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Fonterra Co-operative Group
Page 13
of confidence, the probability (p-value) of the observation under the null hypothesis is assessed. The
degrees of freedom (DF) can be estimated using the Satterthwaite approximation (equation 9) [1].
equation 8
equation 9
where:
݀
= mean of the differences between measured results and certified value
s
m
= standard deviation of differences between measured results and certified value
n
m
= number of replicate analyses of CRM
U
CRV
= uncertainty of certified reference value
k = coverage factor used for calculating expanded uncertainty
n
CRV
= DF
CRV
-1, calculated for k, using a 2-sided t distribution at α = 0.05. An empirical model for
doing this calculation was obtained by fitting 1/DF vs log t
0.05
to a 4th order polynomial for integral
values of DF from 2–100 DF. The maximum relative error over the fitted range was 0.06%.
Separate repeat analyses of NIST 1849a CRM for vitamin D
3
were included as part of various other
validation experiments (Table 12). The
p
-value (0.25) indicates at the 0.05% level of confidence, no bias
between measured results and certified value can be shown. Bias against a CRM is not defined as a
parameter within the SMPR.
Table 12: Results for bias experiment against NIST1849a
Parameter
Value
Certified Value (μg hg
-1
)
11.1
Uncertainty (μg hg
-1
)
1.7
Certified Range (μg hg
-1
)
9.4
–
12.8
Coverage Factor (k):
2
Degrees of Freedom (DF
CRV
)
60
Mean
10.1
Standard Deviation
0.53
Number of Replicates (n)
13
95% Confidence Interval (μg hg
-1
)
9.8
–
10.4
T
stat
1.165
Degrees of Freedom
63.92
p-value
0.25
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VitD-18 (February 2016)
FOR ERP USE ONLY
DO NOT DISTRIBUTE