R: Permutation t-test for two groups of functional data objects.

tperm.fd {fda} | R Documentation

## Permutation t-test for two groups of functional data objects.

### Description

tperm.fd creates a null distribution for a test of no difference between two groups of functional data objects.

### Usage

    tperm.fd(x1fd, x2fd, nperm=200, q=0.05, argvals=NULL, plotres=TRUE, ...)

### Arguments

`x1fd` | a functional data object giving the first group of functional observations.
`x2fd` | a functional data object giving the second group of functional observations.
`nperm` | number of permutations to use in creating the null distribution.
`q` | Critical upper-tail quantile of the null distribution to compare to the observed t-statistic.
`argvals` | If `yfdPar` is a `fd` object, the points at which to evaluate the point-wise t-statistic.
`plotres` | Argument to plot a visual display of the null distribution displaying the `1-q`th quantile and observed t-statistic.
`...` | Additional plotting arguments that can be used with `plot`.

### Details

The usual t-statistic is calculated pointwise and the test based on the maximal value. If `argvals` is not specified, it defaults to 101 equally-spaced points on the range of `yfdPar`.

### Value

A list with the following components:

`pval` | the observed p-value of the permutation test.
`qval` | the `q`th quantile of the null distribution.
`Tobs` | the observed maximal t-statistic.
`Tnull` | a vector of length `nperm` giving the observed values of the permutation distribution.
`Tvals` | the pointwise values of the observed t-statistic.
`Tnullvals` | the pointwise values of of the permutation observations.
`pvals.pts` | pointwise p-values of the t-statistic.
`qvals.pts` | pointwise `q`th quantiles of the null distribution
`argvals` | argument values for evaluating the F-statistic if `yfdPar`is a functional data object.

### Side Effects

a plot of the functional observations

### Source

Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York.

### See Also

`fRegress` `Fstat.fd`

### Examples

    # This tests the difference between boys and girls heights in the
    # Berkeley growth data.

    # First set up a basis system to hold the smooths

    knots  <- growth$age
    norder <- 6
    nbasis <- length(knots) + norder - 2
    hgtbasis <- create.bspline.basis(range(knots), nbasis, norder, knots)

    # Now smooth with a fourth-derivative penalty and a very small smoothing
    # parameter

    Lfdobj <- 4
    lambda <- 1e-2
    growfdPar <- fdPar(hgtbasis, Lfdobj, lambda)

    hgtmfd <- smooth.basis(growth$age, growth$hgtm, growfdPar)$fd
    hgtffd <- smooth.basis(growth$age, growth$hgtf, growfdPar)$fd

    # Call tperm.fd

    tres <- tperm.fd(hgtmfd,hgtffd)

[Package fda version 2.4.8 Index]