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Exercise 7: Accuracy and precision

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Origin of the error :Accuracy and precision

• Systematic (not random)– bias– impossible to be corrected accuracy

• Random– can be evaluated by statistics precision

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Good PrecisionGood Accuracy

Poor PrecisionGood Accuracy

Good PrecisionPoor Accuracy

Poor PrecisionPoor Accuracy

Gold Standard

Silver Standard

Off-Base Model

Hit or Miss Model

Bias and precision

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Accuracy

Closeness of determined value to the true value.

The acceptance criteria is mean value 15% deviation from true value.

At LOQ, 20% deviation is acceptable.

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The accuracy is calculated using the followingequation :

The accuracy at each concentration level mustbe lower than 15% except a LOQ (20%)

Accuracy

valuelTheoritica

valuelTheoriticavalueObservedAccuracy

(%)

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PrecisionThe closeness of replicate determinations of a sample by an assay.

The acceptance criteria is 15% CV. At LOQ, 20% deviation is acceptable.

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Repeatability (r)

Agreement between successive measurements on the same sample under the same conditions

Reproducibility (R)

The closeness of agreement between resultsobtained with the same method under different conditions

PrecisionPrecision

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Precision… Considered at 3 Levels

• Repeatability

• Intermediate Precision

• Reproducibility

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Repeatability

• Express the precision under the same

operating conditions over a short interval of

time.

• Also referred to as Intra-assay precision

– (within day)

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Intermediate Precision

• Between-run, between day repeatability … also named

intermediate precision, which measures precision

with time (often days) and may involve different

analysts, equipment, reagents…

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Precision: measurement

• Should be measured using a minimum of 5 determinations per concentration– A minimum of 3 concentrations in the range

of expected concentrations– The precision at each concentration should

not exceed 15% except for the LOQ (20%)

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Raw data

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Precision: measurement

• for a single measurement : CV(%)

• for intra-day and inter-day precision ANOVA

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Variance of intermediate precision

222withinbetweenTotal

2between

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Estimation of the two components of the variance

• we need a proper statistical model that is the one-way nested analysis of variance model given as :

ijiij wbY With i=1,2..n days and j=1,2,…replicates; in this equation, Yij are observed values, μ is the true value of the common stock solution

being assayed in this experiment, bi is a random component for between-days variation

and wij is another random component for within-day variation. The variance of bi is

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ANOVA

• Allows an estimation of the 2 variance terms

– inter-day mean square (BMS)

– intra-day mean square (WMS)

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The exercise consist to compute these variances

• By hand

• Using an ANOVA (Excel)

• With Analyse- it

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The limit of quantification (LOQ)

• LOQ is the lowest amount of analytes in a sample which can be determined with defined precision and accuracy

• LOQ : 20%

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Limit of quantification (LOQ)

• The lowest standard on the calibration curve is the LOQ if:– no interference is present in the blanks at

retention time of the analyte for this concentration

– the response (analyte peak) has a precision of 20% and accuracy 80-120%

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Three analytical areasThree analytical areas

1 2 3

Xb

not detected Area of detectio

n

Area of quantification

or CV<20%

LOD LOQ