Confidence intervall
- To: mathgroup at smc.vnet.net
- Subject: [mg67658] Confidence intervall
- From: dh <dh at metrohm.ch>
- Date: Tue, 4 Jul 2006 01:56:23 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello, I have a problem that I thought should be rather standard, but I am looking for quit some time for a good answer and I am still at it. As I know that this group is read by quite a few knowledgable people I give it at try. Background: -------------------------------------------------------------- A calibration curve y=f(x) is least square fitted to some calibration points ci=(xi,yi) where y is a random variable and x is known A sample is repeatedly measured: ysi, and xs is determind, so that Mean[ysi] = f[xs] A confidence interval is searched for xs, taking into account that we have small sample sizes. Ansatz: By error propagation we get that part of the variance of xs that is due to the calibration points: varc and that due to the sample: vars. confidence intervall: student Sqrt[varc+vars] where student is the student factor to some confidence level with a unknwon degree of freedom. Now the questthe sample size as well as the variance of calibration and sample are different. --------------------------------------------------- I think the above problem is equivalent to: get a confidence interval for the sum of two (normal) random variables x1,x2 with variances v1,v2 and degree of freedoms:dof1,dof2, where the variances and degree of freedoms differ. In the literature I found the approximation of Welch-Satterthwaite but I found by simulation that this is far from perfect. Does anybody know if an accurate solution or a better approximation is known? Daniel Huber
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