Confidence interval vs. expanded uncertainty

sagevahi

New Member
Hi,

I'm struggling with the difference between confidence interval and expanded uncertainty.

I understand a confidence interval around the mean. For example, a 95% confidence interval around the mean says that if N samples were taken 100 times and a confidence interval was recalculated each time, at least 95 of my confidence intervals would actually contain the true mean.

The expanded uncertainty is X +/- k*s, where:
• X is my best estimate determination of the parameter of interest
• k is my coverage factor, e.g., 2 for 95%
• s is my combined standard uncertainty of X
Is the expanded uncertainty the same concept as confidence interval, but for a specific measurement (whereas the confidence interval was for a collection of measurements, i.e., the mean)? For example, does the expanded uncertainty of 95% mean that if I were to take 100 more measurements, at least 95 of them should fall within the previously determined expanded uncertainty interval?

I have scoured the internet with things like "expanded uncertainty vs. confidence interval" and can't find much.

GretaGarbo

Human
I have heard of confidence intervals many times. But I have never heard of "expanded uncertainty". So I don't know what that is.

Dason

Agreed. Never heard the term until you posted it.

hlsmith

Less is more. Stay pure. Stay poor.
I also have not heard of them. Can you provide a source/citation? From the way you present them, they seem like an industrial engineering or information theory concept.

sagevahi

New Member
Hi all, thanks for responding.

Sure thing, here are some sites that refer to the "expanded uncertainty".
The more I read about it, the more I'm starting to think there's no "meaning" associated with it. It's just a common practice when reporting uncertainty. For example, note that they use 2 for a 95% confidence instead of 1.96.

Here's an example of my question written another way. Let's say I want to measure an area, and this value has 2 sources of uncertainty: length of X and length of Y. My combined standard uncertainty is the square root of sum of squares of the error contributions of X and Y, i.e.:

uncert = sqrt( var(X) + var(Y) )​

Does "Area +/- 1.96*uncert" have any meaning? It corresponds to 95% of the area under the normal curve, but does it also mean anything else?

GretaGarbo

Human
Here is a link to the National Institute of Standards and Technology: https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc57.htm
Frankly, I don't understand that. What about "Definition of standard uncertainty" What if the variabels ar correlated. Should the covariance not be included?

"Expanded uncertainty assures a high level of confidence" But if the variances and/or the coefficients (the a_i) are large, then it will not assure a high level of confidence. And what do they mean by confidence? A confidence interval?

sagevahi

New Member
And what do they mean by confidence? A confidence interval?
You have hit my question exactly! What do they mean by confidence? I can't tell at all. I can't figure out what this value represents.

Regarding your first question about the covariance, I think they are assuming the covariance is zero on a previous page. For example, see the section for "Treatment of covariance terms" on https://www.itl.nist.gov/div898/handbook/mpc/section5/mpc55.htm