to a given matrix.

### Usage

mauchly.test(object, Sigma = diag(nrow = p),
T = Thin.row(proj(M) - proj(X)), M = diag(nrow = p), X = ~0,
idata = data.frame(index = seq_len(p)), ...)

### Arguments

`object` |
object of class `SSD` or `mlm` . |

`Sigma` |
matrix to be proportional to. |

`T` |
transformation matrix. By default computed from `M` and
`X` . |

`M` |
formula or matrix describing the outer projection (see below). |

`X` |
formula or matrix describing the inner projection (see below). |

`idata` |
data frame describing intra-block design. |

`...` |
arguments to be passed to or from other methods. |

### Details

Mauchly's test test for whether a covariance matrix can be assumed to
be proportional to a given matrix.

It is common to transform the observations prior to testing. This
typically involves
transformation to intra-block differences, but more complicated
within-block designs can be encountered,
making more elaborate transformations necessary. A
transformation matrix `T`

can be given directly or specified as
the difference between two projections onto the spaces spanned by
`M`

and `X`

, which in turn can be given as matrices or as
model formulas with respect to `idata`

(the tests will be
invariant to parametrization of the quotient space `M/X`

).

The common use of this test is in repeated measurements designs, with
`X=~1`

. This is almost, but not quite the same as testing for
compound symmetry in the untransformed covariance matrix.

This is a generic function with methods for classes `"mlm"`

and
`"SSD"`

.

### Value

An object of class `"htest"`

### Note

The p-value differs slightly from that of SAS because a second order term
is included in the asymptotic approximation in **R**.

### References

T. W. Anderson (1958). *An Introduction to Multivariate
Statistical Analysis.* Wiley.

### See Also

`SSD`

, `anova.mlm`

### Examples

example(SSD) # Brings in the mlmfit and reacttime objects
### traditional test of intrasubj. contrasts
mauchly.test(mlmfit, X=~1)
### tests using intra-subject 3x2 design
idata <- data.frame(deg=gl(3,1,6, labels=c(0,4,8)),
noise=gl(2,3,6, labels=c("A","P")))
mauchly.test(mlmfit, X = ~ deg + noise, idata = idata)
mauchly.test(mlmfit, M = ~ deg + noise, X = ~ noise, idata=idata)

[Package

*stats* version 2.5.0

Index]