Do a random t-test to the cross-validation results.

`rand.t.test.w(cvoutput, n.perm = 999)`

## Arguments

- cvoutput
Cross-validation output either from `cv.w`

or
`cv.pr.w`

.

- n.perm
The number of permutation times to get the p value, which
assesses whether using the current number of components is significantly
different from using one less.

## Value

A matrix of the statistics of the cross-validation results. Each
component is described below:

`R2`

the coefficient of determination (the larger, the
better the fit).

`Avg.Bias`

average bias.

`Max.Bias`

maximum bias.

`Min.Bias`

minimum bias.

`RMSEP`

root-mean-square error of prediction (the smaller,
the better the fit).

`delta.RMSEP`

the percent change of RMSEP using the current
number of components than using one component less.

`p`

assesses whether using the current number of components
is significantly different from using one component less, which is used
to choose the last significant number of components to avoid
over-fitting.

`-`

The degree of overall compression is assessed by doing
linear regression to the cross-validation result and the observed
climate values.

`Compre.b0`

: the intercept.

`Compre.b1`

: the slope (the closer to 1, the less the
overall compression).

`Compre.b0.se`

: the standard error of the intercept.

`Compre.b1.se`

: the standard error of the slope.

## Examples

```
if (FALSE) {
## Random t-test
rand_pr_tf_Tmin2 <- fxTWAPLS::rand.t.test.w(cv_pr_tf_Tmin2, n.perm = 999)
# note: choose the last significant number of components based on the p-value,
# see details at Liu Mengmeng, Prentice Iain Colin, ter Braak Cajo J. F.,
# Harrison Sandy P.. 2020 An improved statistical approach for reconstructing
# past climates from biotic assemblages. Proc. R. Soc. A. 476: 20200346.
# <https://doi.org/10.1098/rspa.2020.0346>
}
```