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Food Microbiology 30 (2012) 362e371

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Food Microbiology

journal homepage: www.elsevier .com/locate/ fm

The contribution of sampling uncertainty to total measurement uncertaintyin the enumeration of microorganisms in foods

Basil Jarvis a,*, Alan J. Hedges b, Janet E.L. Corry c

aRoss Biosciences Ltd, Upton Bishop, Ross-on-Wye, HR9 7UR, UKbUniversity of Bristol, School of Cellular and Molecular Medicine, University Walk, Bristol, BS8 1TD, UKcUniversity of Bristol, Department of Clinical Veterinary Science, Langford, Bristol, BS40 5DU, UK

a r t i c l e i n f o

Article history:Received 9 September 2011Received in revised form4 January 2012Accepted 5 January 2012Available online 14 January 2012

Keywords:Measurement uncertaintySampling uncertaintyFood microbiologyColony countsMicrobial distributionsAnalysis of variance

* Corresponding author. Tel.: þ44 (0) 1989 720 698E-mail address: basil.jarvis@btconnect.com (B. Jar

1 Variance is the point estimate of sample variance caset ¼ the log10 transformed colony counts obtained fortaken froma single production lot of a product, a lot beinproduced under identical conditions during a definebetween sample variance ¼ estimated variance of the lfor replicate sample units; within sample variance ¼ etransformed colony counts for replicate sub-samplesunits; CVr% ¼ percentage repeatability coefficient ofreproducibility coefficient of variation.

0740-0020/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.fm.2012.01.002

a b s t r a c t

Random samples of each of several food products were obtained from defined lots during processing orfrom retail outlets. The foods included raw milk (sampled on farm and from a bulk-milk tanker), sproutedseeds, raw minced meat, frozen de-shelled raw prawns, neck-flaps from raw chicken carcasses andready-to-eat sandwiches. Duplicate sub-samples, generally of 100 g, were examined for aerobic colonycounts; somewere examined also for counts of presumptive Enterobacteriaceae and campylobacters. Afterlog10-transformation, all sets of colony count data were evaluated for conformity with the normaldistribution (ND) and analysed by standard ANOVA and a robust ANOVA to determine the relativecontributions of the variance between and within samples to the overall variance. Sampling varianceaccounted for >50% of the reproducibility variance for the majority of foods examined; in many cases itexceeded 85%. We also used an iterative procedure of re-sampling without replacement to determine theeffects of sample size (i.e. the number of samples) on the precision of the estimate of variance for one of thelarger data sets. The variance of the repeatability and reproducibility variances depended on the number ofreplicate samples tested (n) in a manner that was characteristic of the underlying distribution. The resultsare discussed in relation to the use of measurement uncertainty in assessing compliance of results withmicrobiological criteria for foods.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction1

Measurement uncertainty is recognized internationally to bean important factor in any form of analysis (Eurachem, 2000, 2007;Anon., 2004; 2006). It comprises two parts: analytical uncertaintyand sampling uncertainty, both aspects being well characterized inthe physical and chemical sciences. In this work we have sought toprovide comparative estimates for the extent of both analyticaland sampling uncertainty based on quantitative microbiologicalexaminations of replicate samples from a range of commercial foods.

; fax: þ44 (0) 1989 720 154.vis).lculated froma data set; a dataa set of replicate sample unitsg defined as a quantity of foodd time period (ICMSF, 2002);og-transformed colony countsstimated variance of the log-taken from individual samplevariation; CVR% ¼ percentage

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In microbiology, analytical measurement uncertainty providesan estimate of the precision of a result determined by a specificmethod carried out within one or more laboratories and by one ormore analysts (Anon., 2006; Augustin and Carlier, 2006; Corry et al.,2007b; Jarvis et al., 2007a,b). Microbiological examinations aredone on defined quantities of a food taken from randomly drawnsamples that are intended to be representative of a lot of raw orprocessed food (ICMSF, 2002). Although there is much evidence forthe heterogeneous distribution of microorganisms in foods andother matrices, relatively little attention has been paid to assess-ment of its effect on the estimated uncertainty of microbiologicalcounts (Reinders et al., 2003; ILSI, 2010; Jarvis and Hedges, 2011).It has long been recognised that the distribution of microorganismsin natural matrices does not conform to the ND. Whilst in simplesuspension the distribution of microorganisms generally conformswell to a Poisson series, there are many cases where this is not so.In solid and particulate substrates the distribution of microorgan-isms is complex (Jones et al., 1948; Jarvis, 2008; Gonzales-Barronet al., 2010); even in liquid foods, such as milk, the distributionmay not be homogeneous due to the presence of clumps and chainsof organisms (Wilson, 1935). Generally, the lognormal statistical

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371 363

distribution adequately describes the heterogeneity of microbialcolony counts made on foods (Kilsby and Pugh, 1981; Corradiniet al., 2001; Reinders et al. (2003); Montville and Schaffner, 2004;Bahk et al., 2007; Park et al., 2008; ILSI, 2010), although Kilsby andBaird-Parker (1983) found that about 8% of samples examineddid not conform to this distribution and other distributions maybe more relevant in particular circumstances (see for example Parket al., 2008; Mussida and Butler, 2011). Jongenburger et al. (2010)and Mussida and Butler (2011) have demonstrated the impor-tance of heterogeneity in the estimation by plating of low levels ofCronobacter spp. in infant formulae. However, these studies wereconcerned with the precision of determination of low colonycounts and their use in estimation of prevalence, rather than themeasurement of the within and between sample variation thatreflects sampling uncertainty.

Ramsay et al. (2001) and Lyn et al. (2002, 2003) showedthat estimates of sampling uncertainty for chemical contaminantsin foodstuffs are often larger than the estimates of analyticalmeasurement uncertainty. Although different food matrices havebeen shown to affect such estimates (Anon., 2006), the data do notprovide an estimate of the component variance between or withinsamples. We showed previously (Jarvis et al., 2007a) that theestimated sampling uncertainty contributed two-thirds to the totalmeasurement uncertainty of aerobic colony counts onprawns,whichsuggests that sampling uncertainty is likely to exceed analyticaluncertainty in the enumeration of microbes in other foods. Ignoringthe impactof sampling uncertainty leads to underestimates of overalluncertainty and may affect adversely the assessment for complianceof food materials with legislative and commercial microbiologicalcriteria.

Our main objective was to investigate whether the number ofsamples needed to increase precision without incurring unaccept-able costs of analysis is similar in chemical and microbiologicalanalyses. Initially, we evaluated the use of alternative procedures forpreparation of primary homogenates of foods and the effects of thequantity of sample examined on the extent of variation in microbialcolony counts (Corry et al., 2010). In the second stage (Jarvis andHedges, 2011), we investigated statistical modelling procedures to

Table 1Summary of colony counts on 10 samples (20 prawn samples) of each of the foods exam

Test Group Product Number ofdata points

Colony count (log10 cfu/g or m

Mean Median Min Q

2

Aerobes Milk, ex-farm 40 3.05 3.04 2.91Milk, ex-tanker 40 5.09 5.05 4.56Sprouted seeds 40 7.57 7.57 7.41Chicken skin, F1b 16 4.86 4.86 4.40Chicken skin, F2b 20 4.84 4.78 4.55Prawns 80 3.53 3.53 2.98Minced meat 40 6.06 6.20 4.94Sandwich, filling 40 6.40 6.30 5.62Sandwich, entire 40 5.72 5.77 5.09

Enterobacteriaceae Milk, ex-farm 40 <1.4 <1.4 <1.4 <

Milk, ex-tanker 40 2.80 2.76 2.23Sprouted seeds 40 6.80 6.81 6.61Chicken skin, F1b 16 3.98 3.98 3.40Chicken skin, F2b 20 4.02 4.00 3.74Prawns 80 <1.4 <1.4 <1.4 <

Sandwich, filling 36 4.91 4.89 3.92Sandwich, entire 40 3.79 3.77 2.70

Campylobacters Chicken skin, F1b 16 3.20 3.21 2.85Chicken skin, F2b 20 1.95 1.92 1.44

a Variance refers to the total variance of all colony counts for each set of samples examb F1 and F2 refer to different flocks of chickens processed sequentially.c Significant at p < 0.05.d The number of values lying outside the 95% CI of the ND probability plot. We note t

determine the number of samples to be tested beyond whichprecision increased only slowly. Here, we report our work withreplicate samples, collected either during production or at retail,to assess the extent of variations in microbial distribution withinindividual lots of food. The uncertainty of qualitative (i.e. presence/absence) methods of analysis for pathogenic organisms is outsidethe scope of the present work but has been studied by Jongenburgeret al. (2011). Neither were we concerned with tests on foods havingmicrobial loads close to the likely limit of detection, which mighthave yielded left-censored data, for which special methods ofstatistical analysis are desirable (Shorten et al., 2006; Lorrimer andKiermeyer, 2007).

2. Materials and methods

2.1. Experimental protocol

Ten, occasionally 20, samples of each product were drawnrandomly from individual production or retail lots, using a randomsampling schedule and recording the sequence in which sampleswere drawn. Foods examined are shown in Table 1. All samples weretransferred chilled to the laboratory and examined after overnightstorage at 2 � 1 �C, or after storage at �20 �C for frozen products.

2.2. Microbiological procedures

2.2.1. Sample preparationFor any one sample set, the individual samples were re-

randomised before examination. The general test protocol (Fig. 1),based on Corry et al. (2010), was used for all foods unless otherwisestated. A 100 g sub-sample of a sample unit was aseptically weighedinto the gauze filter bag inside a sterile plastic Stomacher-400 bag.One hundred ml of chilled diluent was added before treatment for30 s in a Pulsifier� (Microgen Bioproducts Ltd, Camberley, UK).Twenty g of the initial suspension, taken from outside the filterbag, were added to a further 80 ml of diluent and pulsified fora further 30 s to give a 10�1 dilution of the original sub-sample. Thisprocedure was repeated on a second 100 g sub-sample. Maximum

ined.

l) Skewness Kurtosis Number ofoutliers to NormalProbability Plotd

uartiles Max Variancea

5% 75%

2.97 3.11 3.25 0.01 1.7 7.38c 64.79 5.30 5.83 0.13 0.6 �0.41 27.49 7.65 7.74 0.01 0.32 �0.51 14.62 5.02 5.46 0.107 0.47 �0.36 04.62 4.94 5.38 0.066 0.9 �0.02 03.39 3.69 4.11 0.053 �1.28 5.78c 45.93 6.41 6.54 0.235 �1.24 0.55 115.92 6.77 7.79 0.325 0.62 �0.06 25.34 6.02 6.35 0.134 0.02 �1.07 01.4 <1.4 <1.4 e e e e

2.58 3.10 3.27 0.093 0.11 �0.75 06.76 6.88 6.97 0.01 �0.33 �0.06 03.88 4.15 4.52 0.087 �0.13 0.33 03.88 4.11 4.47 0.045 0.78 0.8 01.4 <1.4 <1.4 e e e e

4.40 5.23 5.83 0.277 0.03 �0.75 03.36 4.10 5.65 0.473 0.89 1.41 43.13 3.31 3.38 0.021 �1.07 1.18 01.69 2.25 2.50 0.136 0.15 �0.96 0

ined.

he expectation that 1 in 20 values may be outliers by this criterion.

Fig. 1. Schematic of the general protocol used to produce dilutions for examination by colony counting.

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371364

Recovery Diluent (MRD, Oxoid CM 733) was used for all productsexcept minced meat and chicken neck-flaps, for which MRD plus0.5% Tween-80 (Sigma) (MRDT) was used. The initial 1 in 10 dilu-tions were further diluted serially to 10�5 in MRD for each duplicatesub-sample. Duplicate volumes, 100 ml, of each dilutionwere spreadon the surface of 90 mm diameter plates of appropriate media. Thisprocedure was then repeated for each of the other samples.

2.2.2. Food samples2.2.2.1. Raw milk. Ten 100 ml volumes of milk were collected atirregular intervals over a period of about 10 min into sterile dispos-able plastic bottles from the bulk milk tank of a large dairy farmduring loading into a road tanker. In the UK, farm milk is collectedevery 48 h, so the refrigerated milk tank on the farm containedthe combined outputs from four separatemilking sessions before thesamples were collected. The agitator in the farm bulk tank (temper-ature 4 �C) was run for 5 min before sample taking commenced.

A second set of ten 300 ml milk samples was collected in steriledisposable pots over a period of about 30 min during discharge ofbulkmilk from a different road tanker at a small cheese factory. Thisbulk milk had been collected from a number of dairy farms. Thesamplingwas done at irregular intervals during the discharge of themilk into the silo by means of a sterilised sampling tap on the line.

Before testing in the laboratory, each sample unit of milk wasmixed thoroughly by inverting and shaking 25 times through an arc of30 cm (Anon., 1999), and neither the primary nor secondary dilutionswere pulsified. Aerobic colony counts and Enterobacteriaceae colonycounts were done.

2.2.2.2. Mixed sprouted seeds. We examined commercial packsof mixed sprouted seeds because we anticipated that the resultsmight be more heterogeneous thanwith a single seed type. Sampleswere obtained from a processing plant where seeds are sproutedunder controlled conditions of moisture and temperature. Tensamples, taken from the packaging line at random intervals duringa period of about 1 h (a production lot), consisted of a mixture of fivetypes of sprouts (mung beans, green and brown lentils, aduki beansand chickpeas). The sprouts had been grown separately, washed inpotablewater, centrifugally de-watered andmixed before automated

packaging in 250 g plastic bag retail packs. Colony counts of aerobesand Enterobacteriaceae were done.

2.2.2.3. Frozen raw prawns. A total of 20 samples of frozen de-shelled raw prawns were taken from a single imported consign-ment of 1600 � 12 kg cases (19 tonnes). Approximately 500 gwas removed from each case into a sterile plastic bag using a sterileplastic scoop. Aerobic colony counts and Enterobacteriaceae colonycounts were done.

2.2.2.4. Minced meat. Ten pre-packaged 500 g retail packs ofmincedmeat were obtained at irregular intervals over a productionperiod of 1 h from a single processing lot in a commercial meatplant. Aerobic colony counts were done.

2.2.2.5. Chicken neck-flaps. Neck-flaps are the loose pieces ofskin that remain at the neck end of a processed chicken carcass afterevisceration and removal of the neck, gizzard and crop. A slightlydifferent protocol was used for these. A sample unit consisted ofeight neck-flaps cut from consecutive chicken carcasses on a processline immediately before theyentered the air chiller; ten sample unitswere collected at irregular intervals during the processing of a singleflock (about 30min). Flock 1was the first flock processed on the day,cleaning and disinfection having been done overnight. A further setof samples was then taken from a second flock.

From each sample unit, three or four neck-flaps were placedaseptically in the filter bag of a Stomacher-400 bag and weighed(the weight varied between 80 and 120 g), an equal weight ofdiluent (MRDT) was added and the mixture was pulsified for 30 s.This treatment did not appreciably macerate the neck-flaps; 20 mlof the diluent taken from outside the filter bag was then dilutedwith 80 ml MRD to give an overall 1 in 10 dilution, from whichfurther dilutions were prepared. This procedure was repeated fora second sub-sample of neck-flaps from the same sample unitand for each of the other sample units. Colony counts were done fortotal aerobes, Enterobacteriaceae and campylobacters.

2.2.2.6. Pre-packaged sandwiches. Sandwiches were examined ontwo occasions, once with, and once without, the bread. We were

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371 365

unable to take samples of sandwiches from a commercial produc-tion line, so arrangements were made with a retailer to samplefreshly delivered stock. Ten retail packs were obtained on each oftwo occasions. Each pack comprised one sandwich consisting oftwo rounds of bread with a ‘Chicken Caesar’ filling (cooked chicken,lettuce, tomato and Caesar mayonnaise) cut diagonally into trian-gular halves. On the first occasion, we separately examined onlythe filling (ca. 50 g) from each half sandwich. On the secondoccasionwe again examined each half of each sandwich separately,but included the bread (total sample size ca. 100 g). Aerobic andEnterobacteriaceae colony counts were done.

2.2.3. Microbiological media and incubation conditionsSurface colony counts were done by spreading decimal dilutions

on pre-poured 90 mm diameter agar plates. Aerobic colony countswere done on Plate Count agar (PCA; Oxoid CM 0325) incubatedat 30 �C for 3 days. Enterobacteriaceae were counted on Violet RedBile Glucose agar (VRBG; Oxoid CM0485) incubated at 37 �C for 24h(except for milk where the plates were incubated at 30 �C for 24 h).All purple/red colonies were counted as ‘presumptive’ Enter-obacteriaceae without further confirmation. Campylobacter colonycounts were done on mCCDA (modified cefaperazone charcoaldeoxycholate agar; Oxoid CM739 plus SR155) plates incubatedat 41.5 �C for 48 h in a cabinet (Don Whitley Mark 2�, withoutcatalyst) with microaerobic atmosphere (5% O2: 10% CO2: 85% N2).Representative colonies withmorphology typical for Campylobacterspp. were checked for oxidase production, lack of growth aerobi-cally on blood agar at 41.5 �C for 48 h and positive reaction usingMicrogen Campy latex agglutination test (Microgen Bioproducts,Camberley, UK).

2.2.4. Derivation of colony countsColonies showing the expected colonial characteristics

on each plate were counted and their numbers recorded. Thederived colony counts (as cfu/g or/ml) were determined usingthe weighted mean procedure (Farmiloe et al., 1954) and tookinto account the volume of inoculum, the dilution factor andthe actual weights of the sub-sample used in preparation of the10�1 dilution.

2.3. Statistical procedures

Calculations were done with SAS software (SAS� (2002e2008);SAS Institute Inc., Cary, NC, USA) and Analyze-It� for Excel (Analyse-It Software Ltd, Leeds, UK); all colony counts were log10-transformedbefore statistical analysis.

� Descriptive statistics were determined for each data set ofreplicate log10 colony counts. Assessment of conformity to a NDwas based on standard tests and inspection of normal proba-bility plots.2

� Data sets were examined for trends in the sequence of collec-tion of samples while allowing for possible autocorrelation.

� Analysis of variance of the log-transformed data was done byboth the standard nested-data procedure and a robust proce-dure based on Rousseeux’s Qn estimator (Anon., 1989; Hedgesand Jarvis, 2006; Wilrich, 2007; Hedges, 2008). For eachdata set we derived the component variances, i.e. the betweensample, between sub-sample (within sample) and repeat-ability variances according to the model:

2 Normality tests included ShapiroeWilk, KolmoroveSmirnoff, Cramér-vonMises and AnderseneDarling tests together with normal probability plots withpoint-wise 95% confidence intervals.

mijk ¼ b0 þ b1 samplei þ b2 subsampleij þ 3ijk (1)

for i ¼ 1,...,n (n ¼ number of samples), j ¼ 1,2, k ¼ 1,2 andmijk ¼ colony count as log10 cfu/ml or /g, where b0 is the estimatedmean and expected mean squares for residual error ¼ s23, betweensub-sample error ¼ 2s2subsample þ s23 and between sample error ¼4s2sample þ 2s2subsample þ s23 , fromwhich the components of variance

were extracted. The relative contributions to the total reproduc-ibility variance of the component variances were expressed aspercentages.

� Further analysis was done on a 20-sample data set using 1000-iteration re-sampling without replacement, as described byJarvis and Hedges (2011), to evaluate the relationship betweensample numbers and the precision of the between sample vari-ance estimates, i.e. the variance of the variance (as an estimate ofthe precision of the estimated uncertainty).

3. Results

3.1. Colony counts

A summary of the general distribution parameter estimates foreach set of log10-transformed colony counts is presented in Table 1.In the majority of cases, the overall values of the mean and medianwere similar, indicating that the data conformed reasonably closelyto a symmetrical distribution. Several data sets exhibited evidenceof some skewness or kurtosis; two data sets (ex-farm milk andprawns) showed significant kurtosis and two data sets (mincedmeat and prawns) showed negative skewness. Fourteen of the 17data sets conformed well to ND (i.e. normality was not rejectedby the standard statistical tests). The exceptions were the aerobiccolony counts on the ex-farm milk and the minced meat samples;and the Enterobacteriaceae colony counts on whole sandwiches.

3.1.1. Raw milk samplesThemeanaerobic colonycount ofmilk sampled from the farm tank

was 3.05 log10 cfu/ml (range 2.91e3.25; s2¼ 0.010). Table 2 shows theaerobic colonycounts and thedescriptive statistics for the ex-farmrawmilk and illustrates the high level of homogeneity in the data. Noevidence was found for a trend in the sampling sequence (p > 0.05).Colonycounts of presumptive Enterobacteriaceaewere all<25 cfu/ml.

The mean aerobic colony count of milk samples taken from thebulk tanker was 5.09 log10 cfu/ml (range 4.56e5.83; s2 ¼ 0.130) andthe mean presumptive Enterobacteriaceae colony count was 2.80log10 cfu/ml (range 2.23e3.27, s2 ¼ 0.093). A statistically significantnegative trend (p ¼ 0.03) was seen in the sampling sequence ofthe aerobic colony counts, which was adequately represented bylinear regression incorporating an AR(1) model.3 The log10 cfu/mldecreased by about 0.09 between samples. This suggests thatcontaminants may have been picked up initially from the deliverypipeline, which view is supported by the lack of a trend in thepresumptive Enterobacteriaceae counts. The variance of the colonycounts on samples from the milk tanker was more than 10-foldgreater than that of the ex-farm milk (Table 1) thus showinga greater degree of heterogeneity.

3.1.2. Mixed sprouted seedsThe mean aerobic and presumptive Enterobacteriaceae colony

counts were 7.57 log10 cfu/g (range 7.41e7.74; s2 ¼ 0.010) and 6.80

3 AR(1) is an autoregressive model with autocorrelation between adjacentsamples; AR(2) has autocorrelation between alternate samples.

Table 2Aerobic colony counts at 30 �C for 3 days on samples of ex-farm milk.

Sample Code Test Sequencea Aerobic Colony Count (log10 cfu/ml)

SS1R1b SS1R2b SS1 Mean SS2R1b SS2R2b SS2 Mean Sample Mean

F 1 2.98 3.02 3.00 2.98 3.14 3.06 3.03H 2 2.94 3.11 3.02 3.03 2.90 2.97 3.00C 3 3.06 3.13 3.09 3.11 3.03 3.07 3.08A 4 3.13 3.12 3.12 3.11 3.65 3.38 3.25K 5 3.24 3.06 3.15 3.11 3.04 3.07 3.11D 6 3.11 3.02 3.07 3.26 3.06 3.16 3.11E 7 3.06 2.95 3.01 2.76 3.07 2.91 2.96G 8 3.14 3.09 3.11 2.91 3.06 2.99 3.05J 9 2.99 2.83 2.91 2.90 2.91 2.91 2.91B 10 3.03 2.83 2.93 2.98 2.97 2.98 2.95

Min 2.94 2.83 2.91 2.76 2.90 2.91 2.91Mean 3.07 3.02 3.04 3.01 3.08 3.05 3.05Median 3.06 3.04 3.05 3.00 3.05 3.02 3.04Max 3.24 3.13 3.15 3.26 3.65 3.38 3.25Variance 0.008 0.012 0.007 0.020 0.045 0.020 0.011SD 0.090 0.111 0.081 0.140 0.213 0.140 0.100

a Samples were obtained in the alphabetical sequence and tested in the numerical sequences shown.b SS1R1 ¼ sub-sample 1, replicate analysis 1, etc.

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371366

log10 cfu/g (range 6.61e6.97; s2¼ 0.010), respectively. No statisticallysignificant trends were observed (p > 0.05) in the samplingsequence. As expected for this product, the colony counts werehigh in comparison with many other ready-to-eat foods, but thevariance was low, both probably a consequence of the manner ofpreparation of sprouted seeds prior to packaging.

3.1.3. Frozen raw prawnsThe overall mean aerobic colony count was 3.53 log10 cfu/g

(range 2.98e4.11; s2 ¼ 0.053). No significant trend in the samplingsequence was observed (p > 0.05). Colony counts of presumptiveEnterobacteriaceae were all <25 cfu/g.

3.1.4. Minced meatAerobic colony counts ranged from 4.94 to 6.54 log10 cfu/g with

an overall mean of 6.06 log10 cfu/g and s2 ¼ 0.235 (Table 1). Nosignificant trend was observed (p> 0.05) in the sampling sequence.

3.1.5. Chicken neck-flapsThe overall mean aerobic colony counts (Table 1) were similar

(4.86 and 4.84 log10 cfu/g) in Flocks 1 and 2, respectively, although thevariance was lower on samples from Flock 2. The mean presumptiveEnterobacteriaceae countswere also similar (3.98 and 4.02 log10 cfu/gin Flocks 1 and 2, respectively) and again the variance of Flock 2samples was the smaller. Moderate numbers of campylobacters werefound in samples from Flock 1, which were free-range birds (mean3.20 log10 cfu/g, range 2.85e3.38, s2 ¼ 0.021) whereas the countson Flock 2, which were housed birds, were much lower (mean1.95 log10 cfu/g, range 1.44e2.50, s2 ¼ 0.136). Significant negativetrends were found (p < 0.01) in the sequence of samples from Flock1 for both aerobic colony counts and Enterobacteriaceae, but not forthe campylobacter counts. Both sets of counts decreased by about0.1 log10 cfu/g between samples. The aerobic count series showedno significant autocorrelation, whereas the Enterobacteriaceaecounts were best described by linear regression incorporating an AR(2) model.3 No trends were evident in results on samples takenfrom the second flock. It is possible that the first birds processed inFlock 1 picked up contaminants including Enterobacteriaceae, but notcampylobacters, froman inadequately sanitizedprocess plant;we canoffer no other explanation for the observed trends associatedwith thecolony counts on these birds.

The higher variance in campylobacter colony counts fromFlock 2 suggests either that not all birds were colonized at time of

slaughter or that some birds contained lower numbers in theirintestines. The slaughter process is known to cause extensive cross-contamination between neighbouring carcasses (Corry and Atabay,2001), while numbers of campylobacters on the carcass are alsorelated to numbers in the caecal contents (Rosenquist et al., 2006).

3.1.6. Pre-packaged sandwichesAerobic colony counts on the sandwich fillings ranged from 5.62

to 7.79 log10 cfu/g (mean 6.40; s2 ¼ 0.325); those on the completesandwiches ranged from 5.09 to 6.35 log10 cfu/g (mean 5.72;s2 ¼ 0.134). The presumptive Enterobacteriaceae colony countson the sandwich fillings ranged from 3.92 to 5.83 (mean 4.91log10 cfu/g; s2 ¼ 0.277); those on the complete sandwiches rangedfrom 2.70 to 5.65 (mean 3.79 log10 cfu/g; s2 ¼ 0.473).

We examined sandwiches both with and without the breadbecause, although some laboratories examine only the sandwichfilling, others examine entire sandwiches. Since the two sets ofsamples were from lots prepared on different days, it was notappropriate to compare directly the results of the fillings with thoseof the entire sandwiches. However, when bread was present, thereductions in both the aerobic and Enterobacteriaceae colonycounts were similar (about 18%) suggesting a dilution of the levelsof microbes present in the sandwich fillings. The total variance wasnot significantly different among all four (organism � sandwich)combinations. The striking difference was that, for both aerobesand Enterobacteriaceae, the major source of variation was betweensamples for the filling but within samples for the whole sandwich.

3.2. Analyses of variance

We have shown previously (Hedges and Jarvis, 2006) thatthe standard analysis of variance is often sub-optimal for analysis ofmicrobial data, and that robust methods, which can accommodate‘contaminated’ NDs by reducing the impact of outlier values, areoften more appropriate when testing for statistical significance.In this work we examined our data sets using both the standardANOVA and a robust procedure (Hedges and Jarvis, 2006; Wilrich,2007) based on the Qn estimator of Rousseeuw and Croux (1993).We also used a random effects multilevel model approach; theresults agreed closely with those from the standard nested ANOVA(results not shown).

Since our objective was to estimate the contribution to theoverall variances of the between sample and within sample

Table 3ANOVAs of aerobic colony count data, as log10 cfu/ml, on 10 raw milk sample unitsusing the standard and robust (Qn-based) procedures.

Parameter Milk ex-farm Milk ex-tanker

Standard Qn Standard Qn

Overall Mean 3.05 5.09Overall Median 3.04 5.04Repeatability Variance 0.017 0.016 0.022 0.010Within Sample Variance <0.001 <0.001 0.011 0.008Between Sample Variance 0.007 0.011 0.114 0.106Reproducibility Variance 0.024 0.027 0.147 0.124Repeatability SDa 0.129 0.128 0.147 0.102Within Sample SDa <0.001 <0.001 0.105 0.087Between Sample SDa 0.084 0.103 0.338 0.326Reproducibility SDa 0.154 0.165 0.383 0.352CVr (%)b 4.24 4.22 2.89 2.02CVR (%)c 5.07 5.42 7.53 7.00

a SD ¼ Standard Deviation.b CVr ¼ Repeatability Coefficient of Variation.c CVR ¼ Reproducibility Coefficient of Variation.

Table 4ANOVAs of aerobic colony count data, as log10 cfu/g, on prawns and minced meatsample units using standard and Qn ANOVA.

Parameter Prawns (n ¼ 20) Minced Meat (n ¼ 10)

Standard Qn Standard Qn

Overall Mean 3.53 6.06Overall Median 3.52 6.21Repeatability Variance 0.035 0.011 0.004 0.004Within Sample Variance 0.025 0.007 <0.001 <0.001Between Sample Variance 0.010 0.034 0.246 0.173Reproducibility Variance 0.070 0.052 0.250 0.176Repeatability SDa 0.186 0.104 0.063 0.062Within Sample SDa 0.159 0.084 0.000 0.000Between Sample SDa 0.102 0.185 0.496 0.415Reproducibility SDa 0.265 0.228 0.500 0.420CVr (%)b 5.27 2.95 1.04 0.99CVR (%)c 7.51 6.48 8.25 6.76

a SD ¼ Standard Deviation.b CVr ¼ Repeatability Coefficient of Variation.c CVR ¼ Reproducibility Coefficient of Variation.

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371 367

variances for the different foods it was appropriate to derivethese components by the standard ANOVA procedure, but we showsome ‘robust’ results for comparison. The components of variancedefine the extent of sampling uncertainty as opposed to the(analytical) measurement uncertainty. It should be recalled that theoverall variance of the colony counts provides an estimate of thepopulation variance and is the sum of the component varianceestimates:

s2overall ¼ s2between�samples þ s2within�samples þ s2repeatability (2)

Although ANOVAs were done on all data sets, we illustrate theresults only for a selection. Table 3 summarises the results of thetwo methods of ANOVA of the colony counts from both sets of milksamples. The component variances derived by the two ANOVAprocedures on the ex-farm milk samples were generally similar andboth procedures showed the repeatability variance to bemuch largerthan variance between samples; but the within sample variancecould not be determined. The data from the ex-farm milk samplesshowed evidence of significant kurtosis and slight right-handedskewness and the hypothesis of normality was rejected by allcriteria employed. In contrast, the ex-tankermilk samples conformedto ND, and the standard ANOVA gave higher values for the compo-nent variances thandid the robustmethod such that the repeatabilityand reproducibility CVs were higher for the standard ANOVA.

Analyses of the prawn and minced meat data (Table 4) showmarked differences between the standard ANOVA procedure andthe robust method. The hypothesis of ND was not rejected forthe prawn data but was rejected for the minced meat data.The combined between and within sample components of variancefor the prawns was four times as large as the repeatability varianceby the robust method but approximately equal by the standardANOVA. For the minced meat data, neither method showed anymeasurablewithin sample variance and themajor contributor to theoverall variance was the between sample variance, which wasgreater by the standard ANOVA than by the robust (Qn) method.

The contributions to the reproducibility variance from thecombined between and within sample variances on all the foodsare summarised in Table 5 for aerobic colony counts and in Table 6for presumptive Enterobacteriaceae and campylobacters in foodsexamined for these organisms. With the exception of the ex-farmmilk, where results were extremely homogeneous, the resultsshow that the total sampling variances were generally responsiblefor at least 50%, and in most cases for >85%, of the overall repro-ducibility variance. Note, however, that in this work we useda sample size and preparation procedure that we have previously

shown tominimize analytical variance (Corry et al., 2010; Jarvis andHedges, 2011) and a single analyst was used for each set of samplesdeliberately to maximise repeatability. If multiple analysts and/orsmaller sample weights had been used we would expect theresidual and between sample errors to be greater. In previous workwe have shown that the between sample contribution to repro-ducibility variance ranged from 2.5 to 10.7% (Jarvis et al., 2007b).

An exception to the large contribution of sampling variance wasobserved only for the very homogeneous aerobic colony countson the ex-farm milk. Since the between sample variance was verylow, the relative effect of repeatability error was enhanced, eventhough this error was itself very small. Perhaps more surprising isthe observation that, whereas the repeatability variance of Enter-obacteriaceae in the sandwich filling was greater than the withinsample variance, the conversewas seenwith the entire sandwichesebut this data set did not conform to a ND.

3.3. The impact of sample size on the precision of microbialcolony counts

Resampling without replacement as described previously byJarvis and Hedges (2011) was used to examine the effect of thenumber of samples examined on the precision of the estimate ofvariance and hence also on the derived estimate of uncertainty ofthe colony count. We use the 40 replicate log-transformed colonycounts of the means of the duplicate samples from the 20 samplesof prawns (the log10 values all conforming to ND) to illustrate theeffects. Fig. 2a shows the marked reduction in the actual 95%distribution limits to the variance as n increases from two to eightor more samples. The observed relationship between the 2.5%c2-derived Confidence Limits and the empirical 2.5% distribution ofthe variance (Fig. 2b) was as expected for data from a ND (Jarvis andHedges, 2011), thus agreeing with the standard tests for normality.Taking values for n ¼ 2 and n ¼ 12 of the aerobic colony countsas examples, the observed lower and upper limits of the central 95%distribution of the variance were 0.0005e0.168 for n ¼ 2 and 0.013to 0.049 for n ¼ 12, respectively; the mean variance remainedconstant at 0.034. If we convert these variances to standarddeviations, the average standard deviation is 0.184 log10 cfu/g,with lower and upper 95% limits of 0.022e0.410 for n ¼ 2 and0.114 to 0.221 for n ¼ 12. Since the standard uncertainty is givenby the estimate of standard deviation then the variance of thestandard uncertainty (as measured by the width of the 95%interval) is reduced from 0.388 for n ¼ 2 to 0.107 for n ¼ 12samples, a reduction of two thirds.

Table 5The repeatability and reproducibility standard deviations and coefficient of variation and the relative contributions of within- and between-sample variance to the overallvariance of aerobic colony counts for different food matrices, based on standard ANOVA. The relative contributions of the component variances to the overall variance areshown in italics as percentages.

Sproutedseeds

Ex-farmmilk

Ex-tankermilk

Prawns Mincedmeat

Chickenskin #1

Chickenskin #2

Sandwichfilling

EntireSandwich

Number of samplesa 10 10 10 20 10 8 10 10 10Mean colony count

(log10 cfu/g or/ml)7.56 3.05 5.09 3.53 6.06 4.87 4.84 6.40 5.68

Sr 0.052 0.129 0.147 0.186 0.063 0.083 0.041 0.100 0.074SR 0.106 0.154 0.383 0.265 0.500 0.338 0.243 0.586 0.373CVr (%) 0.69 4.24 2.89 5.27 1.04 1.71 0.85 1.57 1.30CVR (%) 1.40 5.07 7.53 7.51 8.25 6.94 5.02 9.15 6.56Total Variance 0.011 0.024 0.147 0.070 0.250 0.114 0.059 0.344 0.138Repeatability Variance 0.003 0.017 0.022 0.035 0.004 0.007 0.002 0.010 0.005Repeatability Variance (%) 27.3 70.8 15.0 50.0 1.6 6.1 3.4 2.9 3.6Variance within samplesb 0.008 <0.001 0.011 0.025 <0.001 ndc nd 0.086 0.114Within sample Variance (%) 72.7 <0.01 7.5 35.7 0.00 nd nd 25.0 82.6Variance between samples <0.001 0.007 0.114 0.010 0.246 0.107 0.057 0.248 0.019Between sample Variance (%) 0.00 29.2 77.6 14.3 98.4 93.9 96.6 72.1 13.8Total Sampling Variance (%) 72.7 29.2 85.1 50.0 98.4 93.9 96.6 97.1 96.4

a In some data sets it was necessary to exclude individual values for technical reasons.b Between sub-samples.c nd ¼ not determined since duplicate dilution series of these samples were not tested - hence the repeatability variance also includes the contribution from the

sub-samples.

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371368

4. Discussion

4.1. Sampling variance as a major contributor to overallmeasurement uncertainty

It is clear from earlier studies (Corry et al., 2007a; Jarvis et al.,2007a,b) that, although in many instances estimates of repeat-ability uncertainty are relatively low, estimates of reproducibilityuncertainty are often quite large. The actual levels of such estimatesare often dependent upon the test method used, the group ofmicroorganism(s) sought and the nature of the food under evalu-ation even within a single laboratory. Such estimates of reproduc-ibility uncertainty are often much larger (i.e. less precise) thanthat attributable to application of the laboratory methodology, perse. Jarvis et al. (2007a) showed that the estimated between samplevariation of colony count data on prawns accounted for almost60% of the total measurement uncertainty. In the current study,sampling uncertainty accounted for 50% of the total reproducibility

Table 6The repeatability and reproducibility standard deviations and coefficient of variation anvariance of Enterobacteriaceae and Campylobacter colony counts for different foodmatricto the overall variance are shown in italics as percentages.

Enterobacteriaceae

Sprouted seeds Milk ex-tanker Chicskin

Number of samplesa 10 10 8Mean colony count (log10 cfu/g) 6.80 2.80 3.98Sr 0.042 0.051 0.08SR 0.106 0.313 0.29CVr (%) 0.61 1.81 2.10CVR (%) 1.55 11.16 7.36Total Variance 0.012 0.098 0.08Repeatability Variance 0.002 0.003 0.00Repeatability Variance (%) 16.6 3.0 8.1Variance within samplesc 0.005 0.027 ndb

Within sample Variance (%) 41.7 27.6 ndVariance between samples 0.005 0.068 0.07Between sample Variance (%) 41.7 69.4 91.9Total Sampling Variance (%) 83.4 97.0 91.9

a In some data sets it was necessary to exclude individual values for technical reasonsb Between sub-samples.c nd ¼ not determined since duplicate dilution series of these samples were not t

sub-samples.

variance (Table 5). Augustin and Carlier (2006) observed effects onmeasurement uncertainty due to a diversity of factors, including themicroorganisms, the type and source of culturemedium, the platingprocedure and the actual numbers of colonies counted. They notedthat although the uncertainty of the microbiological method cangenerally be well controlled, in some circumstances uncertaintymay be high. They commented also that the uncertainty associatedwith the distribution of microorganisms in a food matrix needs tobe included in any overall assessment of uncertainty.We agreewiththis statement.

In this work we sought deliberately to minimise the uncertaintyof repeatability through use of defined and carefully controlledanalytical procedures including use of a single analyst (Corry et al.,2010). Results presented in Tables 5 and 6 show that the totalvariance between and within samples generally accounted for 50%or more of the overall variance and in many cases exceeded90%. Onemajor exception, highlighted above, concerned the data onthe raw milk samples taken from a refrigerated farm storage tank

d the relative contributions of within- and between-sample variance to the overalles, based on standard ANOVA. The relative contributions of the component variances

Campylobacters

ken#1

Chickenskin #2

Sandwichfilling

EntireSandwich

Chickenskin #1

Chickenskin #2

10 9 10 8 104.02 4.85 3.79 3.20 1.95

3 0.039 0. 345 0.122 0.072 0.0893 0.196 0.556 0.697 0.147 0.337

0.98 7.11 3.22 2.26 4.564.88 11.45 18.38 4.60 17.28

6 0.039 0.309 0.486 0.021 0.1137 0.002 0.119 0.015 0.005 0.008

5.1 38.5 3.1 23.8 7.1nd 0.021 0.377 nd ndnd 7.1 77.6 nd nd

9 0.037 0.168 0.094 0.016 0.10594.9 54.4 19.3 76.2 92.994.9 61.5 96.9 76.2 92.9

.

ested e hence the repeatability variance also includes the contribution from the

Fig. 2. Influence of the number of samples analysed on (a) the lower (7) and upper(6) limits of the actual 95% distribution limits of the variance (B) of aerobic colonycounts on samples of prawns; and (b) the variance (B), 2.5% actual limit (7) and thederived 2.5% c2 -Confidence Limit (,).

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371 369

wheremarked homogeneity of microbial distributionwas observedin the samples. We also observe that the repeatability variance forEnterobacteriaceae on the sandwich fillings accounted for almost40% of the overall variance, which differs markedly from all of theother Enterobacteriaceae counts. This suggests the possibility thatsome of the Enterobacteriaceae on the sandwich fillings may havebeen present as micro-colonies that became disrupted to a varyingextent during preparation and plating of dilutions. The differencesin the colony counts on sandwich fillings and entire sandwichesimply that, in the presence of the bread, replicate sub-samples fromthe same sample differ more than do the samples, themselves.In contrast, we note that duplicate samples tend to differ less in thepresence of bread. How can this be explained? It is possible thatsome organisms will adhere to microscopic particles of bread in themacerate and effectively form ‘aggregates’ which will affect theapparent number of cfus. When duplicate sub-samples are takenfrom a given sample, one of the pair may contain more of the breadmicro-particles with their adherent organisms, than the other.If organisms on the micro-particles are released during preparationof further dilutions, the apparent colony counts will then differ.Hence, over all samples, the means of pairs of duplicates may varyless than the duplicates, themselves; if the fillings are made enmasse thefillingwill tend to homogeneity. Likewise, we can imaginethat duplicate portions drawn from the same sub-sample may beexpected to vary little.

In assessing uncertainty we are concerned with the standarddeviation of the mean, since this is used as the estimate of standarduncertainty (ux). The data summarised in Tables 5 and 6 show that

the estimates of the standard repeatability uncertainty for colonycounts of aerobes, Enterobacteriaceae and campylobacters rangedfrom 0.04 to 0.18, from 0.03 to 0.12 and from 0.07 to 0.09 log10 cfu/g,respectively. These estimates are extremely low by comparisonwithmany published data (Augustin and Carlier, 2006; Jarvis et al.,2007a,b) and probably reflect the relatively large quantity ofsample examined and theuse of a single technician. However, for thesame groups of organisms, the standard reproducibility uncertainty,which includes that due to sampling ranged from 0.11 to 0.59, from0.11 to 0.70 and from 0.15 to 0.34 log10 cfu/g, respectively, indicatingvarying levels of heterogeneity in the different foods. For instance,the colony counts of aerobes in samples of sprouted seeds andex-farmmilk were very homogeneous, whereas very heterogeneouscounts were found in sandwich fillings, on neck-flaps of raw chickenand especially in minced meat. In addition, it was clear that thedistribution of counts from the ex-tanker milk samples was alsoheterogeneous, possibly due to contamination during dischargefrom the tanker.

4.2. Estimation of parameters by modelling distributions

One of our objectives in undertaking this work was to ascertainhow increasing the number of samples affects the precision of a setof data and the degree of confidence that can be placed on itsestimates. Official analyses for chemical constituents and contami-nants (e.g. EU, 2004a,b,c; 2005b) frequently require analysis ofmanymore samples than are used in the microbiological examination offoods. In order to obtain ‘representative’ samples, protocols forchemical analysis often require large quantities of material to bedrawn, macerated, blended and further sub-sampled in order tominimise the between and within sample variance. Even then, asdemonstrated eloquently by Gy (2004a,b), samples may not be trulyrepresentative of a lot because of limitations in the way that thesamples can be drawn. Such sampling protocols are generally notfeasible formicrobiological examination, not least because of the riskof environmental contamination, although we have shown (Corryet al., 2010) that it is possible to composite samples asepticallyusing simple procedures and thereby to reduce significantly thevariance between replicate samples.

In a study of sampling uncertainty in the chemical analysis offoods, Lyn et al. (2007) questioned whether duplicate analysis ofeight samples was sufficient tominimise between sample variability.They concluded that sampling uncertainty constituted a significantproportion of the overall measurement uncertainty and that theprecision of the results, as measured by the 95% c2-CI, is stronglydependent on the number of samples analysed. Previously, Lyn et al.(2002) had applied the concept of the ‘cost of uncertainty’ thatsought to optimise the costs of improving precision by increasing thenumber of samples against the risk of making a wrong decision.Justification of the original concept of using eight duplicate samplesappears to be lost in time (Lyn et al., 2007) although there is referenceto it in Anon. (1989)whilst Anon. (2009b) refers to use of 10 samples.

For most microbiological examinations, individual samples willrarely be truly representative and are often, at best, a series ofrandom samples taken fromdifferent parts of a lot, evenwhen takenover time during a production process. Indeed, many routinemicrobiological examinations are based on examination of a singlesample unit, often without assessment of duplicate sub-samples;such an examination is predicated on what is sometimes referredto as analysis of ‘spot’ samples. Most official quantitative microbio-logical examination of foods use 3-class sampling planswith e.g. fivesamples and defined upper limits of acceptability against which theresults of analyses are compared using a ‘pass or fail’ approach(ICMSF, 2002; EU, 2005a). Such sampling plans are predicated onuseof attributes samplingwithfive individual ‘spot’ samples. It is argued

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371370

that such sampling plans make allowance for lack of precision intesting and for heterogeneous contamination in the setting of criticalvalues. But, it is not possible to use the concept of measurementuncertainty in assessing compliance with such criteria since it is notpossible to estimate precision characteristics for a single sample unit.However, the European Regulation on Microbiological Criteriafor Foods (EU, 2005a) introduced an interesting modification to thisscenario for some process controls (e.g. aerobic and Enter-obacteriaceae colony counts on animal carcasses): this criterion isbased on a requirement that the average dailymean log colony countmust comply with the limits, rather than each individual result. Inour view this is an improvement over the more widely used 3-classattribute plan since it potentially allows application of the concept ofmeasurement uncertainty in the assessment of compliance.

Any analytical result is only an estimate of the true value andis subject to experimental error; it is complete only when accom-panied by a statement of its precision, such as its measurementuncertainty (Taylor and Kuyatt, 1994). In our opinion, use ofunqualified values to decide on the acceptability, or otherwise, ofa lot of product from which the random samples were drawn is atbest misguided.

We used the iterative statistical re-sampling procedure describedpreviously by Jarvis and Hedges (2011) to demonstrate the effect ofsample size (i.e. the number of samples, n) on the precision of thevariance estimates of the aerobic colony counts on prawns. For allvalues of n the estimates of the mean log10 colony count andthe variance remained essentially unchanged. None of the standardtests rejected the hypothesis that the log-transformed data con-formed to a ND and the reductions in the width between the actual2.5% and 97.5% limits of the empirical distribution of the variancebehaved as expected for ND data (Jarvis and Hedges, 2011). Fig. 2demonstrates the increasing precision of the estimate of variancewith increasing sample numbers and confirms our earlier observa-tions (Jarvis and Hedges, 2011).

Although the variance and the mean remain constant, the SEMdiminishes as the number of samples examined increases e thisalso is to be expected since, for a ND, the SEM is inversely related tothe square root of the number of data values (n) onwhich the meanand variance are based. It is widely recognised that for dataconforming to a ND, increasing the sample size from n ¼ 2 to n ¼ 8halves the estimate of the SEM. Less widely recognised, is that theprecision of the estimate of variance, and hence the precision of thestandard uncertainty, is also dependent upon the value of n.

We illustrate this point using data from the aerobic colonycounts on prawns (x ¼ 3:53; s ¼ 0:265); with n ¼ 2, theSEM¼ 0.265/O2¼ 0.187 butwith n¼ 8 the SEM¼ 0.265/O8¼ 0.094.The reportable result of the colony count, based on the expandeduncertainty (Ux ¼ 2s; Anon., 2006), is 3.53 � 0.53 log10 cfu/g, butthe SEM is twice as large if n ¼ 2 than if n ¼ 8. The generaliseduncertainty coverage factor of 2 is predicated on large sample sizesthat conform to ND and provides only a crude approximation forsmaller sample sizes. It would be preferable to use the 2-tailedvalue of t for the relevant degrees of freedom in order to allow for theestimation of variance from a finite sample of size n (Horwitz, 2003;Anon., 2009b). For instance, when n ¼ 2, t0.025,n = 1 z12.7 whilst forn ¼ 8, t0.025,n ¼ 7 z 2.4. Hence it would be more correct to reportthese results as 3:53� 3:37 log10 cfu/g if the data are derived fromduplicate samples and 3:53� 0:64 log10 cfu/g if derived from n ¼ 8samples.

Often the fate of a production lot is dependent upon compliancewith a published criterion. A result reported without its precisionvalues is meaningless; even a result that cites the general expandedanalytical uncertainty without taking into account the samplinguncertainty will grossly underestimate the potential range of datavalues likely to be obtained from a ‘lot’. In assessing compliance, the

use of both sampling uncertainty and the appropriate t value as the‘coverage factor’, may strongly influence the likelihood of a correctdecision (see also Anon., 2009a,b).

4.3. Recommendations

In order to minimise estimates of variance and, hence, ofsampling uncertainty and overall uncertaintywewould recommendthat if the results are of major importance (e.g. for compliance withlegal criteria) analyses should be based on duplicate determinationsfrom at least eight samples (Jarvis and Hedges, 2011). However, thechoice of sample size (i.e. the number of samples) is dependent alsoon cost-benefit assumptions. Ideally, aseptic compositing of primarysamples should be carried out, as described by Corry et al. (2010), inorder to minimize variability.

Whilst the accepted procedure for conversion of estimates ofstandard deviations to expanded uncertainty (Anon., 2004, 2006) ispredicated on a coverage factor of two, this should be replaced by thet-distribution value for the number of samples examined, otherwisethe reported estimate of uncertainty will grossly underestimate thetrue level of uncertainty of an analysis.

5. Conclusions

In his paper on ‘The Certainty of Uncertainty’, Horwitz (2003)expressly excluded analyses of microbiological data. It is with thismatter that we have been concerned both in our present and earlierwork (Corry et al., 2007a,b, 2010; Jarvis et al., 2007a,b, Jarvis andHedges, 2011). There is no doubt that variations in the distributionof microorganisms in foods and other natural materials have a majorinfluence on the overall variability and reliability of quantitativeestimates of microbiological contamination. The analytical measure-ment uncertainty of results arising from application of individualmethods can be controlled provided that care is taken to minimizerepeatability errors. However, overall estimates of uncertainty will beinfluenced more significantly by the extent of microbial variability inthe lot and hence by sampling uncertainty, which is generally largerthan the estimates of analytical measurement uncertainty. This is ofconsiderable significance in relation to assessment of compliancewithlegal or commercial criteria. As noted elsewhere (Anon., 2009a),“recognition that measurements used for control purposes are prone tosampling uncertainty is crucial to improving the reliability of decisions inall regulated sectors. Not only will this improve the effectiveness of .regulation and implementation of policy, but it will also often givefinancial benefits to the users of the regulations”.

Financial and other less tangible benefits result fromminimizingdecision errors. The potential financial and public health reper-cussions that arise fromwrongly approving the use of unacceptablycontaminated foods, and conversely, the financial and environ-mental repercussions of rejecting sound foods are enormous. It isessential to take account of all aspects of uncertainty in theassessment of food quality and safety in order to improve decision-making. Hence, the Horwitz (2003) concept of the ‘certainty ofuncertainty’ is as applicable to quantitative microbiological exam-inations as it is to chemical analyses.

Acknowledgements

This work formed part of a research contract (project E01085)awarded by the UK Food Standards Agency to the University ofBristol. The objectives and approaches were agreedwith the Agency,but they had no involvement in the planning of the work reportedtherein, or the data analysis. The conclusions drawn may not reflectthe views of the Food Standards Agency. We are grateful to themanagement and staff of the food companies that provided access

B. Jarvis et al. / Food Microbiology 30 (2012) 362e371 371

for sampling and to the anonymous reviewers for their helpfulcomments. We particularly acknowledge the technical assistance ofMiss Raquel Pinho. AJH thanks Prof. Anthony Hollander, his Head ofSchool, for providing facilities.

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