Statistics Meeting Book (May 15, 2019)

pC metamer: Report

AOAC International Interlaboratory Study Workbook

Version:

4.1

Blind (Unmatched) Replicates Study Reported Values

Seq.

Item

Symbol

Value 95% LCL 95% UCL

Name of study: Date of study: Sample/Matrix ID: Analyte:

JAOAC (2012) 95(2):411-418

1-Mar-2013

C02

OBPCP

Factor for Units of measurement: Metamer to analyze (C or pC): True value (blank if not known):

0.01

pC

1 Total number of laboratories 2 Total number of replicates

p

13 26

Sum(n(L)) XBARBAR

3 Overall mean of all data (grand mean) 4 Repeatability standard deviation 5 Interlaboratory standard deivation 6 Bias estimate (Measured - True) DERIVED VALUES: 7 Reproducibility standard deviation 8 Root-mean-square-total-error 9 Repeatability relative standard deviation 10 Reproducibility relative standard deviation

3.0226 3.0087 3.0364 0.00563 0.00409 0.00908 0.02370 0.01699 0.03912

s(r) s(L)

b

s(R) rmse

0.02436

RSD(r) RSD(R)

11 HORRAT value

(RSD(r) and RSD(R) are not appropriate for pC data, as they correspond directly to s(r) and s(R) here.)

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copyright 2018 by Least Cost Formulations, Ltd., all rights reserved.

Compare results for C and pC metamers

Metamer Quantity Value

RSD(r)

RSD(R)

C

1.34% 5.52%

pC pC

s(r)

0.00563 1.30%

s(R)

0.02370

5.46%

• RSD(r) for C metamer = 2.303 x s(r) for pC metamer. • RSD(R) for C metamer = 2.303 x s(R) for pC metamer. • No need for RSD(r) and RSD(R) if fit using pC metamer. • RSD(r) and RSD(R) from pC metamer values are unbiased and efficient estimators for these quantities, unlike those derived from C metamer values. • 2.303 = ln(10), an artifact of using log 10 instead of ln

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copyright 2018 by Least Cost Formulations, Ltd., all rights reserved.