INDEX_2008_Statistical-Aspects-of-the-Microbiological-Examination-of-Foods

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301
 ATP Measurements , 180 , 181 , 243 
 Acceptable Quality Level , 78 , 83–91 , 290 
 Acceptance sampling , 22 , 72 , 79 , 82 
 See also Attributes sampling ; Variables 
sampling 
 Accuracy , 186 
 Analysis of variance (ANOVA) , 24 , 189 , 
 198–215 
 quantitative method comparisons , 270–2 
 robust methods , 208–15 
 standard ANOVA procedure , 204–8 
 tests for normality , 199–200 
 tests for outliers , 200–4 
 Anderson–Darling test , 199 
 Appropriate level of protection (ALOP) , 280–1 
 Arithmetic mean , 5 , 8 , 16 
 colony counts , 133–5 
 As-low-as reasonably achievable (ALARA) 
concept , 281 
 Attributes sampling , 72–3 , 79–81 , 82–93 , 296 
 control charts , 251–8 
 disadvantage of , 93 
 sampling plans , 86 , 290–2 
 three-class plans , 86–91 
 two-class plans , 83–6 
 Average run length (ARL) , 229 
 Average sample populations , 5–6 
 Batches , 4 
 Binomial distribution , 19 , 25 , 37 , 73–5, 321–4 
 as model for regular dispersion , 57 
 calculation of expected frequencies , 22–3 
 quantal responses and , 144 
 variance estimation , 217–18 
 tables , 22 
 See also Negative binomial distribution 
 Box–Cox normality plot , 199 
 Bulk compositing , 170 
 Cause and effect diagram , 197 
 Central limit theorem , 7–8 , 24 
 Chi Square tests , 49–50 , 56 
 comparisons of methods , 265 , 274 
 paired sample design , 267 
 unpaired sample design , 268 
 Chitin estimation , 181 
 Class frequency , 13 
 Codex , 281 , 283–4 , 286 , 289 , 292 
 Committee on Food Hygiene (CCFH) , 281 
 Coeffi cient of variation (CV) , 7 
 colony counts , 112–18 
 Collaborative studies , 265 
 Colony counts: 
 arithmetic mean count , 8, 134 
 coeffi cient of variation (CV) , 112–18 
 comparability of methods , 137–8 
 confi dence limits , 128–35 , 140 
 dilution error effects on , 119 
 direct microscopic counts , 177–80 
 geometric mean , 8–9 
 median , 8 
 overall error , 138–40 
 INDEX 
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INDEX302
 Colony counts (continued) 
 pour-plate methods , 121–2 
 range of , 8 
 surface plating methods , 122–4 
 weighted mean count , 134 
 See also Dilution count method 
 Colony selection for identifi cation , 172–5 
 Colworth Droplette method , 122 
 Compositing of samples , 169–72 
 Confi dence limits (CLs): 
 colony counts , 128–35 , 140 
 dilution series , 154–5 , 163 
 for Poisson variable , 48–56 
 prevalence of defectives , 162–5 
 sample value , 77–8 
 Contagious distribution , 45 , 46 , 57–63 
 heterogeneous Poisson distributions , 58 
 lognormal distribution , 62 
 negative binomial distribution as model , 57–62 
 randomly distributed clumps , 58 
 true contagion , 58 
 Continuous variables , 13 
 Control charts , 229–58 
 CUSUM charts , 242–50 
 CUSUM signal chart , 248–51 
 interpretation of , 251 
 for attribute data , 251–8 
 x– and R charts , 230–6 
 interpretation of , 237–42 
 x– and s charts , 237 
 interpretation of , 237–42 
 Control limits , 229–30 , 233–6 
 Counting errors , 135–7 
 Coverage factor , 188 
 Critical control points (CCPs) , 282 
 Cusum charts , 242–50 
 CUSUM signal chart , 248–51 
 interpretation of , 251 
 D’Agostino–Pearson test , 199–200 
 Data sets , 8–11 
 De Man’s Tables , 155 
 Defectives , 72 
 prevalence of , 772–4 
 calculation of , 74 
 quantifi cation based on relative prevalence , 
 162–5 
 Degrees of freedom defi nition, 7 
 Deviation , 7 
 See also Standard deviation 
 Diluent volume errors , 104–5 , 106–8 
 Dilution count method , 143–8 
 multiple test dilution series , 148–62 
 differences between MPN values , 155–61 
 Moran’s test , 151 , 153 
 MPN method , 149–55 , 163 
 multiple tests at several dilution levels , 
 148–55 
 special applications , 161–2 
 Stevens ’ method , 149 
 multiple tests at a single dilution level , 147–8 
 single-tube dilution tests , 144–7 
 Dilution errors: 
 calculation , 110–18 
 diluent volume errors , 104–5 , 106–8 
 effects on colony count , 119 
 Direct microscopic counts , 177–80 
 dilution effect , 180 
 Howard mould count , 179–80 
 Discrete variables , 13 
 Distribution errors , 124–8 , 195–6 
 Drop count method , 125 , 126 , 127 , 128 , 137 
 Electrical impedance measurement , 181–3 
 Enrichment cultures , 166 , 167 , 168 , 169 , 263 
 probability for transfer of viable inoculum , 167 
 Error , 6–7 , 185–6 , 195–8 
 counting errors , 135–7 
 diluent volume errors , 104–5 , 106–8 
 distribution errors , 124–8 , 195–6 
 incubation errors , 135 
 laboratory sampling errors , 103–4 , 196 
 overall error of colony count methods , 
138–40 
 pipette volume errors , 105–8 , 111 , 113–18 
 plating methods , 121–4 
 relative dilution error calculation , 110–18 
 effects on colony count , 119 
 standard , 7 , 10–11 
 worker’s error , 137 
 Expanded uncertainty , 188 
 False negative results , 221 
 rates , 266 , 268 
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INDEX 303
 False positive results , 221 
 rates , 266 , 268 
 Fisher Bacterial Colony Counter , 136 
 Fisher’s index of dispersion , 51 , 124 
 Food safety: 
 criteria , 289 
 law , 280 
 objectives , 280–5 
 risk assessment , 280–5 
 Food Safety Objectives (FSOs) , 282–4 
 Frames, (sampling) , 100 
 Frequency distributions , 13–18 
 relationship between , 37 
 transformations , 37–43 
 types of , 19 
 See also Binomial distribution ; Normal 
(Gaussian) distribution ; Poisson 
distribution; Negative Binomial 
distribution; Trinomial distribution 
 G 2 Test , 51–6 
 Gaussian distribution , See Normal (Gaussian) 
distribution 
 General Homogeneity Test , 53–4 
 followed by analysis of deviance , 54–5 
 Generalized uncertainty method (GUM) , 195–8 
 Geometric mean , 6 , 8–9 
 Good Manufacturing Practices (GMP) , 94 , 288 , 
 291 
 Goodness-of-fi t tests , 50 , 55–6 , 64–6 
 Graphical representation , 269 
 Guard bands , 261 , 296 
 Hazard , 280 
 characterization , 283 
 identifi cation of , 283 
 Hazard Analysis and Critical Control Point 
(HACCP) concept , 282 , 285 
 Heterogeneous distribution , See Contagious 
distribution 
 Homogenizers , 109 
 Howard mould count (HMC) , 179–80 
 Impedance measurement , 181–3 , 260 
 Incubation errors , 135 
 Independent test results , 186–7 
 Index of dispersion , 50 , 51 , 124 
 test , 124 
 Intermediate reproducibility , 188 , 189 
 measurement , 215 
 k estimation , 59–62 , 64–8 
 Kolmogorov–Smirnov test , 200 
 Laboratory profi ciency schemes , 222 
 Level of detection (LOD) , 189–90 , 273 
 estimates , 218–21 
 Lifetime tolerable risk , 281 
 Likelihood Ratio Index , 51–6 
 Limit of detection , 190 , 273 
 Lod50, 188, 189
Lognormal distribution , 62 
 Lot Tolerance Percent Defective (LTPD) , 83 
 Lots , 4–5 
 Lower signal alarm limit (LSAL) , 248–50 
 Maceration , 109 
 McNemar Chi Square test , 266–7 
 Mantel-Haenszel Chi Square test , 268–9, 274 
 Maximum likelihood methods , 31 , 32–3 
 Mean , 5–6 , 16–18 
 arithmetic , 5 , 8 , 16 
 colony counts , 134 
 geometric , 6 , 8–9 
 Measurand , 187 
 Measurement uncertainty , 187–8 
 analysis of variance (ANOVA) , 198–215 
 bottom-up estimation approach , 195–8 
 estimation of quantal method uncertainty , 
 217–22 
 level of detection estimates , 218–21 
 most probable number (MPN) estimates , 
 218 
 reference materials in quantal testing , 
221–2 
 variance based on binomial distribution , 
 217–8 
 intermediate reproducibility measurement , 
 215–6 
 relevance to microbiological criteria , 292–6 
 top-down approach to estimation , 198 
 See also Uncertainty 
 Method comparisons , See Validation 
 Method development , 260–1 
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INDEX304
 Microbiological criteria , 285–92 
 compliance assessment , 294–5 
 data collections , 286–7 
 establishing sampling plans , 289–90 
 relevance of measurement uncertainty , 292–6 
 setting criteria limits , 287–9 
 Microbiological guideline , 285 
 Microbiological reference values , 286 
 Microbiological specifi cation , 285 
 Microbiological standard , 285 
 Microbiological testing , 1–2 
 Moran’s test , 151 , 153 
 Most Probable Numbers (MPNs) , 94 , 148 , 260 
 differences between values , 155–61 
 estimates , 218 
 MPN method for multiple dilution levels , 
 149–55 , 163 
 standard error , 154–55 
 Multi-stage tests: 
 compositing of samples , 169–72 
 selection of colonies for identifi cation , 172–5 
 test procedure , 165–9 
 Multiplication Rule for combined probabilities , 
 21 
 Negative binomial distribution , 19 , 30–6 , 38 , 39 
 as model for contagious distribution , 57–62 
 calculation of expected frequencies , 31–6 
 RNEGBINIMIAL programme , 198 
 tests for agreement , 58–62 , 67–8 
 transformation , 43 
 Normal (Gaussian) distribution , 19 , 24–6 
 transformations , 40–2 
 Normality tests , 199–200 
 Operating characteristics (OC) curves , 83 , 84 , 
 91–3 , 161 
 Outliers: 
 data examination , 269 
 tests for , 200–4 
 Over-dispersion , See Contagious distribution 
 Paired sample design , 263 , 264 
 validation , 265–6 
 performance indicators , 266 
 test for signifi cant difference , 266–7 
 Paired t -test , 270 
 Parameters , 7 
 Pascal’s triangle , 20 
 Performance criteria (PC) , 284 
 Performance indicators: 
 paired sample designs , 266 
 quantitative methods , 269 
 unpaired sample designs , 268 
 Performance objective (PO) , 284 
 Performance standards , 228–9 
 Pipette volume errors , 105–8 , 111 , 113–18 
 Plating methods: 
 comparability of colony counts , 137–8 
 pour-plate , 121–2 
 Spiral Plate (SP) , 122–4 , 126–8 , 136 
 surface plating , 122–4 
 Poisson distribution , 19 , 26–9 , 38–42 
 calculation of expected frequencies , 27–8 
 heterogeneous , 58 
 quantal responses and , 144 
 randomness and , 47 
 transformation , 40–2 
 Poisson lognormal distribution , 62 
 Polymerase chain reaction (PCR) methods , 
 259–60 
 real time (RT-PCR) , 260 
 Population at risk , 281 
 Populations , 3 
 average sample populations , 5–6 
 Pour-plate methods , 121–2 , 137 
 Pre-enrichment incubation , 165–9 
 Precision , 186 
 measure of , 186 
 Prevalence of defectives , 72–4 
 calculation of , 75 
 quantifi cation based on relative prevalence , 
 162–5 
 Probability , 19–21 
 of acceptance , 87–8 , 89 , 90–1 
 Process development , 261 
 Process hygiene criteria , 289 
 Qualitative methods , 189 , 259 , 260 
 validation , 263–9 
 paired sample designs , 265–6 
 unpaired sample designs , 267–9 
 Quality Assurance programmes , 285 
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INDEX 305
 Quantal response tests , 143 , 259 
 estimation of associated uncertainty , 217–22 
 level of detection estimates , 218–21 
 most probable number (MPN) estimates , 
 218 
 variance based on binomial distribution , 
 217–18 
 use of reference materials , 221–2 
 See also Dilution count method ; Multi-stage 
tests 
 Quantitative methods , 188 , 259 , 260 
 validation , 269–72 , 275–6 
 comparison of means , 270–2 
 graphical representation , 269 
 outlier data examination , 269 
 performance parameters , 269–70 
 Quantitative metrics , 284 
 Quantitative Microbiological Risk Assessment 
(QMRA) , 280 
 R charts , 230–6 
 interpretation of , 237–42 
 Random distribution , 45 , 46 , 47–56 
 tests for agreement with a Poisson series , 
 48–56 
 Random numbers , 98–9 
 Random sampling , 98 
 Ratio count technique , 177–8 
 Recursive Median (REMEDIAN) , 189 
 Reference materials in quantal testing , 221–2 
 Reference values , 286 
 Regular distribution , 47 , 48 , 60–145 , 46 , 56–7 
 binomial distribution as model , 56–7 
 Rejectance Quality Level (RQL) , 82 
 Relative sensitivity , 268 
 Relative standard deviation (RSD) , 7 , 10 
 Repeatability , 187 
 standard deviation , 204 , 210 
 variance , 204 
 Reproducibility , 187 
 intermediate , 188 
 measurement , 215–16 
 standard deviation , 204 , 210 
 variance , 204 
 Risk , 280 
 assessment , 280–5 
 characterization , 283 
 lifetime tolerable risk , 281 
 population at risk , 281 
 RNEGBINOMIAL maximum likelihood method 
programme , 198 
 RobStat , 210 , 211–12 
 Robust analysis , 208–15 
 s charts , 237–42 
 interpretation of , 237–42 
 Sample size , 63–4 
 Sample variance , 7 , 9–10 
 Samples , 4–5 
 average sample populations , 5–6 
 compositing of , 169–72 
 representative , 98 
 Sampling , 71 
 accuracy of the sample estimate , 77–8 
 errors , See Error 
 number of samples , 75 
 variation , 78 
 random , 98 
 stratifi ed , 99 
 uncertainty , 190–1 
 See also Acceptance sampling ; Attributes 
sampling ; Variables sampling 
 Sampling plans: 
 attributes sampling plans , 86 , 290–2 
 establishment of , 289–90 
 three-class sample plans , 76–7 , 86–91 , 296 
 two-class sample plans , 79–81 , 90–473–4 , 83–6 
 variables sampling plans , 289–92 
 Selectivity testing , 262–3 
 Sensitivity , 266 
 relative , 268 
 Sequential Attribute Sampling Plans , 86 
 Shapiro–Wilk test , 199 
 Shewhart’s control charts , See Control charts 
 Skips , 144 , 145 , 146 
 Spearman–Kärber method , 218–21 
 Specifi city , 266 
 Spiral Plate (SP) method , 122–4 , 126–8 , 136 , 
 137 
 Spread-plate method , 137 
 Standard deviation , 7 , 10–11 
 relative (RSD) , 7 , 10 
 repeatability , 204 , 210 
 reproducibility , 204 , 210 
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INDEX306
 Standard error , 7 
 most probable number (MPN) , 154 , 155 
 Standard error of the mean (SEM) , 5 , 7 
 Standard uncertainty , 188 
 combined , 188 
 Standards , 261 , 262 
 microbiological , 286 
 performance standards , 228–9 
 Statistical Process Control (SPC) , 6–7 , 225–6 
 performance standards , 228–9 
 setting control limits , 229–30 
 tools for , 227–8See also Control charts 
 Statistical Process Improvement , 226 
 Statistical range 6– , 7 
 Statistical Sampling Tables , 86 
 Stevens ’ method for multiple dilution levels , 
149 
 Stratifi ed sampling , 99 
 Student’s t -test , 128–9 
 Surface plating methods , 122–4 
 Tables of Binomial Probability , 22 
 Tables of the Standardized Normal Deviate , 24 
 Three-class sample plans , 76–7 , 86–91 , 296 
 Total Quality Management (TQM) , 226 , 282 
 Transformations , 37–43 
 back transformations , 41 
 Trend analysis , 226–7 
 Trinomial distribution , 76–7 , 86 
 Trueness , 186 
 Uncertainty , 185 , 187 
 compliance assessment and , 191 
 estimation of , 188–90 
 expanded , 188 
 reporting of , 190 
 sampling , 190–1 
 standard , 188 
 combined , 188 
 See also Measurement uncertainty 
 Under-dispersion , See Regular distribution 
 Unpaired sample design , 263 
 validation , 267–9 
 performance indicators , 268 
 test for signifi cant differences , 268–9 
 Upper signal alarm limit (USAL) , 248 
 Validation , 261–72 
 qualitative methods , 263–7 , 274 
 paired sample designs , 265–7 
 unpaired sample designs , 267–9 
 quantitative methods , 269–72 , 275–6 
 comparison of means , 275–6 
 graphical representation , 269 
 outlier data examination , 269 
 performance parameters , 269–70 
 selectivity testing , 282–3 
 Variables: 
 continuous , 13 
 discrete , 13 
 Variables sampling , 72 , 93–100 
 application , 96–7 
 drawing representative samples , 98–9 
 frames , 100 
 sampling plans , 289–92 
 single or multiple sampling schemes , 100 
 stratifi ed sampling , 99 
 Variance , 6–7 , 9–10 , 16–18 
 population , 7 
 repeatability , 204 
 reproducibility , 204 
 sample , 7 , 9 
 See also Analysis of variance (ANOVA) 
 Verifi cation , 262 
 Weighted mean count , 134 
 Wet compositing , 170 
 Worker’s error , 137 
 World Trade Organization Phytosanitary 
Measures (SPS) , 280 , 281 
 x– charts , 230–42 
 interpretation of , 237–42 
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