# Include Type B in effective degrees of freedom for expanded uncertainty?

This post has sat unanswered for a couple days in the TalkStats forum so I'm hoping somebody here can help me out.

I'm looking for assistance in clarifying how Type B uncertainty is incorporated into the determination of expanded uncertainty. I'm using the Guide to Uncertainty in Measurement (GUM) as the primary reference. This lays out the steps for calculating expanded uncertainty in G.6.4.

In particular, I need input on my interpretation of step 2, computation of the effective degrees of freedom (Veff) through the Welch-Satterthwaite formula (G.2b). From a plain reading of this step, I understand the combined uncertainty (Uc) to contain all Type A and all Type B contributions. In the denominator, the degrees of freedom for individual Type B components (Vi) is often set to infinity (as would be the case for a half-width from an equipment data sheet). This takes that term to zero, though the uncertainty component is still part of the combined uncertainty in the numerator.

I'd be comfortable with this interpretation, except that upon reviewing an example on the NIST site I found that they were excluding the Type B components altogether when calculating Veff.

Can anybody identify which technique is correct? Thanks for the help.

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I think the description in your primary reference treats type B uncertainty contributions as extra variation not obtained from measurements but rather from judgement. It sounds akin to uncertianty in parameters characterized in the prior when Bayesian me6thods are used. NIST does not exclude type B uncertainty they just have a different definition of it and it seems to all fall under the realm of classical frequentist statistics. Many of the things you describe in your post that apparently come from the first reference sound foreign and peculiar to me. –  Michael Chernick Sep 7 '12 at 22:36
The statisticians at NIST that wrote the Engineering Handbook are people I know and have met in person. What they write makes sense to me and I trust them. However this is my opinion and therefore I think is not something to give as an answer. I do think that there may be a difference in terminology of type A and type B uncertainty between the two references and that may be the casue of your confusion. but I cannot say definitively that one is right and the other wrong. –  Michael Chernick Sep 7 '12 at 22:40
Thanks for the comment Michael. As I review these again I don't see any conflict in the definition of Type B, and the calculations in both references are equivalent (aside from the discrepancy in my query). The problem I have with the NIST version is that if the uncertainty is dominated by Type B components and the Type A uncertainty comes from a relatively small sample size, the expanded uncertainty would seem to be artificially inflated by the application of the coverage factor that is only based on Type A sample sizes yet includes Type B. –  Travis R Sep 10 '12 at 17:18
I've since discovered NIST Technical Note 1297, which essentially adopts the ISO Guide to Uncertainty in Measurement for NIST use. In that note, the description of expanded uncertainty in Appendix B would appear to agree with my interpretation of GUM (where Type B components are included in the calculation of effective degrees of freedom). –  Travis R Sep 10 '12 at 18:06