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Analytical Data: Reliability and Presentation.

Byline: Naila Siddique and Shahida Waheed

Summary: Chemical analysis whet her it is used to determine the composition of a sample or to devise a procedure for testing or preparation of another sample requires systematic experiment design and implementation. In order to determine and verify the validity of results various methods are employed to evaluate the data obtained. This process enables the analyst not only to understand the results but to find possible reasons for differences and similarit ies bet ween samples. A simple scheme for carrying out analysis in order to obtain valid and reliable results is out lined in t his paper. Moreover the importance of using reference and quality control materials to obtain quantitative results is also highlighted. To evaluate the performance and capability of a laboratory or ananalytical procedure, parameters such as relative bias, z-scores, u-test, tests for accuracy and precision etc can be used. The use and significance of these parameters is explained using examples in this manuscript. Uncertainties and errors in measurement as well as the limits of detection (LOD) of an experiment al procedure can also provide vital information about the data obtained. Simple calculations are used to explain how these can be obtained and what their magnitude simply.

Key words : Quality assurance (QA), Quality control (QC), Reference materials (RMs ), Relative bias , Z -score, U-test, Precision, Accuracy, Uncertainty, Limits of detection (LODs ).

Introduction

A basic requirement of any scientific study is reliable compositional data. For this purpose various analytical techniques may be used depending upon the nature of the results required. For example if elemental composition is required then techniques such as inductively coupled plas ma atomic e mis s ion s pectrometry (ICP-AES), atomic abs orption s pectrometry (AAS), neutron activation analys is (NAA), X-ray fluores cence s pectros copy (XRF), proton induced X-ray emis s ion (PIXE) etc can be us ed. When analyzing organic s amples , chromatographic techniques , s uch as , gas chromatography (GC), high performance liquid chromatography (HPLC), or other s pectros copy techniques s uch as nuclear magnetic res onance (NMR), infrared s pectros copy (IR), Raman s pectros copy etc can be us ed. The s election of an analytical technique depends on the type of information required and at what s ens itivity level.

For trace analys is involving small amounts of samples a s ens itive and vers atile technique is needed. If the s elected technique does not involve laborious , cos tly and time con s uming s ample preparation s teps prior to meas urements then pos s ible contamination or los s of s ample is avoided. No one technique is ideal and therefore the best suited available technique is selected for analysis . [1-4]

The neutron activation analys is lab oratory (NAA) at the Miniature Neutron Source Reactor (MNSR), Chemis try Divis ion, Pakis tan Ins titute of Nuclear Science and Technology (PINSTECH) wascertified as a tes ting laboratory by the Pakis tan National Accreditation Council (PNAC) on the 19th of April 2005. [5] Since then it has been re-as s es s ed twice and its certification has been extended till 11-04-2016. This certification implies that the data reported by the NAA/ MNSR Laboratory is reliable and acceptable to the PNAC if s ubmitted by any indus try or organization. Reports containing compos itional data are routinely required for trade and to prove the quality of products .

In s cientific literature only data which have been obtained us ing reliable and tes ted procedures are cons idered acceptab le. To produce reliable res ults the analys ts mus t follow s ys tematic procedures . The procedures us ed s hould be tes ted us ing calibration procedures and the analys is of reference or s tandard s amples . Moreover the analys is s hould be carried out efficiently s o that the expenditure of chemical reagents and time is kept to a minimum. This goal is mos t eas ily achieved when fewer and s impler s ample preparation s teps are employed.

This manus cript was undertaken to pres ent the methodology routinely followed for elemental analys is us ing NAA at the NAA/MNSR Laboratory. The information provided in this paper which includes s tep-wis e procedure from s ample's arrival at the laboratory to the s ubmis s ion of res ults is provided as a guide for other analytical chemis ts . The ba s ic aim of this manus cript is to educate, inform or remind analys ts of good experimental design,

sequential and methodical analys is and proper way of reporting the res ults . Therefore this paper will focus on the data obtained and how to unders tand and pres ent it to s how its validity and reliability. The bas ic concepts provided here can be applied to the res ults obtained us ing any analytical procedure to obtain valid res ults in as s hort time as pos s ible. Hence "mock res ults " have been us ed in examples to enable the reader to better unders tand the information provided.

Chemical Analysis

Analytical res ults obtained are only as reliable as the method and care employed to obtain them. Therefore analytical procedures are carefully developed and tes ted prior to analys is of a new type of s ample. Fig. 1 s hows a flow diagram for carrying out chemical analys is . From this figure it can be s een

that once s ampling has been completed and a s ample provided to the analys t, the analys t has to s elect a s uitable analytical technique and prepare the s ample for analys is . In order to do this , s teps may be required which involve drying or grinding of the s ample to obtain a homogeneous s ample which fully repres ents the tes t s ample. After this , repres entative s ub -s amples of the tes t s ample are taken and prepared for meas urement. The s ample preparation s tep is technique dependant and may involve the formation of the s ample in the form of a pellet or dis c for XRF and PIXE analys is or a dis s olution /diges tion procedure to obtain the s ample in a liquid form for GC, HPLC, AAS and ICP-AES. Some non- des tructive techniques s uch as NAA may not even require a s ample preparation s tep which makes contribution from blank minimal. [6].In order to carry out analys is the following s amples are prepared:1. Tes t s ample, us ually meas ured in triplicate or more2. At leas t 2 quality control (QC) materials whos e compos ition is known may be obtained from reputable RM producers3. Reference materials (RMs ) which are us ed forcalibration of ins trument and to obtain quantitative data. Thes e s hould cons is t of ~5 s amples of different concentrations of an element/ compound being s tudied. The data obtained for thes e RMs are us ed to prepare calibration plots . Moreover certified RMs along with s ynthetic or laboratory prepared RMs can als o be us ed to increas e the number of elements / compounds determined in a s ingle analytical procedure.4. In cas es where s ample preparation involvess olvents or s ubs trates a blank is als o prepared.The QC material, RM material and blank are prepared following the procedure employed for tes t s ample preparation, the only difference being is that in place of the tes t s ample the QC material, RM material and s ubs trate (blank) are us ed res pectively. In the next s ection the various calculations undertaken to obtain the res ults of Fe concentration in a tes t s ample are given as an example.

Res ults and Dis cus s ion

The analytical techniques us ed for analys is will provide res ults for the RM, QC material, blank s ample and tes t s ample. In order to unders tand the tools us ed to obtain and evaluate the res ults obtained and what they s ignify, the Fe concentration in a tes t s ample is us ed as an example. An important point to note is that the number of s ignificant figures us ed to report the data s hould be realis tic and cons is tent when performing calculations involving multiple s teps .

To obtain analytical res ults the ins trument needs to be calibrated as dis cus s ed below. However before quantitative data can be pres ented and explained it is bes t to firs t dis cus s meas urement uncertainty and limits of detection (LODs ). Thes e are an es s ential part of any chemical analys is and are required when res ult reports are prepared.

Uncertainty Measurement

All analytical res ults are reported along with their uncertainties or errors . Thes e provide anindication about the s pread or variation in the value of the res ult provided. Meas urement uncertainty analys is may be performed us ing the methodology outlined in JCGM 100: 2008. [7] To calculate the uncertainty for a technique the uncertainty budget has to be prepared and all pos s ible type A and type B s ources of uncertainties identified. For NAA, Type A uncertainties or the random errors which occur in any meas urement include meas urement s tandard deviation (SD), uncertainty in peak area, weighing errors , errors in volume meas urement, s pectral interferences , s umming peaks corrections , uncertainty due to mat rix effect etc while type B s ources of uncertainties include uncertainty as s ociated with calibration of ins truments s uch as weight balance and the detector us ed and uncertainties quoted in the RM certificate. Both thes e uncertainties can be combined in the following way: equationwhere , UncPA, UncW, UncV, UncB, UncD, UncRM etc are the variation in meas urement (s tandard deviation), uncertainty in es timation of peak area, weighing, volume, balance calibration, HPGe detector calibration and RMs uncertainties res pectively. The firs t 4 terms are the type A and the las t 3 are the type B s ources of uncertainty. The uncertainties lis ted in the above equation are by no means exhaus tive and will differ from technique to technique. Therefore the analys t has to determine all pos s ible s ources of uncertainty in their analytical procedure. Coverage factor of k=1 to 3 can be us ed in the above equation. Values of k=1, 2 and 3 imply confidence intervals of 68.27%, 95.45% and 99.99% res pectively.

From equation 1, it can be s een that the meas urement uncertainty can be reduced by reducing all its s ources . However limitations are impos ed on analytical res ults by the ins truments us ed and their capabilities as well as the s tandards and reagents used in carrying out a meas urement. It is bes t to us e RMs which has low uncertainties for all pos s ible elements / compounds . This may not be pos s ible as RM producers provide recommended as well as information values for s ome elements on the RM certificates . In order to obtain an es timate of the uncertainty for an element for which an information value is given, adopting a wors e-cas e s cenario approach, the given value is divided by SQRT(3) as s uming a rectangular dis tribution. However as the given information value mos t probably lies near the centre as compared to the edges , the information value s hould be divided by SQRT(6), as s uming atriangular dis tribution to obtain a meas ure of the uncertainty. The latter approach may be us ed if the RMs us ed are routinely us ed in analys is and in the pas t the information values have provided accurate and precis e res ults .

Limit of Detection (LOD)

Limit of detection (LOD) is defined in many ways and may als o be referred to the minimum detectable net concentration or limit of determination/ limit of decis ion. In its s imples t form it is "the lowes t concentration that can be meas ured with reas onable s tatis tical certainty". [7] Generally LODs are calculated us ing three s tandard deviations as recommended by the Committee of Environmental Improvement of the American Chemical Society. [8] Therefore LODs are obtained from %3 and the concentration of the element/ compound determined as des cribed below.Up to 5 s amples of different concentrations of an element/ compound are prepared and us ed as RM. Here s ome res ults for Fe are given in Table -1. The data in Table-1 s hows how a meas urement parameter s uch as peak area varies with Fe concentration. From this data Fig. 2 is plotted and a s traight line fitted. The intercept (a) and the s lope (b) of the line are given by the equations 2 and 3:

Table-1: Calibration data for Fe synthetic RM.

Fe concentration (mg/kg)###Mean peak area of emitted gamma ray

###10.00.5###72536

###50.02.5###4325216

###100.05.0###9406470

###500.025.0

###1000.050.0

###457492287

###1206356032

Us ing the plot in Fig. 2 and equations 1 to 4the line that bes t fits the data comes out to be;

Peak Area = 118.96 (13.10) [Fe]-3325.35(0.00) (6)The chi-squared for this plot is 0.99 which s hows that this line fits the obs erved data very well.

The Fe peak areas for the tes t and blank s amples are given in Table-2. Thes e are tes t data pres ented here to s how how quantitative res ults are obtained. Here 3 values are given for the peak areas and a mean value is obtained. This is due to the fact that each s ample is analyzed in triplicate. Apart from thes e the different s ources of uncertainties are als o given in the s ame unit (percentage). In order to obt ain the overall combined uncertainty all uncertainties have to be converted to the s ame unit (concentration unit or %). Us ing equation 6 it can be s een that a peak area of 25462 in the tes t s ample corres ponds to the Fe concentration [Fe] of 242 g/g. Similarly the amount of Fe in the blank s ample for a peak area of400 is 31 g/g giving an overall Fe concentration forthe tes t s ample of 211 g/g. Us ing a coverage factor of 2 and the data given in Tables 2 and 3 the meas urement uncertainty can be obtained to give the amount of Fe in the tes t s ample as 21141 g/g while that in the blank is 315 g/g.From Tables 2 and 3 it can be s een that theuncertainty in the [Fe] of the blank s ample is higher than that of the tes t s ample due to the much higher Fe content of the s ample. Similarly the LOD for the blank is lower but clos er to its Fe content. The clos er a value to the LOD for an element/ compound the higher will be its uncertainty and the les s reliable its value will be.

The concentrations for all pos s ible elements / compounds for all s amples (tes t s ample, QC material and blank) may be obtained by repetition of the calculations s hown above. It s hould be noted that the number of elements meas ured in the blank s ample s hould be as few as pos s ible for it to act as a good blank. Moreover the concentration of any element/ compound meas ured in the blank s hould als o be much lower than that meas ured in the actual s ample. Therefore s pec pure reagents are generally us ed in s ample preparation or s ampling media s uch as filters etc are us ed which s hould not contribute to the background. However s ome impurities or s pecies at trace amounts may be pres ent which have to be meas ured and their amounts s ubtracted to obtain the actual concentrations .

Quality assurance / quality co ntrol (QA/QC)

To prove the validity of the results obtained QC materials such as reference materials (RMs ) are us ed. Here the data for an RM are s hown in Table -4 as an example. In this table recommended values provide by the RM producer along with data ob tained during a study are given. The variation in meas urements (SD), meas urement uncertainties and LODs are als o given. An important point to note is that the number of elements lis ted in the QC table s hould contain all of the elements quantified in the tes t s ample.

Clos e examination of Table-4 s hows experimental values to be in clos e agreement with the recommended values . Values for elements that the RM producer has not recommended but has given as information values (Br, Hf, Lu, Sc, Ta, Tb, Th andTb) are included in this table. In order to s ee if theres ults obtained compare well with the recommendedvalues the relative SD (%RSD) can be calculated. If the value of this parameter is ~10% or les s for mos t of the elements s tudied the res ults are probablyreliable. Another quick indicator of data quality isobtained when ratios of the recommended values are obtained with the obs erved values . As can be s een from Table-4 thes e s hould be as clos e to 1.0 as pos s ible. From this table it can be s een that around76% data lies in the range 0.9-1.1 while 92% data liesin the range 0.85-1.15.

Application of t-test

Statis tical tools s uch as t-test may be us ed to verify s imilarities between the 2 data s ets given in Table 4. When t-tes t is applied to the res ults obtained for the RM a value of -0.07 is obtained. At a s ignificance level of 0.05 the value of t for 48 degrees of freedom is 2.01. As the calculated t is lower than this value it s hows that the experimental values for thes e elements do not differ s ignificantly from the recommended values .

Data Evaluation ParametersIn order to carry out more thorough s tudies and evaluate the res ults obtained the following parameters may be calculated.

Relative biasequationIf R.Bias = MAB (Maximum AcceptableBias ) implies s atis factory performance and if R.Bias= MAB means uns atis factory performance [9]MAB values are given by the RM manufacturer and generally have values of 20-25%. Thes e have been obtained and given in Table -5. Scrutiny of the data in Table-5 s hows that all of the reported data have R.Bias less than 20% apart from As . The R.Bias for this analyte is greater than 28% making its value ques tionable. As thes e res ults were obtained us ing NAA it can be s peculated that the lower As value may originate from an over correction due to the pres ence of bromine in the s ample, which may give ris e to s pectral interferences due to inadequate res olution of the two peaks or limitations with the evaluation s oftware.Z-Scoreequationwhere =12.5% of the cons ens us /as s igned value.[9]

If z-s core= 2 s atis factory performance2 less than z-s core less than 3 ques tionable performance and z-s core= 3 uns atis factory performance

Z-Scores were calculated and are als o given in Table-5. From this data once again it can be s een that all of the reported data has z-s cores les s than 2 apart from As which has a z-s core greater than 2 but less than 3 making its value ques tionable. Table 5 als o s hows that all reported res ults have acceptable z-s cores . This s hows that the procedures employed in o btaining the given res ults are good and produce accurate and precis e res ults . However care s hould be exercis ed when meas uring the As concentration in a s ample

u-Testequation

If u less than 2.58 it implies s atis factory performance for a level of probability at 99%. [9]

U-Tes t values were calculated and are givenin Table 5. Thes e fulfill the criteria for good reliable res ults as u less than 2.58 for all of reported data includingAs . Therefore it can be s een that no one parameter shows the reliability of a value as u-test shows that As value is als o reliable whereas R.Bias and z-s core s how the data for this analyte to be ques tionable.

Table-2: Estimation of measurement uncertainty. (Data cited at 95% confidence interval).

###Fe Peak Area###Uncertainty###Budget (%)###Combined Unc

Sample###Value 1 Value 2 Value 3 Mean SD %SD UncPA###UncB UncW###UncV UncD UncRM###(%)

Te st Sample 25210 25437 25739 25462 265 1.04 0.63###4.00 0.50###1.00 1.00 2.00###9.74

###Blank###385###423###392###400 20 5.06 5.00###4.00 0.50###1.00 1.00###16.59

Table-3: Fe concentration and LOD (mg/kg) of test and blank samples. (Data cited at 95% confidence interval).

###[Fe]=(Peak Area+3325.35)/###LO D

###Sample###Peak Area###Unc (mg/kg) 3 Sigma (%)

###118.96 (mg/kg)###(mg/kg)

Te st Sample + Blank Sample###25462###242###24###5.00###12.10

###Blank###400###31###5###8.00###2.51

###Te st Sample###25062###211###41###9.43###19.91

Table-4: Elemental composition of QC material at 95% confidence interval.

###Laboratory Values (mg/kg)###Recommended Values (mg/kg)###Ratio of Recommended

###Element

###Mean###Unc###RSD (% )###SD###LOD###Mean###SD###/Lab Values

###Al###44336###4440###7.4###3268###1215###51800###6475###1.17

###As###8.24###1.26###10.7###0.88###0.25###11.50###1.44###1.40

####B r###216###66###8.9###19.31###113.96###224.00###28.00###1.04

###Ce###63.02###15.96###6.0###3.81###1.30###61.10###7.64###0.97

###Co###8.87###2.14###6.7###0.59###0.30###9.20###1.15###1.04

###Cr###74.00###16.05###5.3###3.87###3.26###74.40###9.30###1.01

###Cs###3.65###0.54###4.9###0.18###0.45###3.73###0.47###1.02

###Eu###0.97###0.30###9.3###0.09###0.06###1.08###0.13###1.11

###Fe###26081###1388###4.2###1099###363###26300###3288###1.01

####Hf###5.75###0.90###3.5###0.24###0.24###6.23###0.78###1.08

###K###19057###5988###11.5###2197###3453###20000###2500###1.05

###La###28.55###5.82###8.7###2.52###1.97###30.20###3.78###1.06

####Lu###0.28###0.11###10.7###0.03###0.02###0.31###0.04###1.11

###Mn###332###46###12.9###43###2###356###45###1.07

###Na###23756###1891###3.7###890###190###23800###2975###1.00

###Rb###73.63###10.36###9.5###7.02###24.35###82.00###10.25###1.11

###Sb###1.34###0.21###10.4###0.14###0.30###1.34###0.17###1.00

####Sc###8.14###1.23###3.7###0.26###0.09###8.32###1.04###1.02

###Sm###4.62###0.41###6.5###0.25###0.07###4.94###0.62###1.07

####Ta###0.93###0.26###10.8###0.10###0.05###0.97###0.12###1.04

####Tb###0.70###0.33###5.7###0.04###0.03###0.63###0.08###0.90

####Th###8.30###1.27###4.8###0.37###0.22###8.89###1.11###1.07

###V###63.92###10.43###6.6###4.20###16.82###73.00###9.13###1.14

####Yb###1.94###0.57###9.3###0.18###0.25###2.08###0.26###1.07

###Zn###151###17###9.0###13.46###3.60###140.60###17.58###0.93

Table-5: Evaluation of data obtained for QC material (Reference Material).

###Trueness###Precision

Element###Rel B ias (% )###z-score###u-test

###A1###A2###Acceptance###P (% )###Acceptance###Final Score

###Al###-14.41###-1.15###-0.95###7464.17###20256.42###A###16.02###A###A

###As###-28.39###-2.27###-1.71###3.26###4.94###A###19.78###A###A

####B r###-3.67###-0.29###-0.11###8.21###185.77###A###33.19###A###A

###Ce###3.14###0.25###0.11###1.92###45.64###A###28.24###A###A

###Co###-3.55###-0.28###-0.13###0.33###6.27###A###27.15###A###A

###Cr###-0.53###-0.04###-0.02###0.40###47.86###A###25.03###A###A

###Cs###-2.25###-0.18###-0.12###0.08###1.85###A###19.48###A###A

###Eu###-10.17###-0.81###-0.34###0.11###0.84###A###33.12###A###A

###Fe###-0.83###-0.07###-0.06###219.14###9207.19###A###13.59###A###A

####Hf###-7.76###-0.62###-0.41###0.48###3.06###A###19.99###A###A

###K###-4.71###-0.38###-0.15###942.80###16742.13###A###33.82###A###A

###La###-5.45###-0.44###-0.24###1.65###17.91###A###23.92###A###A

####Lu###-9.58###-0.77###-0.25###0.03###0.31###A###42.69###N###W

###Mn###-6.87###-0.55###-0.38###24.46###164.63###A###18.61###A###A

###Na###-0.18###-0.01###-0.01###43.99###9094.42###A###14.82###A###A

###Rb###-10.21###-0.82###-0.57###8.37###37.60###A###18.82###A###A

###Sb###-0.06###0.00###0.00###0.00###0.70###A###20.26###A###A

####Sc###-2.20###-0.18###-0.11###0.18###4.15###A###19.58###A###A

###Sm###-6.54###-0.52###-0.44###0.32###1.92###A###15.36###A###A

####Ta###-3.96###-0.32###-0.13###0.04###0.74###A###30.48###A###A

####Tb###10.71###0.86###0.20###0.07###0.87###A###48.60###N###W

####Th###-6.63###-0.53###-0.35###0.59###4.36###A###19.79###A###A

###V###-12.44###-1.00###-0.66###9.08###35.75###A###20.55###A###A

####Yb###-6.57###-0.53###-0.22###0.14###1.62###A###32.02###A###A

###Zn###7.13###0.57###0.41###10.02###62.78###A###16.76###A###A

TruenessFor res ults to be accurate the requirement is[9]A1=A2whereequationThe values of A1 and A2 were calculated and are given in Table-5. From thes e res ults it can be s een that all of the data fulfills the expres s ions A1= A2 meaning that the truenes s of accuracy criteria is fulfilled.

Precision

To check the precis ion of the data the following parameter is calculated: equation

If P = LAP (Limit of Acceptable Precis ion)implies s atis factory performance

LAP data are given by the RM manufacturer and generally have magnitudes of 20-25%. However LAPs may be as high as 40% in s ome cas es . The parameter P has been obtained for all of the elements determined in the RM s ample and are given in Table. From thes e res ults it can be s een that 23 of the 25 elements determined in the RM s ample have P= MAB, only Lu and Tb have P greater than 40 %. This may be due to the higher reported uncertainties for thes e elements which can be reduced by greater care in carrying out analys is as well as us ing RMs with lower uncertainties for thes e elements .

Acceptance Criteria

In order to reach a final decis ion about each value in a data s et the following criteria are us ed. If any of the z or u s core criteria are not fulfilled then the res ult is declared "Not Acceptable". However if all criteria are fulfilled but either truenes s or precis ion criteria is not fulfilled then a further check is applied i.e. the reported res ult relative bias (R.Bias ) is compared with the maximum acceptable bias (MAB) as defined by the RM producer. If R.Bias = MAB, the final s core will be "Warning". "Warning" reflects two s ituations ; 1) the res ult has a s mall meas urement uncertainty; but its bias is s till within MAB or 2) a res ult clos e to the assigned propertyvalue is reported, but the as s ociated uncertainty is large. If R.Bias greater than MAB the res ult will be "Not Acceptable". Evaluation of the results for the RM sample us ing the treatment outlined above provides the outcomes given in Table-5. Therefore only the res ults for Lu and Tb fall into the "Warning" category, while the data for the remaining 23elements are all classified as acceptable.Laboratory ClassificationRM manufacturers , such as the InternationalAtomic Energy Agency (IAEA), us es the following

criteria to evaluate the performance of laboratories which participate in any intercompars ion or proficiency tes t (PT) exercis e: [10]

Group 1: laboratories s coring z-s core less than 3 for =90% of the data;

Group 2: laboratories s coring z-s core less than 3 for 75%to less than 90% of the data;

Group 3: laboratories s coring z-s core less than 3 for 50%to less than 75% of the data;

Group 4: laboratories s coring z-s core less than 3 for less than 50% of the data

If the above criteria are us ed for s elf evaluation by a laboratory or for an analytical procedure, then as all of the data given in Table -4 and5 have ?z- score? less than 3 therefore the laboratory is placed in Group 1. Moreover taking into account all of the acceptance criteria it can be s een from Table -5 that 23 of the 25 res ults reported i.e. 92% are acceptable with only the results for Lu and Tb being deemed uns atis factory.

Graphical representation of QA/QC results

Generally it is better to s how res ults graphically as plots s how mos t trends more clearly and are eas ier to read. Here various parameters , as given in Tables 4 and 5, have been plotted to highlight this point. [10-19] In Fig. 3 the recommended and obs erved laboratory values have been plotted s ide by s ide as bars to s how direct comparis on between the two data s ets . This is s hown as a log plot to include elements with a large range of concentrations . The uncertainties in both data s ets have als o been plotted as error bars . From this plot it can be s een that the bars for the recommended and laboratory values for each element have very s imilar lengths . Table-4 and Fig. 3 are the s imples t ways of comparing RM data with obs erved res ults and can point out outliers and s ignificantly different data points at a glance.

In Fig. 4 the recommended values have been plotted agains t the obs erved values for the RM s ample. This is another s imple way of pres enting the res ults without much data manipulation. As c an be s een from this figure, all data points lie on the y=x line with intercept of zero. This s hows good agreement between the 2 datas ets . Such plots are generally pres ented as log log plots to take into account the large concentration ranges of elements pres ent in the RMs . Uncertainties cited by the RM producer and thos e meas ured are als o plotted to s how any variations in data.

Another graphical method of data pres entation is by plotting the ratios of the recommended to the laboratory values . This has been done in Fig. 5. Thes e values were given in Table -4 but in this plot it can be s een that the elements Al, As , Eu, Rb, Tb and V lie outs ide the 10% range. This parameter s hows the ques tionable character of As which is underes timated s ignificantly in this s tudy. Moreover Tb is over-es timated as it has the lowes t ratio.

Graphically data can be pres ented by utilizing equations 7 to 9 and plotted the Relative Bias , the z-s cores and the u-tes t values . This has been

done in Figs . 6 to 8 res pectively. Therefore in Fig. 6 the Relative Bias (Rel.Bias %) has been plotted for the RM for all the elements meas ured. From this figure it can be s een that the values of this parameter are generally negative in magnitude which means that the obs erved values are les s than the recommended values s ugges ting s light under-es timation. This feature is more evident for the elements As and Tb for reas ons mentioned earlier. In Figs . 7 and 8 the z- s cores and the u-Tes t values have been plotted. From thes e figures it can be s een that As has the highes t magnitude of both thes e parameters . However the magnitudes of both thes e parameters lie within the pres cribed ranges .

From Figs . 3 to 8 the s ame res ults are pres ented in various ways to dis tinguis h between reliable and les s reliable res ults . The s ame res ults are pres ented in Tables 3 and 4. From thes e plots and tables it can be s een that the data obtained for the QC material RM is in very good agreement with the recommended values . Hence the methodology us ed to obtain the res ults reported in Table -4 provided reliable res ults giving the analys t confidence in the reported res ults .Conclus ionThe information pres ented in this paper s hows the importance of unders tanding analytical data and how to pres ent them s o that the reader can eas ily unders tand how they have been obtained. It als o s hows the s ignificance of s imple evaluation tools which can be us ed routinely to evaluate the res ults obtained and provide confidence in the reported res ults . Such tools can be us ed to devis e and tes t new analytical procedures as well as tes t and evaluate the performance of individual laboratories or analys ts .

References

1. S. Waheed, N. Siddique and J. H. Zaidi, Journal of Radioanalytical and Nuclear Chemistry , 289,765, (2011).2. N. Siddique and S. Waheed, Journal ofRadioanalytical and Nuclear Chemistry , 291,817 (2012).3. N. Siddique, S. Waheed and Y. Faiz, Journal ofRadioanalytical and Nuclear C hemistry, 291,919 (2012).4. N. Siddique, Sabiha-Javied, S. Waheed and M.Tufail, Journal of Radioanalytical and NuclearChemistry, 292, 445 (2012).5. http://www.pnac.org.pk/info/Accreditation%20S copes /Finalized%20s copes %20(Feb%202007)/PI NSTECH%20Lab,%20Nilore.pdf http://www.pnac.org.pk/index.php?PageId=876. International Standard ISO/IEC 17025, Secondedition 2005-05-15 General Requirements for the Competence of Tes ting and Calibration Laboratories ISO, Geneva Switzerland7. Quantifying Uncertainty in Nuclear AnalyticalMeas urements , Eurachem/ Citac Guide, (2000)8. R. J. Mes ley, W. D. Pocklington and R. F.Walker, Analyst, 116, 975 (1991).9. A. Shakhas hiro, A. Trinkl, A. Torvenyi, E.

Zeiller, T. Benes ch, U. Sans one. (2006) IAEA/AL/168, Report on the IAEA -CU-2006-06Proficiency Tes t on the determination of major, minor and trace elements in ancient Chines e ceramic, Seibers dorf, Aus tria, November 200610. N. Siddique, S. Waheed, M. Daud, A. Rahman and S. Ahmad, Journal of Radioanalytical and Nuclear Chemistry, 274, 181 (2007).11. S. Waheed, M. Was eem, A. Rahman and S.Ahmad, Geostandards Newsletter, 25, 137 (2001).12. S. Waheed, S. Ahmad, A. Rahman and I. H.Qures hi, Journal of Radioanalytical and NuclearChemistry, 250, 97 (2001).13. S. Waheed, A. Rahman, M. Daud, J. H. Zaidi and S. Ahmad, Radiochimica Acta , 92, 939 (2004).14. N. Siddique, A. Rahman, S. Waheed, M. Was im, M. Daud and S. Ahmad, Journal of Radioanalytical and Nuclear Chemistry , 268,579 (2006).15. S. Waheed, A. Rahman, N. Siddique, S. Ahmad and M. Ros s bach, Accreditation and Quality Assurance, 12, 311 (2007).16. S. Waheed, N. Siddique, M. Arif, I. Fatima, N.Khalid, S. Rahman, M. Daud and M. Was im, Journal of Radioanalytical and Nuclear Chemistry, 277, 539 (2008).17. N. Siddique, A. Rahman, S. Waheed, M. Was im,M. Daud and S. Ahmad, Journal of the Chemica lSociety of Pak istan , 31, 622 (2009).18. S. Waheed, A. Rahman, N. Siddique and S Ahmad, Geostandards and Geoanalytical Research, 31, 133, (2007).19. N. Siddique and S. Waheed, Journal of theChemical Society of Pak istan , 31, 916, (2009).
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Date:Jun 30, 2014
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