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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