Theoretical evaluation of solid sampling–electrothermal atomic absorption spectrometry for screening purposes† Miguel A. Belarra,* Martý�n Resano and Juan R. Castillo Department of Analytical Chemistry, University of Zaragoza, E-50009 Zaragoza, Spain Received 30th October 1998, Accepted 25th January 1999 Obtaining results in the determination of metals by electrothermal atomic absorption spectrometry is conditioned by the non-homogeneity of the sample and the possible appearance of outliers, which make it diYcult to obtain reliable results with only a few measurements.In order to establish the optimum conditions for using the technique as a screening method, 18 000 results corresponding to diVerent possible situations were simulated by computer and subsequently analysed using information theory. In view of the results obtained, it can generally be claimed that the median can be used to better eVect than the mean value as the former is less aVected by the potential presence of outliers.Using the median and with normal working conditions, the minimum number of measurements that need to be carried out to guarantee a recall of over 0.95 in a screening method ranges from 5 to 20, involving between 15 min and 1 h work. One of the main reasons why the determination of metals by analyte distribution is of great importance. Furthermore, under these conditions the appearance of potential outliers is particu- electrothermal atomic absorption spectrometry with direct introduction of solid samples (SS-ETAAS) is not more widely larly problematic for two reasons.First, if a small number of measurements are carried out the influence of potential outliers used is that the relative standard deviation (RSD) values obtained are high, in most cases between 10 and 30%. In a is greater, and second, it is more diYcult to reject them statistically. previous paper it was shown that, in general, with samples of an organic nature these values cannot be attributed to The purpose of this work was to study the influence of sample non-homogeneity and the appearance of potential deficiencies of the technique but are caused by the nonhomogeneity of the small sample masses introduced into the outliers on the results in order to establish the optimum working conditions and to evaluate the possibilities of the atomizer (normally around 1 mg), and also that this problem is diYcult to solve.1 technique in a screening system.Since the median was sometimes found to provide better results than the mean,7 an A second cause of imprecision and bias is the possible appearance of outliers. Despite its importance, this subject has important part of our work consisted in comparing them. In order to do this, 18 000 results were generated with a only been dealt with in depth by Kurfu� rst when overestimated results are obtained, which he classified as either endogenous computer using the empirically observed type of variation and frequency of outliers in SS-ETAAS as input parameters.In (appearance of ‘nuggets’, small particles with an unusually high analyte content) or exogenous (essentially contami- this study the presence of potential outliers of an endogenous nature, which are diYcult to detect and require special treat- nation)2 and developed a method for treating the former.3 In our experience, the appearance of potential outliers should ment, was not considered, so all the outliers were treated as exogenous. The conclusions reached using this simulation are always be taken into account when using SS-ETAAS, since they can considerably aVect the treatment of results even if contrasted with the real experimentally obtained results.few in percentage terms. Moreover, we have found results that provide underestimated values, probably owing to an Simulation design occasional incorrect atomization process, although this is much less frequent.Nine populations of diVerent characteristics with 2000 values The characteristics of SS-ETAAS are well suited to the each were generated to simulate the results obtained by study of the homogeneity of CRMs4 in which the diVerent SS-ETAAS. The procedure given in Table 1 was used for the analyte distributions in the sample pose no problem but are, generation and treatment of results for all the populations. in fact, the object of study and the problem of potential Three of the populations correspond to normal distributions outliers can be overcome by carrying out a large number of with m=100 and three diVerent RSD values (RSDs=10, 20 measurements.2 and 30% representing diVerent degrees of sample non- Apart from this special application, the SS-ETAAS homogeneity); higher RSDs values, which seem improbable, technique seems useful when the aim is to obtain reasonably were not considered. reliable results economically and rapidly.SS-ETAAS is poten- The other six populations take into account the appearance tially useful as a screening method5 since it is possible to take of potential outliers, which was simulated by replacing at advantage of the high throughput of the technique to filter random 100 and 200 values in the former populations (correout the majority of the samples in a two-stage control system.6 sponding to 5 and 10% of the total values) with random results In this situation, sample handling should be minimal and obtained between 0 and 300, so that the appearance of the smallest number of measurements possible should be unusually overestimated results is more probable.carried out, so the influence of an insuYciently homogeneous The mean value (x: p), the median (mp) and the relative standard deviation (RSDp) of the final nine populations are given in Table 2 and the distribution of results of two popu- †Presented at the 8th Solid Sampling Spectrometry Colloquium, Budapest, Hungary, September 1–4, 1998.lations can be seen in Fig. 1. It can easily be appreciated that J. Anal. At. Spectrom., 1999, 14, 547–552 547Table 1 Generation of the populations and calculation of results 1. Three series of 2000 values were generated with a normal distribution with m=100 and a variable RSDs (RSDs=10, 20 and 30%) which represents the non-homogeneity of the sample 2. q values were generated at random ranging from 0 to 300 (q=0, 100, 200), which represent potential outliers 3.q values of each of the normal distributions obtained in (1) were randomly replaced by the q random results obtained in (2) 4. The mean value (X9 p), the median (mp) and the RSD (RSDp) of the final populations were calculated 5. The 2000 values (x1, …, x2000) of each population were grouped into 100 series of 20 correlative values (x1 to x20, x21 to x40, etc.) 6. The mean value [X9 1(n) to X9 100(n)] and the median [m1(n) to m100(n)] of each series were calculated using only the first n values of the series (n= 5, 7, 10, 15, 20) 7.The average value and RSD of the mean values [X9 x: (n) and RSDx: (n)] and the medians [X9 m(n) and RSDm(n)] were calculated n=20 n=15 n=10 n=7 n=5 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 X9 1(n) m1(n) x21 … x40 X9 2(n) m2(n) e e x1981 … x2000 X9 100(n) m100(n) X9 p mp RSDp X9 x: (n) X9 m(n) RSDx: (n) RSDm(n) the mean value moves away from 100 when the number of Table 2 Characteristic values of the nine populations generated outliers increases with a deviation of up to almost 7%, whereas RSDs (%) Outliers (%) x: p mp RSDp (%) its influence on the median is much less marked ( less than 2%).The presence of outliers clearly increases the RSDp values 10 0 100.3 99.7 10.0 (between 25 and 200%). 10 5 103.6 100.2 24.0 In order to simulate the influence of the number of 10 10 105.4 100.4 30.9 measurements carried out to obtain a result, the 2000 values 20 0 100.8 100.9 20.2 for each population were grouped in series of 20 so that 100 20 5 103.9 101.5 30.4 20 10 106.6 101.9 35.6 determinations were simulated for each of the nine cases.For 30 0 100.0 99.6 29.2 each of the 100 series the mean value [ x: 1(n) to x: 100(n)] and the 30 5 103.2 100.2 36.2 median [m1(n) to m100(n)] were calculated in several situations: 30 10 104.9 100.4 40.1 using only the first five, seven, 15 and 20 values (n=5, 7, 10, 15 and 20).Finally, the average value and the RSD of the mean values [ x: x: (n) and RSDx: (n)], and the average value and the RSD of the medians [ x: m(n) and RSDm(n)] were calculated. The results are given in Table 3. Results and discussion Analysis of results using information theory Given the large number of results available, their analysis is complex mainly because the diVerent variables considered (RSDs, number of outliers, use of the mean value or median and number of measurements) may aVect the precision and bias diVerently.Information theory simplifies the study as it makes it possible to calculate a single parameter (total information content, TIC) which includes both precision and bias. The TIC value was therefore calculated for all results using the expression proposed by Eckschlager and Danzer:8 TIC=lb x2-x1 sÓ2p -0.72 d2+sr2 s2 (1) where x2-x1 are the limits of the a priori information, d is the bias, that is, the diVerence between the value of x: x: (n) or of x: m(n) (depending on whether the mean values or medians were used in each series) and 100, s is the standard deviation of the 100 results and sr is the standard deviation of the true value, which was considered to be zero.In view of eqn. (1), the TIC values obtained clearly depend to a great extent on the amount of previous information [ lb (x2-x1)]. This poses no problem for a general treatment since Fig. 1 Distribution of the results of the populations with RSDs=20%: (a) without outliers; (b) with 10% of outliers.the TIC is only used in this study for the purpose of comparison 548 J. Anal. At. Spectrom., 1999, 14, 547–552Table 3 Results of the mean value, relative standard deviation and total information content of each population in function of the number of measurements RSDs (%) Outliers (%) X9 x: (5) X9 m(5) X9 x: (7) X9 m(7) X9 x: (10) X9 m(10) X9 x: (15) X9 m(15) X9 x: (20) X9 m(20) 10 0 101.2 100.9 101.1 100.8 100.7 100.1 100.2 99.8 100.3 99.8 10 5 103.8 100.9 104.5 101.0 104.4 100.6 103.8 100.3 103.6 100.3 10 10 106.9 101.1 107.0 100.9 106.6 100.9 105.6 100.4 105.4 100.4 20 0 101.6 102.1 101.1 102.0 100.9 102.0 100.8 100.6 100.8 100.8 20 5 105.5 102.4 105.7 102.5 104.6 102.4 103.8 100.8 103.9 101.5 20 10 107.1 102.5 108.5 103.0 107.6 103.1 106.5 101.5 106.6 102.0 30 0 100.3 100.5 100.5 100.7 100.3 101.2 99.9 99.6 100.0 100.2 30 5 102.9 101.1 103.1 101.5 103.2 102.2 102.5 100.1 103.2 100.9 30 10 104.4 101.7 104.5 102.0 105.2 103.0 104.2 101.2 104.9 101.2 RSDx: (5) RSDm(5) RSDx: (7) RSDm(7) RSDx: (10) RSDm(10) RSDx: (15) RSDm(15) RSDx: (20) RSDm(20) 10 0 4.2 4.9 3.9 4.6 2.8 3.1 2.4 2.8 2.0 2.4 10 5 11.2 5.6 10.6 4.8 8.3 3.5 6.7 2.9 5.8 2.5 10 10 14.7 6.5 12.1 5.4 10.2 4.1 8.6 3.4 7.1 2.8 20 0 9.0 9.7 7.8 9.1 6.8 7.6 5.4 6.1 4.6 5.5 20 5 14.7 10.0 12.7 9.7 10.8 8.0 8.4 6.6 7.3 5.9 20 10 14.5 9.9 13.6 9.2 11.1 8.0 9.2 6.7 8.5 6.2 30 0 13.0 15.5 11.3 13.5 9.5 10.6 7.3 9.1 6.3 7.3 30 5 16.0 15.6 14.0 14.0 10.9 10.9 9.1 9.0 7.4 7.5 30 10 17.9 16.3 15.8 15.2 12.2 12.1 9.5 9.6 7.8 7.6 TICx: (5) TICm(5) TICx: (7) TICm(7) TICx: (10) TICm(10) TICx: (15) TICm(15) TICx: (20) TICm(20) 10 0 6.5 6.3 6.6 6.3 7.1 6.9 7.3 7.1 7.6 7.3 10 5 5.0 6.1 5.1 6.3 5.3 6.7 5.6 7.0 5.8 7.2 10 10 4.6 5.9 4.8 6.1 5.0 6.5 5.2 6.8 5.4 7.1 20 0 5.4 5.3 5.6 5.4 5.8 5.6 6.2 6.0 6.4 6.1 20 5 4.6 5.2 4.8 5.3 5.1 5.6 5.4 5.9 5.6 6.0 20 10 4.6 5.3 4.6 5.3 4.8 5.5 5.1 5.8 5.2 5.9 30 0 4.9 4.6 5.1 4.8 5.3 5.2 5.7 5.4 5.9 5.7 30 5 4.5 4.6 4.7 4.8 5.1 5.1 5.3 5.4 5.5 5.7 30 10 4.4 4.4 4.5 4.6 4.8 4.9 5.2 5.3 5.3 5.6 and no attempt is made to reach conclusions about absolute cases and diVerent percentages of outliers present) when 10 measurements were carried out to obtain the result (n=10).values with regard to the total amount of information gained. The discontinuous central line represents the situation in which Consequently, for this study values x1=10 and x2=1000 were the mean value and the median provide the same total amount used.The TIC results thus obtained are given in Table 3. of information and the points above the line indicate that better results were obtained when the mean value was used Comparison between the use of mean value and median (the further away from the line the better) while the points Fig. 2 shows the TIC values obtained using the mean value below the line indicate the opposite.against those obtained using the median (for diVerent RSDs In the graph it can clearly be seen that the diVerent behaviours of the mean value and the median depend on the presence of outliers to such an extent that the mean only gives TIC values which are slightly higher than those of the median when outliers are absent. The presence of 5% of outliers causes a marked decrease in the TIC obtained when the mean value is used and this drop increases, although less markedly, when the outliers exceed 10%.It can be observed that when outliers are present the TIC values obtained using the mean value hardly improve when the RSDs value decreases. However, the TIC values obtained when the median is used, which depend to a considerable extent on the RSDs value, depend very little on the presence of outliers. This can be deduced from the verticality of the lines joining points of equal RSDs value. Although the median always gives higher TIC results than the mean value when outliers are present, the diVerence between the two is less noticeable when the RSDs value increases so that when it reaches 30% the diVerences between using the mean and the median, both in the presence and in the absence of outliers, are almost insignificant.The results obtained when the number of measurements carried to obtain the result is 5, 7, 15 or 20 are similar to those previously mentioned for 10 measurements, with the diVerent lines in a slightly diVerent position from those given Fig. 2 Comparison between the TIC values obtained for the diVerent populations using the mean value and the median with n=10. in Fig. 2. J. Anal. At. Spectrom., 1999, 14, 547–552 549Table 5 Percentage variance ascribable to each factor using the mean value and the median Variance (%) Factor Using the mean value Using the median No. of measurements (n) 14.2 13.8 RSDs 21.1 85.1 Percentage of outliers 64.7 1.1 the mean or the median. The cases when outliers are present or absent are studied separately.With regard to the use of either the mean or the median, it can be observed in Table 4 that this has little influence when there are no outliers, but in the presence of outliers it becomes the main source of variance and the results are better with the median. Taking into account this conclusion, the small contribution of the percentage of outliers to the total variance (approximately 4%) could be considered surprising.It is mainly due to the fact that in this analysis only an increase in potential Fig. 3 Comparison between the TIC values obtained using the mean outliers from 5 to 10% was considered which, as can be seen value and the median in function of the number of measurements for in Fig. 2, has a much less marked eVect than an increase from the three populations with RSDs=20%. 0 to 5%. The percentage variances abscribable to each of the first three factors, using the mean value or the median, are Influence of number of measurements presented in Table 5, studying all the populations (with and without outliers). One can now clearly observe the influence In a similar way as in the previous study, Fig. 3 shows the TIC values obtained using the mean and the median when a of the percentage of outliers, which becomes the main source of variance when working with the mean whereas it is almost diVerent number of measurements were carried out to obtain the result for the intermediate case where RSDs=20%. The insignificant when working with the median.The RSDs value, however, is the main contributor to the other two distributions display identical behaviour. As expected, an increase in the number of measurements variance when the median is used while its contribution is less important with the mean. The number of measurements carried leads to improved TIC values but, unlike in the study of the mean and the median, no diVerences can be established out to obtain a result is the least dependent variable of the other factors, given that its variation ranges in all cases from between the diVerent conditions.In fact, the improvement is the same using the mean or the median ( lines with a slope 12.6 to 14.2%. close to unity) and, in proportion, the TIC gain with increase in the number of measurements is almost independent of the Results as a screening method number of outliers. The discussion in the previous sections is based on a very As there is no criterion which makes it possible to relate large number of results (100 per population, each of which is the absolute values of TIC to conventional analytical paramthe mean or median of 5, 7, 10, 15 or 20 values). Consequently, eters, it is impossible to decide with these results which is the general tendencies can be seen but it is impossible to reach most suitable number of measurements to obtain a result, concrete conclusions regarding the number of measurements.taking into account that 20 measurements involve a fourfold Given that the use of SS-ETAAS as a method of screening increase in time to obtain a result compared with five measureinvolves the minimum number of measurements possible, ments. Consequently, the influence of the number of measurestudying this parameter is of fundamental importance. ments will be studied later when the procedure is applied as a Consequently, the recall (the characteristic screening param- screening method.eter) was calculated using the values x: 1(n) to x: 100(n) and m1(n) to m100(n) for each of the nine cases studied: Results of analysis of variance The conclusions drawn from the variance analysis of all the recall= No. of correct identification No. of attempted identifications (2) TIC values obtained coincide perfectly with those reached in individual cases. Table 4 shows the percentage variance ascrib- where correct identifications are considered to be those in able to RSDs, the percentage of outliers, the number of which the value of x: i(n) or mi(n) (i=1, 2, …, 100) is within a measurements carried out to obtain each result and the use of pre-established margin.The results for the case when the margin is ±20% are given in Fig. 4. Logically, the results Table 4 Percentage variance ascribable to each factor with and without depend on the RSDs values and the percentage of outliers, outliers data which can hardly be considered as previously known in the case of a rapid screening method.However, if we consider Variance (%) a recall value 0.95 to be acceptable, it can be seen that when the median was used seven measurements provided correct Populations without Populations with results in all cases unless the RSDs value was 30%, in which Factor outliers outliers case 15 measurements were necessary. No. of measurements (n) 12.6 12.7 In our experience in the field of SS-ETAAS, we have found RSDs (%) 82.7 28.7 RSDs values higher than 30% on only one occasion (for a rice Percentage of outliers 4.0 sample, not previously homogenized, which decreased to less Mean/median 4.7 54.6 than 20% after reduction of the particle size1) and the most 550 J.Anal. At. Spectrom., 1999, 14, 547–552Fig. 5 Distribution of results for the determination of (a) cadmium in sewage sludge and (b) copper in a vitamin complex. Table 6 Characteristic values for the determination of cadmium in sewage sludge and copper in a vitamin complex Cadmium Parameter With outliers Without outliers Copper No.of results 105 96 157 x: p 6.8 6.4 107.1 mp 6.4 6.4 106.4 RSDp (%) 30.7 15.5 18.7 sample dissolution are not statistically significant at the 95% level. Consequently, the data seem similar to those of the Fig. 4 Predicted results of a screening system with a tolerance margin model with RSDs=20% when outliers are absent. of±20%: (a) RSDs=10% ( lines corresponding to the mean and the However, the distribution of the results obtained in the median without outliers overlay); (b) RSDs=20%; (c) RSDs=30%.determination of cadmium in sewage sludge indicates the presence of outliers; the diVerence between the mean and the frequent values are in the 15–25% range. In these conditions, median is statistically significant at the 95% level and and in view of the previous results, it can be said that in the median result is closer to that obtained after sample practice 10 measurements (approximately 30 min work) should dissolution (6.3±0.2 mg kg-1).After eliminating the results guarantee a recall higher than 0.95 for a tolerance margin of outside the interval x:±ts, a normal distribution is obtained ±20% and that frequently (RSDs value lower than 20%) five with the characteristics shown in Table 6. The situation is measurements may be suYcient. therefore similar to the model with RSDs=15% and 10% Clearly, if the tolerance margin desired is smaller, the of outliers.number of measurements should be increased. Hence, for a If the 105 results obtained in the determination of cadmium margin of ±15%, 20 measurements should be carried out and and the 157 obtained in the determination of copper are it does not seem generally possible to guarantee a margin grouped in series of five (21 determinations for cadmium and of ±10%. 31 for copper) and the same calculations are carried out as with the model [calculation of, x: x: (5), x: m(5), RSDx: (5), RSDm(5) Comparison between the model and the results with real samples and the recall of a screening method with a tolerance margin of ±20%, the results of which are given in Fig. 6], the data The eYciency of the model proposed and the validity of the results obtained by its application were compared with the in Table 7 are obtained. The predicted values are also given (in the case of cadmium, intermediate values between RSDs= results obtained experimentally in the determination of cadmium in sewage sludge9 and copper in a vitamin complex,10 10 and 20%) according to the model proposed.The bias percentage was calculated in comparison with that obtained using the results obtained with optimum sample masses in both cases. Their distribution is shown in Fig. 5 and their after sample dissolution. No predicted result is given for copper because the distribution is normal. population data are given in Table 6. The determination of copper in the vitamin complex appears As can be observed in Table 7, the agreement between the experimental results and the model is generally very satisfac- to have a normal distribution, which was confirmed by applying the Kolgomorov–Smirnov test, and the diVerences between tory, supporting the conclusions reached previously with the model.The most significant diVerence is in the cadmium recall the mean value and the median and the value obtained after J.Anal. At. Spectrom., 1999, 14, 547–552 551nations) after rejecting potential outliers by the Dixon Q test with a 95% level (Fig. 6, determinations 3 and 12 would no longer be erroneous, 7 and 18 would still be erroneous and 10 would then become erroneous), a recall of 0.86 is obtained, which despite the additional work for the treatment of results is still clearly lower than that obtained with the median, even if the latter were close to the predicted value (0.95). Conclusions The results obtained in the determination of metals by SS-ETAAS can be compared with a model with two variables: the lack of homogeneity of the small subsamples introduced into the atomizer and the presence of potential outliers.Information theory, which combines bias and imprecision in a single parameter, proved to be very suitable for the analysis of 18 000 results created according to the model proposed and corresponding to diVerent situations of both variables (RSDs= 10, 20 and 30% with 0, 5 and 10% of outliers). Although this data set has been generated according to our experience working with SS-ETAAS, the conclusions drawn might also be applied to other methods that present a similar pattern.The results obtained using the mean value or median with a small number of measurements (5–20) show that the mean value depends greatly on the presence of outliers. Outliers have hardly any incidence on the results obtained using the median, which are only influenced by the RSDs value.Consequently, if screening tests are carried out by SS-ETAAS when the sample characteristics are unknown, the median Fig. 6 Results of a screening system with a tolerance margin of ±20% should be used. If no outliers are present the results are (upper and lower lines) for (a) cadmium in sewage sludge and comparable to those obtained with the mean value and with (b) copper in a vitamin complex. outliers the results are clearly better. If the median is used, with or without outliers, 10 Table 7 Comparison between the predicted values and the results measurements (which involves around 30 min work) are obtained experimentally in the determination of cadmium in sewage suYcient to guarantee a recall higher than 0.95 in a screening sludge and copper in a vitamin complex with n=5 method with a tolerance margin of ±20%, provided RSDs Cadmiuma Coppera values lower than 30% are used, which is usually the case.Mean value Median Mean value Median The authors acknowledge the financial support by the Direccio�n General de Investigacio�n Cientý�fica y Cultura Bias (%) 7.6 (7) 2.2b (2) 4.3b 3.6b (DGICYT, PB 97–0995) RSD (%) 13.8 (15) 7.6 (8) 9.9 (9) 11.1 (10) Recall 0.81 (0.79) 1.00 (0.95) 0.94 (0.96) 0.94 (0.94) aThe predicted values are given in parentheses.bThe bias is not References statistically significant at the 95% level. 1 M. A. Belarra, M. Resano and J. R. Castillo, J. Anal. At. Spectrom., 1998, 13, 489. 2 U. Kurfu� rst, Fresenius’ J. Anal. Chem., 1993, 346, 556. when the median is used, but it should be taken into account 3 U. Kurfu� rst, Pure Appl. Chem., 1991, 63, 1205. that going from 1.00 to 0.95 involves the appearance of a 4 Th.-M. Sonntag and M. Rossbach, Analyst, 1997, 122, 27. single erroneous result. 5 Draft Commission Decision, OV. J. Eur. Commun., 1993, L118, These results show the possibilities of the SS-ETAAS 64. technique as a screening method within the margins previously 6 M. A. Belarra, I. Belategui, I. Lavilla, J. M. Anzano and mentioned, as it makes it possible to obtain a recall of the J. R. Castillo, Talanta, 1998, 46, 1265. 7 M. A. Belarra, I. Lavilla and J. R. Castillo, Analyst, 1995, 120, order of 0.95 in 15 min. If potential outliers are absent 2813. (copper), using the median rather than the mean value does 8 K. Eckschlager and K. Danzer, Information Theory in Analytical not lead to worse results, but with outliers (cadmium) the Chemistry, Wiley, New York, 1994. median is clearly superior. 9 M. A. Belarra, M. Resano, S. Rodrý�guez, J. Urchaga and In the determination of cadmium, the treatment of possible J. R. Castillo, Spectrochim. Acta, Part B, in the press. outliers needs an additional comment. As seen previously, 10 M. A. Belarra, C. Crespo, M. P. Martý�nez-Garbayo and J. R. Castillo, Spectrochim. Acta, Part B, 1997, 52, 1855. obtaining 105 results enables us to eliminate nine outliers after which correct results are obtained. However, if only five results Paper 8/08432G are available (which is the case with any of the 21 determi- 552 J. Anal. At. Spectrom., 1999, 14,