# [ncl-talk] Bootstrapping method for significant test

Dennis Shea shea at ucar.edu
Wed Dec 14 15:45:37 MST 2016

```I think you will have to decide what is best.

[a]
Constrain the F,N,A triplets to be 'coupled'

nBoot =   10000
xBoot = *new*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml>
(nBoot, typeof(F))

do ns=0,nBoot-1                        ; generate multiple estimates
iw = *generate_sample_indices*
<http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
; indices with replacement
xBoot(ns) = (dF(iw)/dN(iw))*(dN(iw)/dA(iw))
end do

[b]

Unconstrained

nBoot =   10000
xBoot = *new*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml>
(nBoot, typeof(F))

do ns=0,nBoot-1                        ; generate multiple estimates
iwF = *generate_sample_indices*
<http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
; indices with replacement
iwN = *generate_sample_indices*
<http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
iwA = *generate_sample_indices*
<http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))

xBoot(ns) = (dF(iwF)/dN(iwN))*(dN(iwN)/dA(iwA))
end do

[c]

ia = *dim_pqsort_n*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/dim_pqsort_n.shtml>(xBoot,
2, 0)        ; sort bootstrap means into ascending order

n025     = *round*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.025*(nBoot-1),3)
; indices for sorted array
n500     = *round*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.500*(nBoot-1),3)
n975     = *round*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.975*(nBoot-1),3)

xBoot_025= xBoot(n025)                 ;  2.5% level
xBoot_500= xBoot(n500)                 ; 50.0% level  (median)
xBoot_975= xBoot(n975)                 ; 97.5% level

On Wed, Dec 14, 2016 at 3:12 PM, Anahita Amiri Farahani <aamir003 at ucr.edu>
wrote:

> Dear all,
>
> I have a product of two partial derivatives : dF/dN*dN/dA and for each of
> the variables (F, N, and A) I have data for 720 times. Each partial
> derivatives are calculated  by linear regression. I was wondering how I can
> calculate the significant test for this product. All examples in NCL to
> estimate linear regression by this function: *regline_stats
> <http://www.ncl.ucar.edu/Document/Functions/Contributed/regline_stats.shtml> *
> give the regression coefficient for two variables.
>
> Thanks,
> Ana
>
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