# [ncl-talk] Bootstrapping method for significant test

Anahita Amiri Farahani aamir003 at ucr.edu
Wed Dec 14 19:02:48 MST 2016

```Thanks a lot, your answer was really helpful and I have another question:

Before I use regCoef function in NCL to calculate linear regression. Using
this function gives other variables such as rcraw_npt, and  rcraw_tval, so
I was able to calculate significance at 95%, 90% and 99% confidence level.
I've put that part of the code here:

do k=0,2999

ab = regCoef(AI_fall(:,k),Nd_fall(:,k))
rcraw_npt=ab at nptxy-2
rcraw_tval=ab at tval
b    = rcraw_tval
b    = 0.5
rcraw_npt=where(rcraw_npt.lt.1,1,rcraw_npt)
rcraw_prob = (1 -
betainc(rcraw_npt/(rcraw_npt+rcraw_tval^2),rcraw_npt/2.0,b) )
sig_fall(k)=where(rcraw_prob.lt.0.95,-999,rcraw_prob)

end do

How can I calculate the significance at different confidence level here by
using xBoot?

Best,
Ana

On Wed, Dec 14, 2016 at 2:45 PM, Dennis Shea <shea at ucar.edu> wrote:

> 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]
> See where your product fits.
>
>    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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>
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