# boot.ratio.test

##### Performs bootstrap ratio test.

Performs bootstrap ratio test which is analogous to a *t*- or *z*-score.

- Keywords
- Bootstrap, multivariate, inference

##### Usage

`boot.ratio.test(boot.cube, critical.value = 2)`

##### Arguments

- boot.cube
an

`array`

. This is the bootstrap resampled data. dim 1 (rows) are the items to be tested (e.g.,`fj`

, see`boot.compute.fj`

). dim 2 (columns) are the components from the supplemental projection. dim 3 (depth) are each bootstrap sample.- critical.value
numeric. This is the value that would be used as a cutoff in a

*t*- or*z*-test. Default is 2 (i.e., 1.96 rounded up). The higher the number, the more difficult to reject the null.

##### Value

A list with the following items: return(list(sig.boot.ratios=significant.boot.ratios,boot.ratios=boot.ratios,critical.value=critical.value))

This is a matrix with the same number of rows and columns as `boot.cube`

. If TRUE, the bootstrap ratio was larger than `critical.value`

. If FALSE, it was smaller.

This is a matrix with bootstrap ratio values that has the same number of rows and columns as `boot.cube`

.

the critical value input is also returned.

##### References

The name bootstrap ratio comes from the Partial Least Squares in Neuroimaging literature. See:
McIntosh, A. R., & Lobaugh, N. J. (2004). Partial least squares analysis of neuroimaging data: applications and advances. *Neuroimage*, *23*, S250--S263.
The bootstrap ratio is related to other tests of values with respect to the bootstrap distribution, such as the Interval-*t*. See:
Chernick, M. R. (2008). *Bootstrap methods: A guide for practitioners and researchers* (Vol. 619). Wiley-Interscience.
Hesterberg, T. (2011). Bootstrap. *Wiley Interdisciplinary Reviews: Computational Statistics*, *3*, 497<U+2013>526.

##### See Also

##### Examples

```
# NOT RUN {
##the following code generates 100 bootstrap resampled
##projections of the measures from the Iris data set.
data(ep.iris)
data <- ep.iris$data
design <- ep.iris$design
iris.pca <- epGPCA(data,scale="SS1",DESIGN=design,make_design_nominal=FALSE)
boot.fjs.unconstrained <- array(0,dim=c(dim(iris.pca$ExPosition.Data$fj),100))
boot.fjs.constrained <- array(0,dim=c(dim(iris.pca$ExPosition.Data$fj),100))
for(i in 1:100){
#unconstrained means we resample any of the 150 flowers
boot.fjs.unconstrained[,,i] <- boot.compute.fj(ep.iris$data,iris.pca)
#constrained resamples within each of the 3 groups
boot.fjs.constrained[,,i] <- boot.compute.fj(data,iris.pca,design,TRUE)
}
#now compute the bootstrap ratios:
ratios.unconstrained <- boot.ratio.test(boot.fjs.unconstrained)
ratios.constrained <- boot.ratio.test(boot.fjs.constrained)
# }
```

*Documentation reproduced from package InPosition, version 0.12.7.1, License: GPL-2*