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Guidelines for evaluating and expressing the uncertainty of NIST measurement results
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TL;DR
This NIST Technical Note 1297 (1994) gives guidelines for evaluating and expressing measurement uncertainty at NIST, adopting the CIPM/ISO Guide approach. It defines Type A and Type B evaluations, combined and expanded uncertainty, and reporting conventions, with \(k=2\) as the NIST default coverage factor.
Key findings
- NIST policy: represent each uncertainty component by a standard uncertainty \(u_i\), combine them by the root-sum-of-squares method into the combined standard uncertainty \(u_c\), and report expanded uncertainty \(U = k u_c\) with \(k=2\) by convention, or report \(u_c\); other \(k\) values require established and documented requirements.
- Type A evaluations use statistical methods; Type B evaluations use other means. The A/B distinction is not the same as “random”/“systematic.” Type B examples include dividing a quoted 95% interval by 1.960 and a 99% interval by 2.576; for a rectangular distribution \(u_j = a/\sqrt{3}\), for triangular \(u_j = a/\sqrt{6}\), and for normal models \(u_j \approx 1.48a\) for a 50% interval, \(u_j \approx a\) for 67%, and \(u_j \approx a/3\) for 99.73%.
- Coverage: when the normal distribution applies and \(u_c\) has negligible uncertainty, \(U=2u_c\) defines an interval with approximately 95% confidence and \(U=3u_c\) greater than 99%. Table B.1 gives \(t\)-factors; for example, if \(\nu_{\text{eff}}=8\), \(k_{95}=2.3\) rather than 2.0.
- Reporting examples use a nominal 100 g mass standard: \(m_s=(100.02147 \pm 0.00070)\) g with \(u_c=0.35\) mg and \(k=2\) gives approximately 95% confidence; a second example uses \(k=2.26\) based on \(t\) for \(\nu=9\); a third reports \(u_c=0.35\) mg with approximately 68% confidence. An end-gauge calibration uncertainty budget example gives combined standard uncertainty \(u_c(l)=34\) nm.
Methods
- Design: consensus/guideline document, the 1994 second edition of NIST TN 1297, based on the CIPM 1981 recommendation and the ISO *Guide to the Expression of Uncertainty in Measurement*; intended for NIST measurement results.
- Data or sample: no empirical sample; illustrative examples include a nominal 100 g mass standard and an end-gauge calibration uncertainty budget.
- Main analysis: conceptual and policy guidance with formulas, including the law of propagation of uncertainty Eq. (A-3), Type A standard deviation of the mean Eq. (A-5), Type B assumed distributions, the Welch-Satterthwaite effective degrees of freedom, and \(t\)-distribution coverage factors.
Limitations
- Stated in the paper: the guidance is not NIST policy unless directly quoted; the Technical Note does not give detailed statistical techniques for Type A evaluations; Type B degrees of freedom are “more problematic”; the coverage-factor procedure is approximate and “should not be interpreted as being rigourous”; and it is generally not possible to know all uses of a measurement result.
- Stated in the paper: Type B evaluations depend on scientific judgment and available information, and Type A evaluations based on limited data are not necessarily more reliable than soundly based Type B evaluations.
- Evident from the text: this is a policy/guidance document rather than an empirical validation study, and its numerical examples are illustrative rather than generalizable results.
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41 Own interpretation · 30 Sources not found · 9 No basis given · 1 Not checked yet · 1 Own method · 1 Own result
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In the paper
“Table B.1 (to be discussed below), if ν eff = 8, k 95 = 2.3 rather than 2.0.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In the common case discussed in subsection A.4 where x i = X i and u(x i ) = s(X i ), the degrees of freedom of u(x i ) is ν = n 1.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.3
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In the paper
“To be consistent with current international practice, the value of k to be used at NIST for calculating U is, by convention, k = 2.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 6.5
What the sources say
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In the paper
“Thus the terms”
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“If m i parameters are estimated by fitting a curve to n data points by the method of least squares, the degrees of freedom of the standard uncertainty of each paramter is n m.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.3
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Under the assumption that this practice is followed, the degrees of freedom of u(x i ) may be taken to be ν i → ∞.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.3
hedgedconditional- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: It is common practice to carry out Type B evaluations in a manner that ensures underestimation is avoided.
- Rests on an assumption: When lower and upper limits are set for Type B evaluations, they are usually chosen so that the probability of the quantity lying outside these limits is extremely small.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Hence ν eff is a key factor in determining k .”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.2
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“For a combined standard uncertainty u ( y), the”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.2
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“For example, the result of a measurement after correction (see subsection 5.2) can unknowably be very close to the unknown value of the measurand, and thus have negligible error, even though it may have a large uncertainty (see the Guide [2]).”
What the sources say
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In the paper
“The best estimate of the value of the quantity is then (a + + a ) / 2 with u j = a / ⎯ √3, where a = (a + a ) / 2.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 4.6
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- Probably not a substantial claim. 49
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“There is not always a simple correspondence between the classification of uncertainty components into categories A and B and the commonly used classification of uncertainty components as”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 2.3
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In the paper
“it is imperative that the referenced documents be kept up-to-date so that they are consistent with the measurement process in current use.”
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In the paper
“In both cases, the report of uncertainty must document what was done and why.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 6.6
What the sources say
- Not matchedcites Appendix C
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In the paper
“To estimate the value of such a coverage factor 1/2 (A-5) requires taking into account the uncertainty of u c ( y), that is,”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.2
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“When this is done, the c basis for such a statement must be given.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 7.1
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In the paper
“A description of how k was chosen when k is not taken equal to 2.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 7.1
What the sources say
- Not matchedcites Appendix C
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plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The four-step procedure is included in these guidelines because it is expected to find broad acceptance internationally, due in part to its computational convenience, in much the same way that k = 2 has become the conventional coverage factor.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.1
hedgeddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Report U together with the coverage factor k used to obtain it, or report u .c”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 7.1
What the sources say
- Not matchedcites Appendix C
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Since the early 1980s, an international consensus has been developing on a uniform approach to the expression of uncertainty in measurement.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 1. Background
What the sources say
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In the paper
“The CIPM approach does not specify how the relation between k and p is to be established.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 6.4
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Commonly, u is used for reporting results of c determinations of fundamental constants, fundamental metrological research, and international comparisons of realizations of SI units.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 5.3
What the sources say
- Not matchedcites Appendix C
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plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“A detailed description of how each component of standard uncertainty was evaluated.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 7.1
What the sources say
- Not matchedcites Appendix C
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plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In principle, an uncertainty component arising from a systematic effect may in some cases be evaluated by method A while in other cases by method B (see subsection 2.2), as may be an uncertainty component arising from a random effect.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, only if quantitative and thoroughly documented statements of uncertainty accompany the results of NIST calibrations can the users of our calibration services establish their level of traceability to the U.S. standards of measurement maintained at NIST.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > FOREWORD
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: It is generally agreed that the usefulness of measurement results, and thus much of the information that NIST provides as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this case, and in other similar cases where ν ( y) is comparatively small and an interval eff of u c having a level of confidence close to a specified level is required, it is unlikely that the uncertainty of u ( y) would be c considered negligible.Instead, the small value of ν eff , and thus the uncertainty of u ( y), would probably be taken into c account when determining k p .”
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“Further, it is recognized c that international, national, or contractual agreements to which NIST is a party may occasionally require deviation from NIST policy.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 6.6
What the sources say
- Not matchedcites Appendix C
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hedgedconditional- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this regard, the interval defined by U in the second example might be a conventional confidence interval (at least approximately) if all the components of uncertainty are obtained from Type A evaluations.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 7.3
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“It should also be noted that in a 1986 recommendation [9], the CIPM requested that what is now termed combined standard uncertainty u be used”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 5.3
What the sources say
- Not matchedcites [9]
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plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The use of a single approach within the Institute rather than many different approaches would ensure the consistency of our outputs, thereby simplifying their interpretation.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > FOREWORD
hedgeddirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“However, although the procedure is based on a proven approximation, it should not be interpreted as being rigourous because the approximation is extrapolated to situations where its applicability has yet to be fully investigated.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > B.1
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Equation (A-3 ) is based on a first-order Taylor series approximation of Y = f(X 1 , X 2 , . . ., X N ) and is conveniently referred to as the law of propagation of uncertainty.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“There are national as well as international standards that discuss the characterization of test methods by interlaboratory comparisons.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.4.2
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If a standard uncertainty is obtained from a source outside of the current measurement process and the nature of its individual components are unknown (which will often be the case), it may be classified as having been obtained from a Type B evaluation.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
hedgedconditional- Asserted: passes — The authors put it forward as true.
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In the paper
“When NIST authors participate in such characterization or measurement programs, NIST policy allows for the results to be expressed as required by the relevant standards (see Appendix C, section 4).”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.4.2
What the sources say
- Not matchedcites Appendix C
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In short, both u(x i ) and u i ( y) can be viewed as components of uncertainty that give rise to the combined standard uncertainty u ( y) of the measurement result y.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“(This is an example of a situation in which all significant components of uncertainty are not taken into account.)”
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In this same vein, if the combined standard uncertainty u ( y) of the measurement result y is obtained from Type A c standard uncertainties (and covariances) only, it too may be considered Type A, even though no direct observations were”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
hedgedconditional- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In Eq. (D-1), both u(x i ) and u i ( y) can be considered components of uncertainty of the measurement result y.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plaincorrelational- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, such identification can also be given in a table which lists the components of standard uncertainty.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“A valid statement of reproducibility requires specification of the conditions changed.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus t of this Technical Note and of the p Guide and t 1 α are related by p 1 2α.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Similarly, if a combined standard uncertainty is obtained from Type B standard uncertainties (and covariances) only, it too may be considered Type B.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Clearly, the values of t p (ν ) defined in this way differ from the values of t p (ν ) defined as in this Technical Note and in the Guide, and given in Table B.1 (which is of the same form as that given in reference [10]).”
boosted- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“Many of NIST's sister national standards laboratories as well as a number of important metrological organizations, including the Western European Calibration Cooperation (WECC) and EUROMET, have adopted the approach recommended by the International Committee for Weights and Measures (CIPM) in 1981 [1] and reaffirmed by the CIPM in 1986 [2].”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 1. Background
What the sources say
- Not matchedcites [1]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
In the paper
“In particular, it elaborates upon the NIST policy regarding the SI and explains why abbreviations such as ppm and ppb and terms such as normality and molarity should not be used.”
What the sources say
- Not matchedcites [D.3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“On the other hand, a standard uncertainty known to be composed of components obtained from Type A evaluations alone should be classified as a Type A standard uncertainty, while a standard uncertainty known to be composed of components obtained from Type B evaluations alone should be classified as a Type B standard uncertainty.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In such cases the magnitude of the uncertainty ascribable to the measurement result may be significantly smaller than when that result is expressed in the relevant SI unit.”
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, if the input estimates x i are uncorrelated, Eq. (A-3) of Appendix A may be written as (D-1)”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“If a test method is employed at NIST to obtain measurement results for reasons other than those described above, it is expected that the uncertainties of these measurement results will be evaluated and reported according to section 2 of the NIST policy (see Appendix C).”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.4.2
What the sources say
- Not matchedcites Appendix C
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“In many cases a measurand Y is not measured directly, but is determined from N other quantities X 1 , X 2 , . . ., X N through a functional relation f: Y f (X 1 , X 2 , . . ., X N ).”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“As pointed out in the Guide, the result of a measurement is sometimes expressed in terms of the adopted value of a measurement standard or in terms of a conventional reference value rather than in terms of the relevant unit of the SI.”
What the sources say
- Not matchedcites Guide
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The approach to evaluating and expressing the uncertainty of a measurement result on which the NIST policy and this Technical Note are based is applicable to evaluating and expressing the uncertainty of the estimated value of a measurand that is defined by a standard method of measurement.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.4 Measurand defined by the measurement method; characterization of test methods; simple calibration D.4.1
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
None of the sources cited for this claim have been checked yet.
In the paper
“This situation is similar to the NIST policy on the use of units that are not part of the SI: the SI units must be stated first, with the units that are not part of the SI in parentheses (see subsection D.6.2).”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.1.2
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus the function f of Eq. (A-1) should express not simply a physical law but a measurement process, and in particular, it should contain all quantities that can contribute a significant uncertainty to the measurement result.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may state two separate claims as one.
In the paper
“NIST Special Publication 811, 1995 Edition [D.3], gives guidance on the use of the SI and on the rules and style conventions regarding quantity and unit symbols.”
What the sources say
- Not matchedcites [D.3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The development of the Guide is providing further impetus to the worldwide adoption of the CIPM approach.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 1. Background
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: fails — It may be too vague to check against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Execution of test methods according to these standards, both in the characterization stage and in subsequent measurement programs, often calls for the expression of uncertainties in terms of defined measures of repeatability and reproducibility.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.4.2
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Further, it views the concept of precision as encompassing both repeatability and reproducibility (see subsections D.1.1.2and D.1.1.3)”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > D.1.2
What the sources say
- Not matchedcites [D.2]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Included among the quantities X i are corrections (or correction factors) as described in subsection 5.2, as well as quantities that take into account other sources of variability, such as different observers, instruments, samples, laboratories, and times at which observations are made (e.g., different days).”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The CIPM approach is based on Recommendation INC-1 (1980) of the Working Group on the Statement of Uncertainties [3].”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 1. Background
What the sources say
- Not matchedcites [3]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Equally important, the CIPM approach has come into use in a significant number of areas at NIST and is also becoming accepted in U.S. industry.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > 1. Background
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“If the standard uncertainty from an outside source is known to be composed of components obtained from both Type A and Type B evaluations but the magnitudes of the individual components are unknown, then one may indicate this by using (A,B) rather than (B) in a table such as D.1.”
§ Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results > Additional information
hedgedconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“As pointed out in the Guide, the t-distribution is often tabulated in quantiles.”
What the sources say
- Not matchedcites Guide
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper relies on this without support.
In October 1992, a new policy on expressing measurement uncertainty was instituted at NIST.
“In October 1992, a new policy on expressing measurement uncertainty was instituted at NIST.”
The paper relies on this without support.
In general, the result of a measurement is only an approximation or estimate of the value of the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.
“In general, the result of a measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, that is, the measurand, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty.”
The paper relies on this without support.
Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.
“Although the vast majority of NIST measurement results are accompanied by quantitative statements of uncertainty, there has never been a uniform approach at NIST to the expression of uncertainty.”
The paper relies on this without support.
It is generally agreed that the usefulness of measurement results, and thus much of the information that NIST provides as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.
“It is generally agreed that the usefulness of measurement results, and thus much of the information that we provide as an institution, is to a large extent determined by the quality of the statements of uncertainty that accompany them.”
The paper relies on this without support.
The Guide represents the current international view of how to express uncertainty in measurement based on the CIPM approach.
“Although the Guide represents the current international view of how to express uncertainty in measurement based on the CIPM approach, it is a rather lengthy document.”
The authors state this as an assumption.
A correction (or correction factor) is applied to compensate for each recognized systematic effect that significantly influences the measurement result, and every effort has been made to identify such effects.
“It is assumed that a correction (or correction factor) is applied to compensate for each recognized systematic effect that significantly influences the measurement result and that every effort has been made to identify such effects.”
The paper relies on this without support.
The reliability of evaluations of components of uncertainty depends on the quality of the information available.
“Because the reliability of evaluations of components of uncertainty depends on the quality of the information available, it is recommended that all parameters upon which the measurand depends be varied to the fullest extent practicable so that the evaluations are based as much as possible on observed data.”
The paper relies on this without support.
For some commercial, industrial, and regulatory applications of NIST results, a measure of uncertainty that defines an interval about the measurement result within which the value of the measurand is confidently believed to lie is often required.
“for some commercial, industrial, and regulatory applications of NIST results (e.g., when health and safety are concerned), what is often required is a measure of uncertainty that defines an interval about the measurement result y within which the value of the measurand Y is confidently believed to lie.”
The authors state this as an assumption.
The possible estimated values of the standard are approximately normally distributed with approximate standard deviation u_c.
“Since it can be assumed that the possible estimated values of the standard are approximately normally distributed with approximate standard deviation u , the c”
The paper relies on this without support.
Some users of NIST measurement results may automatically interpret U = 2u_c and u_c as defining intervals with levels of confidence of 95 percent and 68 percent, respectively.
“Some users of NIST measurement results may automatically interpret U = 2u and u as quantities that c c define intervals having levels of confidence corresponding to those of a normal distribution, namely, 95 percent and 68 percent, respectively.”
The paper relies on this without support.
It is not possible to know in detail all uses to which a particular NIST measurement result will be put.
“In general, it is not possible to know in detail all of the uses to which a particular NIST measurement result will be put.”
The paper relies on this without support.
It is common practice to carry out Type B evaluations in a manner that ensures underestimation is avoided.
“However, it is common practice to carry out such evaluations in a manner that ensures that an underestimation is avoided.”
The paper relies on this without support.
When lower and upper limits are set for Type B evaluations, they are usually chosen so that the probability of the quantity lying outside these limits is extremely small.
“For example, when lower and upper limits a and a + are set as in the case discussed in subsection A.5, they are usually chosen in such a way that the probability of the quantity in question lying outside these limits is in fact extremely small.”
The paper relies on this without support.
Precision is often taken to mean simply repeatability.
“Nevertheless, precision is often taken to mean simply repeatability.”
The paper relies on this without support.
It will take some time before the meanings of standard uncertainty, combined standard uncertainty, expanded uncertainty, and their relative forms become well known.
“However, since it will take some time before the meanings of these terms become well known, they should be defined at the beginning of a paper or when first used.”
Citations
Cites
Addelman, S., Box, G. E. P., Hunter, W. G., & Hunter, J. S. (1979) · Technometrics · doi:10.2307/1267766 · Cited by 6,753
Natrella, M. G. (1963) · doi:10.6028/nbs.hb.91 · Cited by 593
The Statistical Analysis of Experimental Data.
David, H. T., & Mandel, J. (1966) · Journal of the American Statistical Association · doi:10.2307/2282811 · Cited by 436
Realistic evaluation of the precision and accuracy of instrument calibration systems
Eisenhart, C. (1963) · Journal of Research of the National Bureau of Standards Section C Engineering and Instrumentation · doi:10.6028/jres.067c.015 · Cited by 200
Guide for the use of the International System of Units (SI)
Taylor, B. N., & Taylor, B. N. (1995) · doi:10.6028/nist.sp.811e1995 · Cited by 87
Self-citationUncertainty, Calibration and Probability
Dietrich, C. F. (2017) · Routledge eBooks · doi:10.1201/9780203734759 · Cited by 60
The Statistical Analysis of Experimental Data
Mandel, J., & Mansfield, J. E. (1965) · Physics Today · doi:10.1063/1.3047724 · Cited by 21
Giacomo, P. (1987) · Metrologia · doi:10.1088/0026-1394/24/1/007
Research works printed but not linked: 5
- CIPM, BIPM Proc.-Verb. Com. Int. Poids et Mesures 54, 14, 35 (1986) (in French);
- CIPM, BIPM Proc. Verb. Com. Int. Poids et Mesures Measurement Results, NIST Technical Note 1297, 49, 8-9, 26 (1981) (in French);
- CIPM, BIPM Proc.-Verb. Com. Int. Poids et Mesures 54, 14, 35 (1986) (in French);
- R. Kaarls, "Rapport du Groupe de Travail sur l'Expression des Incertitudes au Comité International des Poids et Mesures," Proc.-Verb. Com. Int. Poids et Mesures 49, A1-A12 (1981) (in French);
- I, H. H. Ku, Editor (U.S. Government Printing Office, Washington, DC, 1969), pp. 21-48.
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Metadata
- Authors
- Taylor, B. N.
- Affiliations
- National Institute of Standards and Technology (US)
- Corresponding author
- Taylor, B N
- ORCID
- Taylor, B N
- Venue
- National Institute of Standards and Technology, NIST Technical Note 1297
- Publisher
- National Bureau of Standards
- Published
- 1994
- OpenAlex
- W4300497458
- Cited by
- 2,833
- References
- 7
- Citations by year
- 2026: 82 · 2025: 104 · 2024: 109 · 2023: 110 · 2022: 133 · 2021: 141 · 2020: 156 · 2019: 141 · 2018: 150 · 2017: 135 · 2016: 116 · 2015: 105 · 2014: 103 · 2013: 100 · 2012: 112
- Type
- report
- Language
- en
- Open access
- gold
- doi.org
- Topics
- Physical Sciences › Physics and Astronomy › Instrumentation › Scientific Measurement and Uncertainty Evaluation
- Physical Sciences › Engineering › Mechanical Engineering › Advanced Measurement and Metrology Techniques
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Keywords
- measurement uncertainty, uncertainty analysis, uncertainty expression, measurement results, NIST guidelines
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