# Re: [ferret_users] Trend error and significance

• To: ferret_users@xxxxxxxx, siva <sivamtech07@xxxxxxxxxxxxxx>
• Subject: Re: [ferret_users] Trend error and significance
• From: yangxing zheng <yangxingz@xxxxxxxxx>
• Date: Fri, 07 Aug 2009 08:51:29 -0700 (PDT)
• Sender: owner-ferret_users@xxxxxxxx

Hi Siva,

I think David Wang has provided a method that posted couple months ago. I copy the message for you, as shown below:

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BTW, there is a caveat that the approximation of 95% confidence interval by "two sigma" can only be used when the degree of freedom is sufficient large. This student's t-table makes it clear (t = slope/sigmab).

http://www.ncsu.edu/chemistry/resource/t-table.html

D.

On Thu, Mar 5, 2009 at 7:08 PM, David Wang wrote:
Hi Ferreters,

I recently wanted to calculate the 95% confidence interval for a linear regression by the way of regresst.jnl, and found it's quite straightforward. There is a question on this in the archive that remains unanswered (http://www.pmel.noaa.gov/maillists/tmap/ferret_users/fu_2006/msg00428.html). So I put forth my two cents here risking everybody has already known it.

The idea is that 95% confidence interval is about "two sigma" (http://en.wikipedia.org/wiki/Uncertainty#Measurements). So the problem boils down to estimating the sampling standard deviation of the regression slope. Following Wilks's book (statistical methods in atmospheric science, chapter 6.2), the sampling distribution for slope is Gaussian and its sampling standard deviation is given in the equation 6.18b. In Ferret, after regresst.jnl, issue the following two commands:

let >let sigmab = ((qvar/pvar-slope*slope)/(ones[t=@sum]-2))^0.5

And the 95% error bar is 2*sigmab. If the confidence interval at a different significance level (say, 90%) is desirable, one can simply go to the lookup table for the t-test and figure out how many "sigma" s/he needs.

HTH,
D.
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--- On Fri, 8/7/09, siva <sivamtech07@xxxxxxxxxxxxxx> wrote:

From: siva <sivamtech07@xxxxxxxxxxxxxx>
Subject: [ferret_users] Trend error and significance
To: ferret_users@xxxxxxxx
Date: Friday, August 7, 2009, 9:04 PM

Hi all,

I want to do trend analysis.

Actually i am able to get trend of a particular variable, using regresst.jnl. But there is no variable inside this JNL, defining trend error and confidence level of the trend.

Is there any function/JNL for getting these?

Regards

S.Siva Reddy
Senior Research Fellow
UCESS/INCOIS