chemical thermodynamics of neptunium and plutonium - U.S. ...

C.2 Two or more independent source data 825under Section C.2.1. It can be seen from Eq. (C.4) thatσ Xis directly dependent onthe absolute magnitude of the σ i values, and not on the dispersion of the data pointsaround the mean. This is reasonable because there are no discrepancies among the X i ,and because the σ i values already represent the 95% confidence level. The selecteduncertainty σ Xwill therefore also represent the 95% confidence level.In cases where all the uncertainties are equal σ i = σ ,Eqs.(C.3) and(C.4) reduceto Eqs. (C.5)and(C.6).X = 1 Nσ X=σ√NN∑X ii=1(C.5)(C.6)Example C.1:Five data sources report values for the thermodynamic quantity X. The reviewer hasassigned uncertainties that represent the 95% confidence level as described in SectionC.1.i X i σ i1 25.3 0.52 26.1 0.43 26.0 0.54 24.85 0.255 25.0 0.6According to Eqs. (C.3)and(C.4), the following result is obtained:X = (25.3 ± 0.2)The calculated uncertainty σ X= 0.2 appears relatively small but is statistically correct,for the values are assumed to follow a Gaussian distribution. As a consequence ofEq. (C.4), σ Xwill always come out smaller than the smallest σ i . Assuming σ 4 = 0.10instead of 0.25 would yield X = (25.0 ± 0.1), andσ 4 = 0.60 would result in X =(25.6±0.2). In fact, the values (X i ±σ i ) in this example are at the limit of consistency,that is, the range (X 4 ± σ 4 ) does not overlap with the ranges (X 2 ± σ 2 ) and (X 3 ± σ 3 ).There might be a better way to solve this problem. Three possible alternatives seemmore reasonable:i. The uncertainties σ i are reassigned because they appear too optimistic after furtherconsideration. Some assessments may have to be reconsidered and the uncertaintiesreassigned. For example, multiplying all the σ i by 2 would yieldX = (25.3 ± 0.3).