Uncertainty in Microbiological counting

T&M 2011 Workshops 19 – 20 September

Steve Sidney

Introduction

• Uncertainty of Measurement (UoM)

• Approaches

• A2LA G108 Guide

What is measurement uncertainty ?

• Measurement results are never exact

• It is a measure for the accuracy of the result

• Measurement uncertainty is derived from standard deviations

• Definition: Measurement uncertainty is ”A parameter associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand” (VIM1 and GUM [1])

Definition

• Measurement uncertainty is ”A parameter associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand” (VIM and GUM)

Sources of uncertainty

• There are many possible sources of uncertainty, e.g. sampling, instrument drifts and calibration, homogenisation and dilution effects, human factors, environmental effects, etc.

How to calculate

• Bottom up

Guide to the expression of the uncertainty in measurement – GUM

• To down

Take sufficient measurements under changed circumstances

Pro’s and Con’s

• GUM

– Model

– Quantify the effect of all the sources

– Can be demonstrated

• Top down

– Can be difficult to control the changes

A2LA G108

• Various examples

• Eg1 & 2

Procedure based on ISO TS19036 (Animal Feeding – Guide on UM)

• Eg3

Procedure based on ISO 5725-2 ( Accuracy of measurement methods – Part 2)

A2LA G108

MU Source Type of Replicate

Reproducibility Recovery True Plate

Random Error X X X X

Counting Error X X X X

Dilutions X X X

Environment X X

Equipment X X

Analyst X X

A2LA G108

• Use control samples NOT test samples

• Analysed through all steps of method under the following conditions

– Different days

– In duplicate, different analysts

– Different equipment ( eg balances, pipettors..)

– Different media / reagents

• Matrix assumed to be the same

Example 1

• Transform raw data to log10 (duplicates)

• Calculate mean of all replicates

• Calculate the differences

• Square the differences

• Add differences and divide by 2n (n= total number of pairs)

• Take square root (pooled reproducibility SD)

Example 1

• Convert SD into RSD, dividing by mean in step 2

• Apply coverage factor (k=2 for 95%) by multiplying by 2

Raw Data (actual CFU

recovered) – 1st Replicate

Log10 Value

Raw Data (actual CFU

recovered) – 2nd Replicate

Log10 Value

Difference between

Replicates (log10 Value)

Difference between

Replicates Squared

131 2.1173 142 2.1523 -0.035 0.00123

69 1.8388 90 1.9542 -0.1154 0.01332

45 1.6532 76 1.8808 -0.2276 0.0518

40 1.6021 55 1.7404 -0.1383 0.01913

31 1.4914 20 1.301 0.1903 0.03623

33 1.5185 40 1.6021 -0.0835 0.00698

31 1.4914 62 1.7924 -0.301 0.09062

37 1.5682 50 1.699 -0.1308 0.0171

186 2.2695 167 2.2227 0.0468 0.00219

218 2.3385 258 2.4116 -0.0732 0.00535

200 2.301 243 2.3856 -0.0846 0.00715

39 1.5911 54 1.7324 -0.1413 0.01997

217 2.3365 180 2.2553 0.0812 0.00659

119 2.0755 133 2.1239 -0.0483 0.00233

28 1.4472 46 1.6628 -0.2156 0.04648

106 2.0253 112 2.0492 -0.0239 0.00057

107 2.0294 89 1.9494 0.08 0.0064

45 1.6532 62 1.7924 -0.1392 0.01937

98 1.9912 128 2.1072 -0.116 0.01345

240 2.3802 220 2.3424 0.0378 0.00143

Calculations

• Mean of 40 results (1, 9219)

• Summed differences / 2n (n=20) (0,00919)

• Square root of summed diff’s ( 0,0959)

• RSD (Mean / sq rt of summed diff’s = 0,0499)

• Multiply by k=2 (0,0998)

Calculate lab result

• Example – 150 CFU

• 150 in log10 = 2,1761

• Expanded uncertainty = 2,1761 * 0,0998 = 0,2172 (log value)

• Add and subtract and take anti-log

• Interval 1,9589 – 2,2933 ( 90 – 248 CFU)