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

`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]