mauchley.test {stats} | R Documentation |

## Mauchley's test of sphericity

### Description

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

### Usage

## S3 methods for class 'SSD' or 'mlm'
mauchley.test(object, Sigma = diag(nrow = p),
T = Thin.row(proj(M) - proj(X)), M = diag(nrow = p), X = ~0,
idata = data.frame(index = seq(length = 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 |

`...` |
For consistency with generic |

### Details

Mauchley'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
compund symmetry in the untransformed covariance matrix.

### 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.

### References

TW 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
mauchley.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")))
mauchley.test(mlmfit, X = ~ deg + noise, idata = idata)
mauchley.test(mlmfit, M = ~ deg + noise, X = ~ noise, idata=idata)

[Package

*stats* version 2.1.0

Index]