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artem
USA
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 Posted - 05/28/2009 : 2:08:29 PM
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Origin Ver. 7.5 and Service Release 7:
Operating System: Vista Home Basic
Generating a Parameters worksheet after using NLSF advanced fitter produces a column Err with the "Error on the parameter value" (Origin help seems to use error and standard error interchangeably), and a column ConfIntv, which should be "Confidence interval. Calculated based on a linear approximation and is given by Standard Error * t, where t is the critical value of the t distribution for the given confidence level" according to Origin Help. I assume t is given by ttable(conf level, dof), but this doesn't give me the relation between Err and ConfIntv as stated above.
For example, I get p=0.1544, err=0.0067, and confintv=0.01474
for one parameter in a fit of 15 data points with 4 total parameters (nlsf.dof=11) using the default confidence level (nlsf.conf=0.95.) TTABLE(.95,11)=1.795885, so confintv should be 0.0067*1.795885=0.01203, but the value in the confintv column is 0.01474. What am I missing here?
Thanks,
Tony
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artem
USA
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Posted - 05/28/2009 : 3:49:57 PM
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After further examination, it looks like Origin uses a confidence level of 0.975 to go from Err to ConfIntv, rather than the specified 0.95. For all four parameters in the example given in my original post, the ratio ContIntv/Err is 2.20099, which is the t value given by TTABLE(.975,11)=2.20099. Changing the confidence level to 0.68 produces ContIntv/Err=1.04149, which corresponds to a confidence level of 0.84: INVT(1.04149,11)=0.8400.
???????,
Tony |
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easwar
USA
1965 Posts |
Posted - 05/28/2009 : 4:26:31 PM
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Hi Tony,
The Confidence Interval (or more accurately the confidence interval half width) is defined as:
CIHW = Standard_Error_of_Parameter * ttable( alpha/2, DOF)
where DOF=n-p is degrees of freedom, and alpha is Significance Level.
Significance level is different from Confidence Level, and the two are related by:
significance level = 1 + Confidence level
Thus for confidence level of 0.95, we get
alpha/2 = (1+0.95)/2 = 0.975
This is why you are reproducing the values when plugging in 0.975 into the ttable function instead of plugging in 0.95
Hope this helps.
Easwar
OriginLab
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artem
USA
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Posted - 05/28/2009 : 5:25:16 PM
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Thanks Easwar, you are right. I knew this at one point long ago, but it had slipped my feeble mind. I appreciate your setting me straight.
Tony |
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NLSF Parameter worksheet