# Re: Fw: Re: Re: confidence interval/level

From: Dennis Shea <shea_at_nyahnyahspammersnyahnyah>
Date: Fri Sep 20 2013 - 10:42:15 MDT

(i) B = 1-p**(1/(df/2-1)) where B=coherence-squared

(ii) Solving for p

p = (1-B)^(df/2-1)

Looking at Table 1 of the article

n = 4
df = 8.0 ; degrees of freedom

(i) What coherence-squared (coherence)
is needed for a significance level of p=0.05

B = 1.0-p^(1.0/(df/2.0 -1.0)) ; ===> 0.6315969

b = sqrt(B) ; coherence==>0.7947307

===

(ii) At what probability level does a calculated coherence-squared
(coherence^2) fall ... given an estimated 'df'

B = 0.63

p = (1-B)^(df/2-1) ; ==> 0.05

Sometimes statistics are returned via

P = 1-p ; P=0.95

That is the way I sent you

P = 1.-(1.-coh)^(df/2.-1.)

Hope that helps

On 9/19/13 12:10 PM, 朱学明 wrote:
>
> Hi Dennis,
> I am still confused on your example and do not know how to caculate spec@coher_probability exactly. Can you tell me what is the coh, why you set it as 0.5 in your example? Is it the confidence level(0.9, 0.95, 0.99) or spec@coher? What is the relationship between df and jave? Is df twice of jave?
> Also, I found the formula
> B=1-p**(1/(df/2-1)) (1)
> from the reference, but your example is
> p = 1.-(1.-coh)**(df/2.-1.) (2)
>
> why are they different? Is the p in (2) same as p or B in (1) ? Which one is the spec@coher_probability from the function specxy_anal in NCL?
>
> Thanks.
>
> 2013-09-19
>
>
>
> Xueming Zhu 朱学明
> Key Laboratory of Research on Marine Hazards Forecasting (LoMF), SOA
> National Marine Environmental Forecasting Center (NMEFC)
> No.8, Dahuisi Road, Haidian District, Beijing, 100081
> People's Republic of China
> Tel:+86-10-82481923
>
>
>
> 发件人：Dennis Shea <shea@ucar.edu>
> 发送时间：2013-09-19 01:13
> 主题：Re: [ncl-talk] confidence interval/level
> 收件人："朱学明"<557xiaozhu@163.com>
> 抄送："ncl-talk@ucar.edu USERS"<ncl-talk@ucar.edu>
>
>
> Comments on the Determination of Significance Levels
> of the Coherence Statistic
> Paul Julian
> Journal of the Atmospheric Sciences, 1975
> Volume 12, pp836-837
>
>
> http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281975%29032%3C0836%3ACOTDOS%3E2.0.CO%3B2
>
> eg:
> coh = .5
> df = 6
> p = 1.-(1.-coh)**(df/2.-1.)
> print("p="+p)
>
>
>
> On 9/18/13 8:54 AM, 朱学明 wrote:
>> Hi Dennis,
>> can you show me how does NCL caculate the spec@coher_probability?
>> Thanks.
>>
>> 2013-09-18
>>
>>
>>
>> 朱学明
>>
>>
>>
>> 发件人：Dennis Shea <shea@ucar.edu>
>> 发送时间：2013-09-18 07:29
>> 主题：Re: [ncl-talk] confidence interval/level
>> 收件人："朱学明"<557xiaozhu@163.com>
>> 抄送："ncl-talk@ucar.edu USERS"<ncl-talk@ucar.edu>
>>
>> spec = specxy_anal(x,y,d,sm,pct)
>> PHASE = spec@phase
>> PHASE@_FillValue = 1e20
>> PHASE = where(spec@coher_probability(1).le.0.95,PHASE@_FillValue,PHASE)
>>
>> =========
>> See: http://www.ncl.ucar.edu/Applications/xy.shtml#ex25
>>
>> The right (R) plot should
>>
>>
>> resR = True ; plot mods desired
>> resR@xyMarkLineModes = "Markers" ; choose which have markers
>> resR@xyMarkers = 16 ; choose type of marker
>> resR@xyMarkerColor = "red" ; Marker color
>> resR@xyMarkerSizeF = 0.005 ; Marker size (default 0.01)
>>
>>
>> plot = gsn_csm_xy2(wks,spec@frq,spec@coher,PHASE,resL,resR)
>>
>>
>> On 9/17/13 4:04 PM, 朱学明 wrote:
>>> Hi all,
>>> I have tried to use the function specxy_anal get the coherance and phase of two timeseries data based on the example script spec_2.ncl. But I just want to get the coherence and phase satisfy the 0.95 confidence level, the picture likes that in the attachment. How can I do that?
>>> It looks like that the output of function specx_ci is not what I want.
>>>
>>> Any help would be appreciated. Thanks.
>>>
>>> 2013-09-18
>>>
>>>
>>>
>>> 朱学明
>>>
>>>
>>>
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Received on Fri Sep 20 10:42:25 2013

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