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This "rule" is not meant to be taken as unive\ rsally applicable, but a useful guide subject to other information.

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Extra cost is the outcome of false rejection of manufact\ ured items: the material is unnecessarily re-worked or scrapped. The probability of false rejection is greater when the uncertainty is greater. There are also penalties for false acceptance, likewise dependent on uncertainty.

)/Contents(Extra cost is the outcome of false rejection of manufactured items: the material is unnecessarily re-worked or scrapped. The probability of false rejection is greater when the uncertainty is greater. There are also penalties for false acceptance, likewise\ dependent on uncertainty.)/Type/Annot/Subj(Note)/Rect[331.318726 101.472443 351.318726 119.472443]/CreationDate(D:20060508143427+01'00')/NM(M2GYUIgdQAfYoztkat1Z0C)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508144044+01'00')/P 131 0 R/T(ubca445)/Popup 169 0 R/AP<>>> endobj 169 0 obj<> endobj 170 0 obj<

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The uncertainty that delivers the minimal long term aver\ age cost is 'fit for purpose'.

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The fit-for-purpose uncertainty should be optimally appo\ rtioned between sampling and analytical components. Equal contributions is close to optimal unless the costs of sampling and analysis are grossly disproportionate.

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Uncertainty that is fit for purpose is a key concept in \ the revised Harmonised Protocol for Proficiency Testing \(Pure Appl Chem 2006, 78, 145-196.\)

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Typical results from a round of a proficiency test. To e\ nable us to make judgements about the results, we have to convert them to a score.

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Using simple statistics ensures that, outliers aside, ab\ out 95% of the participants obtain a z-score between -2 and +2. This is comforting for the participants and the provider, but provides a false sense of security. Such a score merely describes the outcome: it tells us nothing about whether the results are \ of appropriate quality or not.

)/Contents(Using simple statistics ensures that, outliers aside, about 95% of the participants obtain a z-score between -2 and +2. This is comforting for the participants and the provider, but provides a false sense of security. Such a score merely describes the out\ come: it tells us nothing about whether the results are of appropriate quality or not.)/Type/Annot/Subj(Note)/Rect[332.142914 541.582397 352.142914 559.582397]/CreationDate(D:20060508145842+01'00')/NM(EdeZRFpzIOOJo1opn2qmyA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508150234+01'00')/P 13 0 R/T(ubca445)/Popup 181 0 R/AP<>>> endobj 180 0 obj[179 0 R 181 0 R 182 0 R 183 0 R 184 0 R 185 0 R 186 0 R 187 0 R 188 0 R 189 0 R] endobj 181 0 obj<> endobj 182 0 obj<

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Using robust statistics eliminates some of the problems \ of outlying results, but still only describes the results.

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An ideal scoring system should be simple and universally\ applicable and understandable. A score of \(say\) 3.2 should have the same significance to all analysts and end-users, regardless of the analyte and its concentration, the test material, the physical principle of the test method, or the laboratory carryi\ ng out the work. The z-score, when properly constructed, comes closest to the ideal.

)/Contents(An ideal scoring system should be simple and universally applicable and understandable. A score of \(say\) 3.2 should have the same significance to all analysts and end-users, regardless of the analyte and its concentration, the test material, the physica\ l principle of the test method, or the laboratory carrying out the work. The z-score, when properly constructed, comes closest to the ideal.)/Type/Annot/Subj(Note)/Rect[78.296722 542.406616 98.296722 560.406616]/CreationDate(D:20060508150547+01'00')/NM(srYCUf8VwjbnK_U3Sj4kRD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508151031+01'00')/P 13 0 R/T(ubca445)/Popup 185 0 R/AP<>>> endobj 185 0 obj<> endobj 186 0 obj<

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Using an uncertainty that is fit for purpose allows us t\ o construct a universal scale for z-scores.

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Even apparently simple questions about analytical data o\ ften requires the use of statistical methods that are beyond an elementary treatment. Although the theory of these methods may be complex and difficult to understand for non-experts, they are often easy to use if the right software is available.)/Contents(Even apparently simple questions about analytical data often requires the use of statistical methods that are beyond an elementary treatment. Although the theory of these methods may be complex and difficult to understand for non-experts, they are often e\ asy to use if the right software is available.)/Type/Annot/Subj(Note)/Rect[79.120895 102.296616 99.120895 120.296616]/CreationDate(D:20060508151403+01'00')/NM(zV-q1yImv1RvVDGlEbyzqB)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508151708+01'00')/P 13 0 R/T(ubca445)/Popup 189 0 R/AP<>>> endobj 189 0 obj<> endobj 190 0 obj<

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This algorithm starts with initial estimates of the mean\ and variance. At each iteration, results outside a range defined by these statistics and a coverage factor k are replaced by the boundary values. \(k usually takes the value of 1.5.\) The updated estimate of the mean is the mean of the modified results.\ The updated variance is the variance of the modified results times a factor dependent on k. The iteration is repeated to satisfactory convergence.

)/Contents(This algorithm starts with initial estimates of the mean and variance. At each iteration, results outside a range defined by these statistics and a coverage factor k are replaced by the boundary values. \(k usually takes the value of 1.5.\) The updated e\ stimate of the mean is the mean of the modified results. The updated variance is the variance of the modified results times a factor dependent on k. The iteration is repeated to satisfactory convergence.)/Type/Annot/Subj(Note)/Rect[103.022003 565.483459 123.022003 583.483459]/CreationDate(D:20060508151804+01'00')/NM(uAk9sG_O1iizUalV8UX6bC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508152715+01'00')/P 26 0 R/T(ubca445)/Popup 192 0 R/AP<>>> endobj 191 0 obj[190 0 R 192 0 R] endobj 192 0 obj<> endobj 193 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 0 194 0000000125 65535 f 0000000016 00000 n 0000000158 00000 n 0000000457 00000 n 0000002052 00000 n 0000002190 00000 n 0000002327 00000 n 0000002464 00000 n 0000002602 00000 n 0000007006 00000 n 0000011369 00000 n 0000015087 00000 n 0000027947 00000 n 0000029090 00000 n 0000029235 00000 n 0000029518 00000 n 0000032044 00000 n 0000032182 00000 n 0000032320 00000 n 0000032458 00000 n 0000041771 00000 n 0000042032 00000 n 0000042222 00000 n 0000042506 00000 n 0000045796 00000 n 0000049205 00000 n 0000052468 00000 n 0000052613 00000 n 0000052912 00000 n 0000056162 00000 n 0000056299 00000 n 0000056436 00000 n 0000057748 00000 n 0000057987 00000 n 0000058159 00000 n 0000058444 00000 n 0000073022 00000 n 0000073291 00000 n 0000076380 00000 n 0000084867 00000 n 0000090674 00000 n 0000092134 00000 n 0000092264 00000 n 0000092562 00000 n 0000093991 00000 n 0000094129 00000 n 0000094267 00000 n 0000094405 00000 n 0000106815 00000 n 0000107059 00000 n 0000107242 00000 n 0000107528 00000 n 0000111130 00000 n 0000119525 00000 n 0000124893 00000 n 0000127623 00000 n 0000133205 00000 n 0000133335 00000 n 0000133572 00000 n 0000136803 00000 n 0000136939 00000 n 0000137079 00000 n 0000143337 00000 n 0000148636 00000 n 0000148766 00000 n 0000148955 00000 n 0000151337 00000 n 0000151476 00000 n 0000151613 00000 n 0000153659 00000 n 0000156643 00000 n 0000156773 00000 n 0000157023 00000 n 0000159049 00000 n 0000159186 00000 n 0000159284 00000 n 0000159382 00000 n 0000167892 00000 n 0000170857 00000 n 0000175148 00000 n 0000179632 00000 n 0000179762 00000 n 0000179950 00000 n 0000181616 00000 n 0000181714 00000 n 0000184735 00000 n 0000187525 00000 n 0000187709 00000 n 0000187755 00000 n 0000187801 00000 n 0000187847 00000 n 0000188252 00000 n 0000188503 00000 n 0000205435 00000 n 0000205696 00000 n 0000220119 00000 n 0000220165 00000 n 0000220211 00000 n 0000220309 00000 n 0000220356 00000 n 0000220492 00000 n 0000220540 00000 n 0000220588 00000 n 0000220636 00000 n 0000220684 00000 n 0000220930 00000 n 0000221061 00000 n 0000221191 00000 n 0000221239 00000 n 0000221287 00000 n 0000221335 00000 n 0000221383 00000 n 0000221431 00000 n 0000221479 00000 n 0000221527 00000 n 0000221575 00000 n 0000221622 00000 n 0000221669 00000 n 0000221716 00000 n 0000224814 00000 n 0000224851 00000 n 0000224876 00000 n 0000224985 00000 n 0000225020 00000 n 0000225215 00000 n 0000000127 00001 f 0000225294 00000 n 0000000129 00001 f 0000225520 00000 n 0000000166 00001 f 0000225618 00000 n 0000225672 00000 n 0000225820 00000 n 0000226044 00000 n 0000226770 00000 n 0000226872 00000 n 0000227119 00000 n 0000227168 00000 n 0000227217 00000 n 0000229578 00000 n 0000229846 00000 n 0000230211 00000 n 0000230344 00000 n 0000230809 00000 n 0000231074 00000 n 0000231355 00000 n 0000231760 00000 n 0000232204 00000 n 0000265557 00000 n 0000292889 00000 n 0000311795 00000 n 0000322064 00000 n 0000322295 00000 n 0000322616 00000 n 0000337781 00000 n 0000337920 00000 n 0000338056 00000 n 0000342489 00000 n 0000347249 00000 n 0000348011 00000 n 0000348061 00000 n 0000348177 00000 n 0000348342 00000 n 0000348363 00000 n 0000348884 00000 n 0000348905 00000 n 0000000167 00001 f 0000000000 00001 f 0000349428 00000 n 0000350520 00000 n 0000350645 00000 n 0000351341 00000 n 0000351423 00000 n 0000351540 00000 n 0000352506 00000 n 0000352623 00000 n 0000353445 00000 n 0000353571 00000 n 0000354371 00000 n 0000354486 00000 n 0000355699 00000 n 0000355797 00000 n 0000355914 00000 n 0000356667 00000 n 0000356784 00000 n 0000358103 00000 n 0000358220 00000 n 0000358943 00000 n 0000359060 00000 n 0000360191 00000 n 0000360306 00000 n 0000361753 00000 n 0000361787 00000 n 0000361904 00000 n trailer <<84293e6c83ba61449b1ee7bc5c367249>]>> startxref 365360 %%EOF 126 0 obj<> endobj 128 0 obj<> endobj 158 0 obj<

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This "rule" is not meant to be taken as unive\ rsally applicable, but a useful guide subject to other information. It is based on the notion that one way to reduce uncertainty is to repeat the measurement. A mean of four results \(properly repeated\) has half of the uncertainty of a single result at f\ our times the cost.

)/Contents(This "rule" is not meant to be taken as universally applicable, but a useful guide subject to other information. It is based on the notion that one way to reduce uncertainty is to repeat the measurement. A mean of four results \(properly repeated\) has h\ alf of the uncertainty of a single result at four times the cost.)/Type/Annot/Subj(Note)/Rect[70.879135 102.296631 90.879135 120.296631]/CreationDate(D:20060508142933+01'00')/NM(jduF4PlZ80cQnJf7wmpWMC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508153433+01'00')/P 131 0 R/T(ubca445)/Popup 160 0 R/AP<>>> endobj 194 0 obj null endobj 195 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 126 1 0000369402 00000 n 128 1 0000369628 00000 n 158 1 0000369726 00000 n 194 2 0000370906 00000 n 0000370928 00000 n trailer <]/Prev 365360 >> startxref 374384 %%EOF 126 0 obj<> endobj 128 0 obj<> endobj 171 0 obj[170 0 R 172 0 R 173 0 R 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 196 0 R 197 0 R] endobj 186 0 obj<

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Using an uncertainty that is fit for purpose allows us t\ o construct a universal scale for z-scores. It also provides a rational basis for setting action limits

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Even apparently simple questions about analytical data o\ ften requires the use of statistical methods that are beyond an elementary treatment. Although the theory of these methods look complex and difficult to understand at first, they are often conceptually simpler than the forbidding statistical notation sugg\ ests, and easy to use if the right software is available.

)/Contents(Even apparently simple questions about analytical data often requires the use of statistical methods that are beyond an elementary treatment. Although the theory of these methods look complex and difficult to understand at first, they are often conceptual\ ly simpler than the forbidding statistical notation suggests, and easy to use if the right software is available.)/Type/Annot/Subj(Note)/Rect[79.120895 102.296616 99.120895 120.296616]/CreationDate(D:20060508151403+01'00')/NM(zV-q1yImv1RvVDGlEbyzqB)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508154156+01'00')/P 13 0 R/T(ubca445)/Popup 189 0 R/AP<>>> endobj 189 0 obj<> endobj 190 0 obj<

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This algorithm starts with initial estimates of the mean\ and variance. At each iteration, results outside a range defined by these statistics and a coverage factor k are replaced by the boundary values. \(k usually takes the value of 1.5.\) The updated estimate of the mean is the mean of the modified results.\ The updated variance is the variance of the modified results times a factor dependent on k. The iteration is repeated to satisfactory degree of convergence.

)/Contents(This algorithm starts with initial estimates of the mean and variance. At each iteration, results outside a range defined by these statistics and a coverage factor k are replaced by the boundary values. \(k usually takes the value of 1.5.\) The updated e\ stimate of the mean is the mean of the modified results. The updated variance is the variance of the modified results times a factor dependent on k. The iteration is repeated to satisfactory degree of convergence.)/Type/Annot/Subj(Note)/Rect[103.022003 565.483459 123.022003 583.483459]/CreationDate(D:20060508151804+01'00')/NM(uAk9sG_O1iizUalV8UX6bC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508154258+01'00')/P 26 0 R/T(ubca445)/Popup 192 0 R/AP<>>> endobj 192 0 obj<> endobj 196 0 obj<

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The total cost has a distinct minimum.

\ )/Contents(The total cost has a distinct minimum.)/Type/Annot/Subj(Note)/Rect[336.263794 540.75824 356.263794 558.75824]/CreationDate(D:20060508153544+01'00')/NM(9G6eWwfNzfXsOImD1NM6SD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508153602+01'00')/P 1 0 R/T(ubca445)/Popup 197 0 R/AP<>>> endobj 197 0 obj<> endobj 198 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 126 1 0000374680 00000 n 128 1 0000374906 00000 n 171 1 0000375004 00000 n 186 1 0000375102 00000 n 188 3 0000375945 00000 n 0000377210 00000 n 0000377337 00000 n 192 1 0000378804 00000 n 196 3 0000378930 00000 n 0000379530 00000 n 0000379645 00000 n trailer <<0cbd43b81977af40908d2c143278c005>]/Prev 374384 >> startxref 383101 %%EOF 126 0 obj<> endobj 128 0 obj<> endobj 191 0 obj[190 0 R 192 0 R 199 0 R 200 0 R] endobj 199 0 obj<

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Testing materials for heterogeneity is an important part\ of validating materials for proficiency tests or as reference materials. If we take some of the distribution units at random, the concentration of the analyte is different in each one. ALL MATERIALS ARE HETEROGENEOUS! An obvious way to demonstra\ te these differences in composition is to set up a randomised experiment where each unit \(say a sample packet\) is analysed in duplicate.

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Testing materials for heterogeneity is an important part\ of validating materials for proficiency tests or as reference materials.

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Testing materials for heterogeneity is an important part\ of validating materials for proficiency tests or as reference materials. If we take some of the distribution units at random, the concentration of the analyte is different in each one. Remember that ALL MATERIALS ARE HETEROGENEOUS! An obvio\ us way to demonstrate these differences in composition is to set up a randomised experiment where each unit \(say a sample packet\) is analysed in duplicate. However, analysing the results is another area where a sophisticated statistical approach is need\ ed.

)/Contents(Testing materials for heterogeneity is an important part of validating materials for proficiency tests or as reference materials. If we take some of the distribution units at random, the concentration of the analyte is different in each one. \rRemember th\ at ALL MATERIALS ARE HETEROGENEOUS!\r\rAn obvious way to demonstrate these differences in composition is to set up a randomised experiment where each unit \(say a sample packet\) is analysed in duplicate. However, analysing the results is another area whe\ re a sophisticated statistical approach is needed.\r)/Type/Annot/Subj(Note)/Rect[330.494598 540.75824 350.494598 558.75824]/CreationDate(D:20060508154501+01'00')/NM(CKhkKZrGbr086Twgm_74nB)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060508155901+01'00')/P 26 0 R/T(ubca445)/Popup 200 0 R/AP<>>> endobj 200 0 obj<> endobj 204 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 126 1 0000390171 00000 n 128 1 0000390397 00000 n 199 2 0000390495 00000 n 0000392164 00000 n 204 1 0000392291 00000 n trailer <<94db9d75beb3fd488b9c53bb9b0910a9>]/Prev 389815 >> startxref 395747 %%EOF 41 0 obj<> endobj 56 0 obj<> endobj 126 0 obj<> endobj 128 0 obj<> endobj 191 0 obj[190 0 R 192 0 R 199 0 R 200 0 R 205 0 R 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R 211 0 R 212 0 R] endobj 205 0 obj<

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If the measurements are made by using an analytical meth\ od of high precision \(small error bars\) the experiment will detect significant variation among the units, even if the variation is inconsequential in terms of the proposed usage.

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If a method of lower precision is used \(wide error bars\ \), the variation may be found to be non-significant even in instances where it has a consequential magnitude. This is a fairly common situation in practice.

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Both of these limitations of the standard approach to an\ alysis of variance lead to an unduly high false rejection rate \(i.e., rejecting material that is good enough for its intended use\). This can be avoided by testing for 'sufficient homogeneity', using a criterion that is based on fitness for purpose.

)/Contents(Both of these limitations of the standard approach to analysis of variance lead to an unduly high false rejection rate \(i.e., rejecting material that is good enough for its intended use\). This can be avoided by testing for 'sufficient homogeneity', usin\ g a criterion that is based on fitness for purpose.)/Type/Annot/Subj(Note)/Rect[65.934097 94.879028 85.934097 112.879028]/CreationDate(D:20060509104716+01'00')/NM(jX-4qSOq5qgaKOZZcCyVOB)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509105522+01'00')/P 26 0 R/T(ubca445)/Popup 210 0 R/AP<>>> endobj 210 0 obj<> endobj 211 0 obj<

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Dotplots and histograms are often difficult to interpret\ . For example, is the aflatoxin dataset \(from a proficiency test\) unimodal but skewed, bimodal, or multimodal? Such questions often cannot be answered absolutely, but we can make progress if we have a particular model in mind. One way to do that is to c\ onstruct a kernel density.

)/Contents(Dotplots and histograms are often difficult to interpret. For example, is the aflatoxin dataset \(from a proficiency test\) unimodal but skewed, bimodal, or multimodal? Such questions often cannot be answered absolutely, but we can make progress if we hav\ e a particular model in mind. One way to do that is to construct a kernel density.)/Type/Annot/Subj(Note)/Rect[332.967072 102.296616 352.967072 120.296616]/CreationDate(D:20060509105601+01'00')/NM(YpFUjSU0LocOngPnty0ULD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509110159+01'00')/P 26 0 R/T(ubca445)/Popup 212 0 R/AP<>>> endobj 212 0 obj<> endobj 213 0 obj<

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In a kernel density, each datapoint is represented by a \ particular density function called a kernel. It is usual \(but not a requirement\) to use a normally distributed kernel.

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The densities of the kernels is added across the range o\ f the data, and the resultant curve, normalised to unit area, is the kernel density.

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The appearance of the kernel density depends on the size\ of the smoothing parameter h, which is the standard deviation of the kernel used. In some instances \(e.g., proficiency testing\), we have a good idea of how the data should look, and we can use a appropriate value of h.

)/Contents(The appearance of the kernel density depends on the size of the smoothing parameter h, which is the standard deviation of the kernel used. In some instances \(e.g., proficiency testing\), we have a good idea of how the data should look, and we can use a a\ ppropriate value of h.)/Type/Annot/Subj(Note)/Rect[334.615448 320.703247 354.615448 338.703247]/CreationDate(D:20060509110804+01'00')/NM(w8U5W9wlGPAtYFHZtE_whA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509111105+01'00')/P 41 0 R/T(ubca445)/Popup 219 0 R/AP<>>> endobj 219 0 obj<> endobj 220 0 obj<

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This is a kernel density produced by setting h equal to \ 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From this we might want to investigate the theory that two i\ nconsistent analytical methods were in use by the participants.

)/Contents(This is a kernel density produced by setting h equal to 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From\ this we might want to investigate the theory that two inconsistent analytical methods were in use by the participants.)/Type/Annot/Subj(Note)/Rect[75.000015 101.472443 95.000015 119.472443]/CreationDate(D:20060509111117+01'00')/NM(eRVvWjTi7Y5kmZ9HGj6SlD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509111914+01'00')/P 41 0 R/T(ubca445)/Popup 221 0 R/AP<>>> endobj 221 0 obj<> endobj 222 0 obj<

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A normal distribution calculated from the data does not \ match the data closely and might lead to erroneous conclusions. For example the mode of the normal curve is clearly different from the mode of the kernel density.

)/Contents(A normal distribution calculated from the data does not match the data closely and might lead to erroneous conclusions. For example the mode of the normal curve is clearly different from the mode of the kernel density.)/Type/Annot/Subj(Note)/Rect[332.142914 104.769135 352.142914 122.769135]/CreationDate(D:20060509111939+01'00')/NM(5wHrtiLtDiLIm2VJS6M4BA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509112238+01'00')/P 41 0 R/T(ubca445)/Popup 223 0 R/AP<>>> endobj 223 0 obj<> endobj 224 0 obj<

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In such cases we can do better by modelling the data as \ a mixture of several normal distributions in unknown proportions \(p\).

)/Contents(In such cases we can do better by modelling the data as a mixture of several normal distributions in unknown proportions \(p\). )/Type/Annot/Subj(Note)/Rect[70.054962 567.131897 90.054962 585.131897]/CreationDate(D:20060509112328+01'00')/NM(GOohA6qQa3ZLWB3DIqihDC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509112947+01'00')/P 56 0 R/T(ubca445)/Popup 226 0 R/AP<>>> endobj 225 0 obj[224 0 R 226 0 R 227 0 R 228 0 R 229 0 R 230 0 R 231 0 R 232 0 R] endobj 226 0 obj<> endobj 227 0 obj<

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The procedure starts with either rough estimates of the \ parameters or by initial attribution of probabilities \(1 or 0\) segregating the data into groups. The M-step estimates the parameters \(mean, variance, proportion\) for each group, with the estimates weighted by the probabilities of group membership. The\ E-step estimates new group probabilities based on the current parameter estimates. The procedure is iterated to convergence.

)/Contents(The procedure starts with either rough estimates of the parameters or by initial attribution of probabilities \(1 or 0\) segregating the data into groups. The M-step estimates the parameters \(mean, variance, proportion\) for each group, with the estimate\ s weighted by the probabilities of group membership. The E-step estimates new group probabilities based on the current parameter estimates. The procedure is iterated to convergence.)/Type/Annot/Subj(Note)/Rect[519.230835 539.109924 539.230835 557.109924]/CreationDate(D:20060509112953+01'00')/NM(AzS6bz2YSIhNyDw0Y6Sz7C)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509113702+01'00')/P 56 0 R/T(ubca445)/Popup 228 0 R/AP<>>> endobj 228 0 obj<> endobj 229 0 obj<

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Here the aflatoxin data has been modelled by a mixture \(\ red curve\) of two normal distributions \(blue curves\). The kernel density \(black curve\) is shown for comparison. The mode of the higher normal corresponds closely with that of the kernel density. \(It is emphasised that the kernel density an\ d the mixture model are derived directly from the data by quite different procedures. The two distributions look rather different, but that is because the kernel density is broadened by the smoothing procedure.\)

)/Contents(Here the aflatoxin data has been modelled by a mixture \(red curve\) of two normal distributions \(blue curves\). The kernel density \(black curve\) is shown for comparison. The mode of the higher normal corresponds closely with that of the kernel density\ . \r\r\(It is emphasised that the kernel density and the mixture model are derived directly from the data by quite different procedures. The two distributions look rather different, but that is because the kernel density is broadened by the smoothing proc\ edure.\))/Type/Annot/Subj(Note)/Rect[74.175842 323.999969 94.175842 341.999969]/CreationDate(D:20060509113708+01'00')/NM(L9K-R_OTR-czrVnHp5mCtA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509114800+01'00')/P 56 0 R/T(ubca445)/Popup 230 0 R/AP<>>> endobj 230 0 obj<> endobj 231 0 obj<>>> endobj 232 0 obj<> endobj 233 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 41 1 0000396043 00000 n 56 1 0000396188 00000 n 126 1 0000396333 00000 n 128 1 0000396559 00000 n 191 1 0000396657 00000 n 205 29 0000396771 00000 n 0000397768 00000 n 0000397885 00000 n 0000398836 00000 n 0000398953 00000 n 0000400093 00000 n 0000400218 00000 n 0000401423 00000 n 0000401538 00000 n 0000402417 00000 n 0000402515 00000 n 0000402632 00000 n 0000403437 00000 n 0000403554 00000 n 0000404637 00000 n 0000404754 00000 n 0000406031 00000 n 0000406147 00000 n 0000407110 00000 n 0000407225 00000 n 0000408006 00000 n 0000408088 00000 n 0000408205 00000 n 0000409608 00000 n 0000409735 00000 n 0000411308 00000 n 0000411434 00000 n 0000411726 00000 n 0000411842 00000 n trailer <]/Prev 395747 >> startxref 415298 %%EOF 63 0 obj<> endobj 70 0 obj<> endobj 126 0 obj<> endobj 128 0 obj<> endobj 220 0 obj<

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This is a kernel density produced by setting h equal to \ 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From this we might want to investigate the theory that two i\ nconsistent analytical methods were in use by the participants. The kernel density is essentially a visual and non-parametric method. The position of modes can be determined, and their standard errors estimated, but the procedures are lengthy eve\ n for modern PCs. Mixture models provide a much quicker parametric method.

)/Contents(This is a kernel density produced by setting h equal to 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From\ this we might want to investigate the theory that two inconsistent analytical methods were in use by the participants.\r\rThe kernel density is essentially a visual and non-parametric method. The position of modes can be determined, and their standard er\ rors estimated, but the procedures are lengthy even for modern PCs. Mixture models provide a much quicker parametric method.)/Type/Annot/Subj(Note)/Rect[75.000015 101.472443 95.000015 119.472443]/CreationDate(D:20060509111117+01'00')/NM(eRVvWjTi7Y5kmZ9HGj6SlD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509115559+01'00')/P 41 0 R/T(ubca445)/Popup 221 0 R/AP<>>> endobj 221 0 obj<> endobj 229 0 obj<

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Here the aflatoxin data has been modelled by a mixture \(\ red curve\) of two normal distributions \(blue curves\). The kernel density \(black curve\) is shown for comparison. The mode of the higher normal corresponds closely with that of the kernel density. \(It is emphasised that the kernel density an\ d the mixture model are derived directly from the data by quite different procedures. The two distributions look rather different, but that is because the kernel density is broadened \(to a predictable extent\) by the smoothing procedure.\)

)/Contents(Here the aflatoxin data has been modelled by a mixture \(red curve\) of two normal distributions \(blue curves\). The kernel density \(black curve\) is shown for comparison. The mode of the higher normal corresponds closely with that of the kernel density\ . \r\r\(It is emphasised that the kernel density and the mixture model are derived directly from the data by quite different procedures. The two distributions look rather different, but that is because the kernel density is broadened \(to a predictable ex\ tent\) by the smoothing procedure.\))/Type/Annot/Subj(Note)/Rect[74.175842 323.999969 94.175842 341.999969]/CreationDate(D:20060509113708+01'00')/NM(L9K-R_OTR-czrVnHp5mCtA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509115749+01'00')/P 56 0 R/T(ubca445)/Popup 230 0 R/AP<>>> endobj 230 0 obj<> endobj 231 0 obj<

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If the variances of the mixture model components are bro\ adened to the same degree as the kernel density, the two models produce very similar results. However, it is far easier to estimate parameters with the mixture model.

)/Contents(If the variances of the mixture model components are broadened to the same degree as the kernel density, the two models produce very similar results. However, it is far easier to estimate parameters with the mixture model.)/Type/Annot/Subj(Note)/Rect[332.967072 325.648315 352.967072 343.648315]/CreationDate(D:20060509114804+01'00')/NM(Yd7H1ArvFeNkt9xSikVPBB)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509115843+01'00')/P 56 0 R/T(ubca445)/Popup 232 0 R/AP<>>> endobj 232 0 obj<> endobj 234 0 obj<

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Uncertainty is undoubtedly important and, in the past, a\ nalytical chemists have tended to underestimate it. However, physical metrologists currently have an undue and unfortunate influence on the conduct of analytical chemistry. By dominating ISO committees they can enforce their approach. By concentrating on \ issues of traceability to SI units, they divert attention away from the real technical problems that analysts encounter.

)/Contents(Uncertainty is undoubtedly important and, in the past, analytical chemists have tended to underestimate it. However, physical metrologists currently have an undue and unfortunate influence on the conduct of analytical chemistry. By dominating ISO committe\ es they can enforce their approach. By concentrating on issues of traceability to SI units, they divert attention away from the real technical problems that analysts encounter.)/Type/Annot/Subj(Note)/Rect[76.648361 534.164856 96.648361 552.164856]/CreationDate(D:20060509120038+01'00')/NM(nZVyuiHhRczQJ_W4o1MnzA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509122905+01'00')/P 63 0 R/T(ubca445)/Popup 236 0 R/AP<>>> endobj 235 0 obj[234 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R] endobj 236 0 obj<> endobj 237 0 obj<

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Accreditation assessors and editors of journals now tell\ you that expressions such as % and ppm are incorrect, and insist that you use 'dimensionless units' such as mg kg-1

)/Contents(Accreditation assessors and editors of journals now tell you that expressions such as % and ppm are incorrect, and insist that you use 'dimensionless units' such as mg kg-1)/Type/Annot/Subj(Note)/Rect[337.087952 537.461548 357.087952 555.461548]/CreationDate(D:20060509121347+01'00')/NM(q_FyL6HIYOHAZOTYgUXwRC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509121801+01'00')/P 63 0 R/T(ubca445)/Popup 238 0 R/AP<>>> endobj 238 0 obj<> endobj 239 0 obj<

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In this experiment, a length of silver alloy wire is sus\ pended from a bar at distance A \(in mm\) from the pivot and counterbalanced with the blue weight. With the bar locked, the alloy is removed from the bar and the silver chemically separated from the base metals.

)/Contents(In this experiment, a length of silver alloy wire is suspended from a bar at distance A \(in mm\) from the pivot and counterbalanced with the blue weight. With the bar locked, the alloy is removed from the bar and the silver chemically separated from the \ base metals.)/Type/Annot/Subj(Note)/Rect[73.351669 323.175781 93.351669 341.175781]/CreationDate(D:20060509122956+01'00')/NM(FrlF3Oi57AnOHyY8VjyT7C)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509123652+01'00')/P 63 0 R/T(ubca445)/Popup 240 0 R/AP<>>> endobj 240 0 obj<> endobj 241 0 obj<

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Equilibrium is restored by suspending the separated silv\ er on the bar at distance B.

)/Contents(Equilibrium is restored by suspending the separated silver on the bar at distance B. )/Type/Annot/Subj(Note)/Rect[331.318726 323.175781 351.318726 341.175781]/CreationDate(D:20060509123438+01'00')/NM(26Gcmzw1rtD9F4EEwgVs2D)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509123615+01'00')/P 63 0 R/T(ubca445)/Popup 242 0 R/AP<>>> endobj 242 0 obj<> endobj 243 0 obj<

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The proportion of silver \(A/B\) is dimensionless and no\ t traceable to ANY unit. Most analytical results are similarly a ratio of a physical quantity that is a surrogate for mass.

)/Contents(The proportion of silver \(A/B\) is dimensionless and not traceable to ANY unit. Most analytical results are similarly a ratio of a physical quantity that is a surrogate for mass.)/Type/Annot/Subj(Note)/Rect[74.175842 101.472443 94.175842 119.472443]/CreationDate(D:20060509123713+01'00')/NM(MtqU_7rpv-FLaLxRuv7SAD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509124238+01'00')/P 63 0 R/T(ubca445)/Popup 244 0 R/AP<>>> endobj 244 0 obj<> endobj 245 0 obj<

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The trend of a large number \(more than 5000\) of RSDR v\ alues from interlaboratory studies follows closely the function shown. Individual results are scattered around the line, in a large part because of the large random variability of standard deviation estimates.

)/Contents(The trend of a large number \(more than 5000\) of RSDR values from interlaboratory studies follows closely the function shown. Individual results are scattered around the line, in a large part because of the large random variability of standard deviation \ estimates.)/Type/Annot/Subj(Note)/Rect[333.79126 541.582397 353.79126 559.582397]/CreationDate(D:20060509124424+01'00')/NM(P1J5GBkqRICevflsyb6xpD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509125013+01'00')/P 70 0 R/T(ubca445)/Popup 247 0 R/AP<>>> endobj 246 0 obj[245 0 R 247 0 R] endobj 247 0 obj<> endobj 248 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 63 1 0000416187 00000 n 70 1 0000416332 00000 n 126 1 0000416477 00000 n 128 1 0000416703 00000 n 220 2 0000416801 00000 n 0000418608 00000 n 229 4 0000418734 00000 n 0000420365 00000 n 0000420491 00000 n 0000421462 00000 n 234 15 0000421589 00000 n 0000422980 00000 n 0000423078 00000 n 0000423205 00000 n 0000424076 00000 n 0000424193 00000 n 0000425254 00000 n 0000425371 00000 n 0000426070 00000 n 0000426187 00000 n 0000427072 00000 n 0000427188 00000 n 0000428245 00000 n 0000428279 00000 n 0000428396 00000 n trailer <]/Prev 415298 >> startxref 431852 %%EOF 80 0 obj<> endobj 126 0 obj<> endobj 128 0 obj<> endobj 235 0 obj[234 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R 255 0 R 256 0 R] endobj 245 0 obj<

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The trend of a large number \(more than 5000\) of RSDR v\ alues from interlaboratory studies follows closely the function shown. Individual results are scattered around the line, in a large part because of the large random variability of standard deviation estimates. We can use this function as a bench\ mark for uncertainty estimates, on the grounds that all random effects in a method will be adequately represented in an interlaboratory study. \(We have to remember that a random effect in such a study will look like a systematic effect to a particular la\ boratory.\)

)/Contents(The trend of a large number \(more than 5000\) of RSDR values from interlaboratory studies follows closely the function shown. Individual results are scattered around the line, in a large part because of the large random variability of standard deviation \ estimates. \r\rWe can use this function as a benchmark for uncertainty estimates, on the grounds that all random effects in a method will be adequately represented in an interlaboratory study. \(We have to remember that a random effect in such a study wil\ l look like a systematic effect to a particular laboratory.\)\r\r)/Type/Annot/Subj(Note)/Rect[333.79126 541.582397 353.79126 559.582397]/CreationDate(D:20060509124424+01'00')/NM(P1J5GBkqRICevflsyb6xpD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509130233+01'00')/P 70 0 R/T(ubca445)/Popup 247 0 R/AP<>>> endobj 246 0 obj[245 0 R 247 0 R 249 0 R 250 0 R 251 0 R 252 0 R 253 0 R 254 0 R 257 0 R 258 0 R] endobj 249 0 obj<

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'Bottom-up' models represent the complete process of mea\ surement and are represented by 'fishbone' or 'cause-and-effect' diagrams. They rely on both a correct model and an ability to estimate the uncertainty in every comparison. This is difficult to execute in the complex operations of chemical measurement and\ more often leads to underestimated uncertainty.

)/Contents('Bottom-up' models represent the complete process of measurement and are represented by 'fishbone' or 'cause-and-effect' diagrams. They rely on both a correct model and an ability to estimate the uncertainty in every comparison. This is difficult to execu\ te in the complex operations of chemical measurement and more often leads to underestimated uncertainty.)/Type/Annot/Subj(Note)/Rect[82.417603 540.75824 102.417603 558.75824]/CreationDate(D:20060509130235+01'00')/NM(g3Ny1Iep9DdmCkN24hUCcD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509131057+01'00')/P 70 0 R/T(ubca445)/Popup 250 0 R/AP<>>> endobj 250 0 obj<> endobj 251 0 obj<

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According to metrological dogma, interlaboratory studies\ should underestimate uncertainty for the majority of laboratories, so should be invariably smaller than bottom-up estimates. Few DIRECT comparisons \(e.g., same test material, same method\) are available, and even those are difficult to interpret because\ pure 'bottom-up' methods are hardly ever used in reality. This figure shows one such comparison \(unpublished\). Each point represents a separate example. For two analytes the bottom-up relative uncertainty is less than a half of the RSDR.

)/Contents(According to metrological dogma, interlaboratory studies should underestimate uncertainty for the majority of laboratories, so should be invariably smaller than bottom-up estimates. Few DIRECT comparisons \(e.g., same test material, same method\) are avai\ lable, and even those are difficult to interpret because pure 'bottom-up' methods are hardly ever used in reality. This figure shows one such comparison \(unpublished\). Each point represents a separate example. For two analytes the bottom-up relative unc\ ertainty is less than a half of the RSDR. )/Type/Annot/Subj(Note)/Rect[72.527481 323.175781 92.527481 341.175781]/CreationDate(D:20060509131143+01'00')/NM(CicdZPojRB39eX-rIdS6UC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509133014+01'00')/P 70 0 R/T(ubca445)/Popup 252 0 R/AP<>>> endobj 252 0 obj<> endobj 253 0 obj<

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In this study, uncertainty was estimated by a ruggedness\ study that attempted to emulate interlaboratory variation in procedure. All of the test materials were foodstuffs. In each instance the estimate is lower than the collaborative trial result.

)/Contents(In this study, uncertainty was estimated by a ruggedness study that attempted to emulate interlaboratory variation in procedure. All of the test materials were foodstuffs. In each instance the estimate is lower than the collaborative trial result.)/Type/Annot/Subj(Note)/Rect[335.439606 323.999969 355.439606 341.999969]/CreationDate(D:20060509132217+01'00')/NM(gAtuEn5Ui0KSjVjq5d-jEC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509134434+01'00')/P 70 0 R/T(ubca445)/Popup 254 0 R/AP<>>> endobj 254 0 obj<> endobj 255 0 obj<

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Fitness for purpose is determined both by the uncertaint\ y of the result and the end-user's requirement. Metrology cannot tell us what the latter amounts to.

)/Contents(Fitness for purpose is determined both by the uncertainty of the result and the end-user's requirement. Metrology cannot tell us what the latter amounts to.)/Type/Annot/Subj(Note)/Rect[339.560486 100.648254 359.560486 118.648254]/CreationDate(D:20060509133746+01'00')/NM(y0XVU1PUrEngO1ykLrVzEA)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509134115+01'00')/P 63 0 R/T(ubca445)/Popup 256 0 R/AP<>>> endobj 256 0 obj<> endobj 257 0 obj<

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In this instance, within-laboratory estimates of uncerta\ inty are mostly less than the collaborative trial result.

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The two examples shown were taken virtually at random. I\ n both instances the means and dispersions are not significantly different.

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If the measurements are made by using an analytical meth\ od of high precision \(small error bars\) the experiment will detect significant variation among the units, even if the variation is inconsequential in relation to the proposed usage.

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The densities of the kernels are added across the range \ of the data, and the resultant curve, normalised to unit area, is the kernel density.

)/Contents(The densities of the kernels are added across the range of the data, and the resultant curve, normalised to unit area, is the kernel density.)/Type/Annot/Subj(Note)/Rect[71.703308 321.527435 91.703308 339.527435]/CreationDate(D:20060509110602+01'00')/NM(Udy9BwndRhifHUMETBp1fC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509140350+01'00')/P 41 0 R/T(ubca445)/Popup 217 0 R/AP<>>> endobj 217 0 obj<> endobj 220 0 obj<

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This is a kernel density produced by setting h equal to \ 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From this we might want to investigate the theory that two i\ nconsistent analytical methods were in use by the participants. The kernel density is essentially a visual and non-parametric method. The position of modes can be determined, and their standard errors estimated, but the procedures are lengthy even for\ modern PCs. Mixture models provide a much quicker parametric method.

)/Contents(This is a kernel density produced by setting h equal to 0.75 times the reproducibility standard deviation expected from the Horwitz function. \(This is usually a good strategy.\) The kernel density shows a mode with a strong shoulder on the low tail. From\ this we might want to investigate the theory that two inconsistent analytical methods were in use by the participants.\rThe kernel density is essentially a visual and non-parametric method. The position of modes can be determined, and their standard erro\ rs estimated, but the procedures are lengthy even for modern PCs. Mixture models provide a much quicker parametric method.)/Type/Annot/Subj(Note)/Rect[75.000015 101.472443 95.000015 119.472443]/CreationDate(D:20060509111117+01'00')/NM(eRVvWjTi7Y5kmZ9HGj6SlD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509140524+01'00')/P 41 0 R/T(ubca445)/Popup 221 0 R/AP<>>> endobj 221 0 obj<> endobj 241 0 obj<

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Equilibrium is restored by suspending the separated silv\ er on the bar at distance B. \(The counter-weight stays in the same position.\)

)/Contents(Equilibrium is restored by suspending the separated silver on the bar at distance B. \(The counter-weight stays in the same position.\))/Type/Annot/Subj(Note)/Rect[331.318726 323.175781 351.318726 341.175781]/CreationDate(D:20060509123438+01'00')/NM(26Gcmzw1rtD9F4EEwgVs2D)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509140925+01'00')/P 63 0 R/T(ubca445)/Popup 242 0 R/AP<>>> endobj 242 0 obj<> endobj 243 0 obj<

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The proportion of silver \(A/B\) is dimensionless and no\ t traceable to ANY unit. Most analytical results are similarly a ratio involving a physical property of the analyte that is a surrogate for mass.

)/Contents(The proportion of silver \(A/B\) is dimensionless and not traceable to ANY unit. Most analytical results are similarly a ratio involving a physical property of the analyte that is a surrogate for mass.)/Type/Annot/Subj(Note)/Rect[75.000015 101.472443 95.000015 119.472443]/CreationDate(D:20060509123713+01'00')/NM(MtqU_7rpv-FLaLxRuv7SAD)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509141037+01'00')/P 63 0 R/T(ubca445)/Popup 244 0 R/AP<>>> endobj 244 0 obj<> endobj 253 0 obj<

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In this study, uncertainty was estimated by a ruggedness\ study that attempted to emulate interlaboratory-sized variation in procedure. All of the test materials were foodstuffs. In each instance the estimate is lower than the collaborative trial result.

)/Contents(In this study, uncertainty was estimated by a ruggedness study that attempted to emulate interlaboratory-sized variation in procedure. All of the test materials were foodstuffs. In each instance the estimate is lower than the collaborative trial result.)/Type/Annot/Subj(Note)/Rect[335.439606 323.999969 355.439606 341.999969]/CreationDate(D:20060509132217+01'00')/NM(gAtuEn5Ui0KSjVjq5d-jEC)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509142414+01'00')/P 70 0 R/T(ubca445)/Popup 254 0 R/AP<>>> endobj 257 0 obj<

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In this instance, within-laboratory estimates of uncerta\ inty are mostly less than the collaborative trial result. Of course, it is eminently possible for an individual laboratory to provide results with a uncertainty smaller than the interlaboratory SD, but most do not. Laboratories claiming such a c\ apability \(e.g., national reference laboratories\) must go to extraordinary lengths to substantiate their claim. Some laboratories may consistently provide results with a greater uncertainty. If such results are unfit for purpose, they will eventually be\ detected by proficiency tests.

)/Contents(In this instance, within-laboratory estimates of uncertainty are mostly less than the collaborative trial result.\r\rOf course, it is eminently possible for an individual laboratory to provide results with a uncertainty smaller than the interlaboratory S\ D, but most do not. Laboratories claiming such a capability \(e.g., national reference laboratories\) must go to extraordinary lengths to substantiate their claim. Some laboratories may consistently provide results with a greater uncertainty. If such resu\ lts are unfit for purpose, they will eventually be detected by proficiency tests.)/Type/Annot/Subj(Note)/Rect[72.527481 101.472427 92.527481 119.472427]/CreationDate(D:20060509134451+01'00')/NM(SeVYpODIhOXXqWx8sJSZ5A)/Name/Comment/Subtype/Text/C[1.0 1.0 0.0]/M(D:20060509142322+01'00')/P 70 0 R/T(ubca445)/Popup 258 0 R/AP<>>> endobj 258 0 obj<> endobj 263 0 obj<>stream Microsoft PowerPoint - plymouth2ubca445 endstream endobj xref 126 1 0000446049 00000 n 128 1 0000446275 00000 n 205 2 0000446373 00000 n 0000447376 00000 n 212 1 0000447493 00000 n 216 2 0000447619 00000 n 0000448426 00000 n 220 2 0000448543 00000 n 0000450343 00000 n 241 4 0000450469 00000 n 0000451268 00000 n 0000451385 00000 n 0000452314 00000 n 253 1 0000452430 00000 n 257 2 0000453463 00000 n 0000455184 00000 n 263 1 0000455309 00000 n trailer <]/Prev 445439 >> startxref 458765 %%EOF