Environ. Sci. Technol. 2006, 40, 7012-7017
Predicting Uncertainty in the Ecotoxicological Assessment of Solid Waste Leachates B E N O ˆI T J . D . F E R R A R I , * , † J E A N - F R A N C¸ O I S M A S F A R A U D , ‡ ARMAND MAUL,§ AND J E A N - F R A N C¸ O I S F EÄ R A R D ‡ University of Geneva, F.-A. Forel Institute, 10 route de Suisse, CH-1290 Versoix, Switzerland, University of Metz, E.S.E., CNRS UMR 7146, Campus Bridoux, rue Delestraint, F-57070 Metz, France, and University of Metz, L.M.A.M., CNRS UMR 7122, Ile du Saulcy, F-57045 Metz, France
Environmental managers need suitable technological methods to use in optimization studies to improve management of hazardous waste. One of the challenges to achieving a reliable hazardous waste classification is the improvement of procedures used for the ecotoxicological characterization of solid waste leachates. Indeed, this step requires data that meet levels of acceptable quality if scientifically based decisions are to be made. In this study, we illustrate how the variability associated with the successive steps of a procedure used to assess ecotoxicological hazard of solid waste (i.e., primary sampling, laboratory sampling, toxicity measurements) can contribute to the overall variability of the ecotoxicity results. To this end, a municipal solid waste incinerator bottom ash and a slag from a second smelting of lead were studied using a nested experimental design. The results showed that the waste sampling design is of major importance for limiting the final variability of toxicity test parameters. At the opposite, increasing the number of replicates at the toxicity test level has negligible impact on this variability. Our approach could be of great practical interest in ecotoxicological studies not only for ensuring a safe classification for these materials, but also for improving sampling protocols and facilitating less time-consuming and less expensive ecotoxicological evaluations.
Introduction Ecotoxicological characterization is a crucial step in the environmental hazard assessment of solid waste. In the European Union (EU), hazardous character of waste depends on 14 criteria (Council Directive 91/689/EEC, see ref 1). The last criteria (i.e., H14) concerns the ecotoxic property of wastes, for which the French Ministry of Environment (2) has proposed a framework based on both chemical and ecotoxicological determinations (Figure 1). According to this proposal, the ecotoxicity of a residue should be assessed through either its chemical composition or its ecotoxicological characteristics by applying a battery of bioassays (1, * Corresponding author phone: (+41)229509212; fax: (+41)227551382; e-mail:
[email protected]. † University of Geneva, F.-A. Forel Institute. ‡ University of Metz, E.S.E., CNRS UMR 7146. § University of Metz, L.M.A.M., CNRS UMR 7122. 7012
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3). Nevertheless, if the chemical characterization is inconclusive, ecotoxicological characterization is necessary (4). In any case, either approach can be used on raw waste (i.e., direct procedure) or its leachate prepared in well-defined conditions (i.e., nondirect procedure). Generally, primary samples of solid waste are collected and eventually pretreated in order to obtain in fine test samples at the laboratory. In nondirect procedures, a given mass (test portion) of the test sample is mixed with a fixed volume of water to generate a leachate, which is further submitted to aquatic bioassays. All these steps may contribute to the overall variability of the final ecotoxicity results and thus to the uncertainty in any hazardous waste classification methodologies. Until now, no ecotoxicological study has clearly underlined the influence of waste sampling on this variability. To fill the gap, this work aims at assessing two different solid wastes using a nested experimental design. This approach allows splitting of the total observed variability into the components of variance associated with the heterogeneity characterizing the successive steps of the procedure used to assess ecotoxicological hazard of solid waste: (i) the primary sampling, (ii) the laboratory sampling, and (iii) the toxicity measurements.
Materials and Methods Although our study focused on solid wastes, we adopted the IUPAC terminology recommended for soil sampling in the field (5) to describe samples obtained along the procedure from field sampling to analytical samples (Figure 2). Origin, Quality, Pretreatment, and Preservation of the Samples of Wastes. Two different solid wastes have been tested: (i) a municipal solid waste incinerator bottom ash (BA) and (ii) a slag from a second smelting of lead (2SL). After a period of maturation (3 months for BA and 6 months for 2SL) to ensure their complete oxidation and stability, approximately 40 tons of BA and 500 kg of 2SL were deposited on the CERED experimental platform (Research and Waste Elimination Test Center) near St. Marcel (Eure, France) for research purposes dealing with a multidisciplinary French national research program entitled “Waste Ecocompatibility” (6). On this occasion, the quality of each waste was evaluated by determining its elemental composition and leachate components (see Tables S1 and S2 in the Supporting Information). At the same time, primary samples used in our study were obtained from each deposit as described later, and sent directly to the laboratory. Within 4 days after arrival at the laboratory, BA primary samples were entirely crushed to a particle size less than 4 mm in a jaw crusher, as required by the leaching procedure (see below) in order to obtain the desired test samples (Figure 2). Because 2SL waste already had a granulometry lower than 4 mm, no crushing step was necessary. In this case, primary samples were thus considered as test samples. For both wastes, the water content was determined by drying 3 aliquots (100 g each) of each test sample at 105 ( 5 °C until a constant weight was acheived. Dry weights obtained were then considered for determining the liquid-to-solid (L/S) ratios in the leaching procedure. All test samples were stored at ambient temperature inside closed containers to prevent any contact with the atmosphere prior to their use for experimental purposes within a 3-month period. Experimental Design. For each waste, experiments were arranged according to a two-factor nested design where a q ) 4 random level factor was nested in a factor with p ) 3 random levels (Figure 2). 10.1021/es052491z CCC: $33.50
2006 American Chemical Society Published on Web 10/19/2006
FIGURE 1. Criteria and methods for the assessment of the ecotoxicity of wastes (after ref 2).
FIGURE 2. Experimental nested design (terminology according to ref 5). In this nested design, the first source of variability considered is associated with the “primary sampling” procedure. This procedure was performed using a grab sampling method. Practically, using a shovel with a nominal
2 kg capacity, increments were sampled manually at 10 sampling points randomly chosen on the waste deposit in order to produce 3 primary samples identified as A, B, and C (p ) 3). The second source of variability is associated with the “laboratory sampling” procedure. This procedure includes the pretreatment of primary samples, the test portion sampling, and the leaching test. After pretreatment, four test portions of 100 g each, on a dry matter basis (q ) 4), were prepared from each of the test samples (A, B, and C) at weekly intervals (A1-A4, B1-B4, and C1-C4, respectively; Figure 2) using a grab sampling method. Briefly, each test portion was obtained using a spatula by randomly taking small aliquots of the corresponding test sample, which was previously mixed to ensure a better homogeneity. These test portions were then submitted to a leaching procedure (see below). Note that leachates of test portions A1, B1, and C1 were prepared at the same time, whereas A1-A4 were prepared at four different times. The last source of variability corresponds to the “toxicity measurement” error. To estimate that, the ecotoxicity of each leachate was assessed with the bacterial Microtox and the algal growth inhibition tests were performed in parallel, with r ) 3 replicates. Finally, eight different nested designs (2 wastes × 2 L/S ratios × 2 ecotoxicity tests) were carried out, leading to a total of 96 leaching tests and 288 ecotoxicity tests. Batch Leaching Procedure. The test portions (i.e., 100 g on dry matter basis) were submitted to the leaching methodology described in the draft European standards EN 12457-1 (7) and EN 12457-2 (8) using a L/S ratio equal to 2:1 and 10:1, respectively (see Figure S1 in Supporting Information). After 24 h of leaching, each mixture was allowed to settle during 15 min and centrifuged during 10 min at 1400g to remove suspended matter from the leachates. pH and conductivity were then measured (see Table S3 in Supporting VOL. 40, NO. 22, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Information). Finally, the resulting supernatants were assessed immediately for ecotoxicity without filtration and pH adjustment. Ecotoxicological Characterization of Leachates. The Microtox test was performed according to a slightly modified version of the standard AFNOR T90-320-3 (9). Details of the procedure used are given in the Supporting Information. Briefly, after 30 min of exposure at 15 ( 0.5 °C, light emission of the bacterium Vibrio fischeri was measured using a Microtox temperature-controlled photometer (Microtox Analyzer model 500). Results were corrected by timedependent change in light emission under control conditions. The growth inhibition of the algae Pseudokirchneriella subcapitata (formerly Selenastrum capricornutum) was assayed following the standard AFNOR T90-375 (10) using sterile 96-well microplates as modified by Radetski et al. (11) (see details in Supporting Information). After 72 h of exposure under continuous illumination (72 µE/m2/s) and controlled constant temperature (24 ( 2 °C), algae were enumerated using a Coulter Counter (model ZM, 70-µm cell aperture, Coulter Electronics, Toronto, ON). Data Analysis. For each test, results were expressed as effective concentrations EC50 corresponding to a percentage of leachate in the exposure medium that produced a 50% effect on the assessment endpoint (i.e., bacterial bioluminescence or algal growth). Microtox EC50 values were determined by fitting a log-linear regression model using the Microtox data capture and reporting software (Version 7.80, Microbics Corp, Carlsbad, CA). For algal tests, EC50 values were calculated by performing a nonlinear regression on Hill’s model (12), with the REGTOX software (Version EV7.0.4., E. Vindimian, available free at http://eric.vindimian.9online.fr/ en_index.html). Differences between EC50 values from the two wastes, L/S ratios, and toxicity tests were evaluated through the Mann-Whitney U test. To characterize the different sources of variability observed in experimental measurements, toxicity data were analyzed using a hierarchical analysis of variance (ANOVA). Thus, the q ) 4 random levels of the “laboratory sampling” factor are nested within each of the p ) 3 random levels of the “primary sampling” factor. The errors, in turn, are nested within the levels of the two previous factors. To this end, experimental EC50 values obtained in each of the eight nested designs were previously log-transformed. The logarithmic transformation facilitates the computation of the coefficients of variation associated with the variability specific to the different levels in the experimental design. Then, ANOVAs were performed after verifying homogeneity of the variances using the Cochran’s test. For all statistical tests used in this study, the significance level (R) was set at 0.05 and calculations were performed using SPSS software v13.0 (SPSS Inc., Chicago, IL).
Results and Discussion Regardless of the test and the L/S ratio used, the range of reported EC50 values obtained from BA leachates varied from 38% to 1.1% (Figure 3a), whereas it varied from 0.63% to 0.013% for 2SL leachates (Figure 3b). These results clearly show that the 2SL leachates displayed a higher toxicity than the BA leachates and agree with observations previously reported using a battery of 5 aquatic species from 3 trophic levels (13). Considering the cutoff values defined in the French proposal for the H14 criterion assessment (2), Ferrari and Fe´rard (1) proposed to classify these two residues as hazardous. The algal test was more sensitive to BA leachates than the Microtox test (Figure 3a; Mann-Whitney U test, p < 0.05, two-tailed) whereas the contrary was observed for the 2SL leachates (see Figure 3b). The sensitivity of algal test for BA leachates had previously been shown (4, 14, 15). To date, for 7014
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FIGURE 3. Box and whiskers plots (dash line/line ) mean/median, box limits ) 25-75%, errors bars ) 10-90%, dots ) min-max) of the EC50 obtained for the algal test and for the Microtox test on leachates of (a) BA and (b) 2SL using L/S ratios of 2 and 10. Box plots followed by the same letter are not significantly different according to the Mann-Whitney U test (r ) 0.05, two-tailed). the 2SL leachates, no comparison could be made since no results have been previously reported in the literature for this type of waste. Leachates prepared using a L/S ratio of 10:1 were significantly less toxic than those prepared using a L/S ratio of 2:1 in three out of four cases (Figure 3a and b; MannWhitney U test, p < 0.05, two-tailed). Leaching is a complex phenomenon where many factors (e.g., chemical composition, pH, redox potential, complexation, contact time, biological activity, particle size, aqueous solvent) may influence the speciation and the release of contaminants from a considered waste over prolonged time intervals (16, 17). In this sense, the chemistry of leachates prepared using L/S ratios of 2:1 and 10:1 is probably very different and hence greatly influences toxicity results. Nevertheless, regarding pH and conductivity measurements obtained in this study (see Table S3 in Supporting Information) and the elemental concentrations measured in leachates prepared using a L/S of 10:1 (see Table S2 in Supporting Information), some conclusions can be advanced to explain the toxicity results. Whatever the bioassay used to assess the 2SL leachates, EC50 values increased by a factor of approximately 5 when the L/S ratio changed from 2 to 10. In such case, the dilution of highly water soluble components may determine the toxicity response. However, conductivity differs by only a factor of approximately 3 between the 2 L/S ratios (i.e., 157 000 µS/cm for L/S ) 2 vs 53 000 µS/cm for L/S ) 10). Thus, other
parameters, such as the extremely high pH of leachates (i.e., 12.2 for L/S ) 2 and 11.9 for L/S ) 10) or the concentration of the solubility-controlled constituents (i.e., As, Pb, and Zn for the most relevant in 2SL leachates), may also contribute to the toxicity response. In the case of BA leachates, even if conductivity differed by a factor of approximately 4, the L/S ratio did not influence the EC50 values for the same bioassay. Since the pH of leachates is quite equivalent for the two L/S ratio used (i.e., 9.6 for L/S ) 2 and 10.0 for L/S ) 10), it is suspected to play a role in the toxicity response. Table 1 summarizes ANOVA results for the eight different nested designs (see detail of results in Tables S4 and S5 in Supporting Information). Two cases out of the eight groups of log-transformed data (sample size N ) 36 divided into k ) 12 subgroups) showed that their variances could not be considered homogeneous (Cochran’s test, p < 0.05). Nevertheless, failure to meet the assumption of homogeneity of variances is not fatal to ANOVA, which is relatively robust, particularly when groups are of equal sample size. Regarding the primary sampling level, none of the eight designs displayed in Table 1 showed a significant effect (i.e., all the calculated p-values are above the 0.10 probability level). This indicates the absence of a noticeable heterogeneity at this level in the hierarchical experiment. For the laboratory sampling level, all the tests performed but one (BA, L/S ) 10, Algal test, p ) 0.06) were highly significant (p < 0.01). Consequently, there is evidence of some degree of heterogeneity at laboratory sampling level, which might be related to the pretreatment of primary samples plus test portion sampling plus leaching step. Table 2 displays the components of variance s2E, s2L and s2S, associated with the toxicity measurement error, the laboratory sampling, and the primary sampling, respectively. These components were obtained from the mean squares (MS) calculated in ANOVA (see Tables S4 and S5 in Supporting Information) as follows:
s2E ) MSE
(a)
MSL - MSE s2L ) r
(b)
MSS - MSL qr
(c)
s2S )
TABLE 1. Summarized ANOVA for Nested Waste-Leaching Log-Transformed Dataa L/S ratio 2
10
toxicity test
source
algal
primary sampling laboratory sampling microtox primary sampling laboratory sampling algal primary sampling laboratory sampling microtox primary sampling laboratory sampling
CV ) 100xe(ln10) S - 1 2 2
(d)
where s2 is the component of variance considered. Assuming there is a component of variance characterizing each of the 3 sources of variability (i.e., primary sampling, laboratory sampling, toxicity measurement), mean values, m(s2), of the components of variance associated with each of the three factors under study (i.e., bioassay, L/S ratio, waste) were calculated. Thus, each mean was calculated using the 4 values estimating the same level factor as mentioned in Table 2, resulting in the six values reported in Table 3. This approach allows ranking of the CVs obtained in Table 3 in decreasing order CV(L/S)2) > CV(Algal test) > CV(L/S)10) > CV(Microtox test) > CV(BA) > CV(2SL). But, Table 3 also reveals that the greatest variability is related to the laboratory sampling procedure. This is not surprising owing to the multiplicity
2SL p-value
0.27 2.92 × 10-10 0.30 1.56 × 10-6 0.14 0.06 0.49 1.95 × 10-3
0.45 8.79 × 10-12 0.80 1.83 × 10-4 0.71 1.25 × 10-4 0.28 2.64 × 10-6
a Detailed results are given in Tables S4 and S5 in Supporting Information.
TABLE 2. Components of Variance, and Corresponding Coefficient of Variation (CV), Estimated from the ANOVA for the Nested Experiments (See Text); s2E (respectively s2L and s2S) Is the Estimated Component of Variance Associated with the Experimental Toxicity Error (respectively, the Laboratory Sampling Procedure and the Primary Sampling) factors waste
L/S ratio
BA
2
estimated component of variance toxicity test algae microtox
10
algae microtox
2SL
2
algae microtox
10
algae microtox
where MSE is the residual mean square and r is the number of replications, MSL is the mean square for the laboratory sampling factor with q random levels, and MSS is the mean square for the primary sampling factor. In addition, the coefficient of variation (CV), expressed as a percentage, which is associated with each component of variance, was calculated as follows:
BA p-value
s2E (CV in %)
s2L (CV in %)
s2S (CV in %)
0.001274 (8.2) 0.001664 (9.4) 0.009122 (22.3) 0.003360 (13.4) 0.002471 (11.5) 0.000531 (5.3) 0.003235 (13.1) 0.000240 (3.6)
0.010593 (24.0) 0.005481 (17.2) 0.003714 (14.1) 0.003724 (14.1) 0.028759 (40.6) 0.000904 (6.9) 0.005855 (17.8) 0.000742 (6.3)
0.001455 (8.8) 0.000605 (5.7) 0.002474 (11.5) 0.000000a (0.0) 0.000000a (0.0) 0.000000a (0.0) 0.000000a (0.0) 0.000093 (2.2)
a Negative estimates of the components of variance calculated on the basis of the expected mean squares for nested experiments (see Tables S4 and S5 in Supporting Information), were rounded to zero.
of steps in the procedure before obtaining a leachate, then leading to toxicity differences between leachate samples. Procedures for obtaining representative samples from particulate materials have been studied for some time in the minerals industry, leading to the development of the Gy sampling theory (18-20). According to this theory, constitution heterogeneity and distribution heterogeneity are the main components of the sampling error when addressing the concentration of one critical element in a particulate material. In our work, chemical analysis was not the measurement endpoint but rather the toxicity of waste leachates. The Gy’s theory is in this case of limited value since toxicity measurement integrates not only one critical component but the mixture of several ones and different factors such as pH, solubility, and also antagonism or synergism phenomena. Nevertheless, a parallel with the Gy sampling theory can be done to identify how to improve our sampling protocol in ecotoxicological evaluation of solid waste leachates. This theory delineates seven major categories of sampling error that cover differences within samples in addition to the error introduced by the analytical method (20). However, only three categories seem to be relevant to this study: the fundamental error, the segregation error, and the delimitation error. Fundamental error can be reduced by comminution or by increasing the sample mass. When using larger test portions, the segregation error determines VOL. 40, NO. 22, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 3. Means of Estimated Components of Variance (m(s2E ), m(s2L ), and m(s2S)), and Corresponding Coefficient of Variation (CV), Characterizing the Variability at Each Level in the Nested Experimental Designa m(s2E) (CV in %)
m(s2L) (CV in %)
m(s2S) (CV in %)
algal test
microtox
L/S ) 2
L/S ) 10
BA
2SL
0.004026 (14.7)
0.001449 (8.8)
0.011434 (25.0)
0.003509 (13.7)
0.001134 (7.8)
0.000023 (1.1)
a
These estimates were obtained by considering all the numerical results as presented in Table 2 (see text for explanation).
the variance. In our study, test portions of 100 g each were prepared from 2SL or crushed BA test samples. This mass was calculated from Gy’s theory as suitable to minimize the fundamental error when subsampling in materials with a 4 mm maximum particle size. As a consequence, the mass was not taken into account in our test on the source of uncertainty and CV calculations. Thus, segregation error should predominate even if it can be minimized by homogenizing the sample, which is the case in this study. In addition to the segregation error, the delimitation error should be considered here. Gerlach et al. (19) showed that this error source affects specifically grab sampling, which is the technique used in our study to prepare test portions. Even more, in this study, the experimental variability also includes the variability due to time. Indeed, test portions constituted from three test samples of waste were submitted to a stepwise leaching procedure and then, the procedure were repeated at four different times (see Figure 2). Regarding the CV associated with m(s2L) values presented in Table 3, the L/S ratio of 10:1 leaching procedure gave a better precision than the L/S ratio of 2:1 leaching procedure (i.e., 13.7% vs 25% respectively). This finding may be relevant for the development of classification methods for waste such as the proposal of the French Ministry of Environment (2) based on ecotoxicological cutoff values (see Figure 1). One of the most important elements of any preliminary approach purporting to identify solid waste as hazardous for the environment should be to minimize the risk for classifying a waste as being non-hazardous whereas it actually is (i.e., type II error risk or consumer’s risk). Waste classification methods are based on the comparison of toxicity results with specified thresholds of toxicity. So, the range of the confidence interval of EC50 value is of crucial importance regarding the final decision. Here, we emphasized the incidence of the L/S ratio on the overall variability of the EC50 estimation associated with any experimental design. Thus, according to the present study, a L/S ratio of 10:1 seems to be more suitable than a procedure using a L/S of 2:1 to improve the precision. So, our results substantiate rather than refute the use of a L/S ratio of 10:1 for a preliminary environmental hazard assessment of solid wastes as proposed by the French Ministry of Environment (2). The second source of variability is linked to toxicity tests. It may be related to the test species (i.e., their intra and interspecific variability) or the experimental procedure (i.e., material, methods, and operator skills) including culturing of test organisms. Globally, whatever the bioassay used, all CV associated with s2E values are inferior to 22.3% (Table 2), which is relatively satisfying. Thellen et al. (21) reported in an intercalibration exercise to assess the performance of the algal microplate toxicity assay that cadmium and phenol toxicity test reproducibility was reflected by CV of 24.3% and 34.9%, respectively. In addition, as presented in Table 3, the Microtox test yielded a better precision than the algal test (i.e., 8.8% vs 14.7%, respectively). This could be related to the test conditions that are quite different between the two bioassays. Moreover, unlike the algal test for which our own laboratory culture is used as inoculum, the Microtox test uses bacteria supplied by Azur Environmental and preserved by an exclusive process of lyophilization. Therefore, the 7016
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organism supply is very stable and highly standardized and consequently a high reproducibility is assured (22). Finally, the third source of variability is associated with the primary sampling procedure. Globally, the CV estimates related to s2S values presented in Table 2 are weak and even undetectable for four out of eight cases (i.e., CV s2S ≈ 0 in Table 2). However, regarding the CV associated to m(s2S) (Table 3), the variability was higher for BA than for 2SL (i.e., 7.8% vs 1.1%, respectively). Such results clearly show that the primary sampling procedure applied to collect heterogeneous waste samples in this study may be considered more efficient for 2SL. Considering segregation and delimitation errors (19), sampling protocol of BA should be improved, for example, by obtaining a composite primary sample from more than 10 increments or by properly homogenizing the sample, which is, in our case, not realistic because of the size of the BA deposit (i.e., 40 tons). With variance components in hand, it is possible to predict the confidence interval for the EC50 mean produced by any experimental design (i.e., with different combinations of p, q, and r). Assuming that log(EC50) data of replicated toxicity tests obtained for a granular waste submitted to a unique L/S ratio are normally distributed, the mean µ and the variance σ2 of the distribution can be estimated by the mean value of pqr log(EC50) data (i.e., xj ) and s2m, respectively. According to Snedecor and Cochran (23), s2m is calculated as follows:
s2m )
m(s2S) m(s2L) m(s2E) + + p pq pqr
(e)
Finally, the equation to calculate the confidence intervals (CI) of µ at the probability level (1 - R), is given as
CI1-R ) xj ( t(1-R/2) xs2m with pqr degrees of freedom (f) µ As µ corresponds to the log-transformed geometric mean µg of EC50 data, eq f can be rearranged in this way:
log(µg) ) xj ( t(1-R/2)
x
m(s2S) m(s2L) m(s2E) + + p pq pqr
(g)
Finally, the confidence interval for µg at the probability level (1 - R) is expressed as follows:
As an example, eq h can be used to calculate the 95% confidence interval for µg obtained in the experiment (BA, L/S ) 2, Algal test). For p ) 3, q ) 4, r ) 3, and m(s2) values reported in Table 3, and t(0.95, df)36) ) 2.028, thus the 95% confidence interval is
CIµ0.95 ) [10xj ÷ 1.194; 10xj × 1.194] g
TABLE 4. Comparison of Several Sampling Designs for the Particular Case of the Algal Test Performed on BA Leachates with a L/S Ratio of 2 Taken as an Example waste L/S ratio p value q value 1 3 1 1 1 1 a
toxicity test r value
variance S2m
coefficient of variation (%)
confidence interval at 95% levela
1 1 1 3 1 ∞
0.016594 0.005531 0.006287 0.013910 0.001134 0.012568
30.3 17.2 18.4 27.7 7.8 26.2
39-257 58-172 56-179 42-237 78-128 44-227
1 1 3 1 ∞ 1
In each case, the estimated mean has been standardized as 100%.
In other terms, the optimal allocation of experimental effort to each level (primary sampling, laboratory sampling, and toxicity measurement) for decreasing the total variance can be determined. As an example, we studied again the specific case of the algal test performed on BA leachates with a L/S ratio of 2. The results in Table 4 were calculated on the basis of the estimates of the components of variance corresponding to each level (see Table 3) by considering a few combinations of p, q, and r. These results emphasize the effects of various experimental designs on the precision of the estimated mean. The total variance is maximal when the product pqr is 1. When considering a given case defined by a fixed pqr value other than 1, say 3 as an illustration, then it arises that allocating experimental efforts to the level of primary sampling (p ) 3 and q ) r )1), that is, more generally at the upper levels of the experimental design, is the best way for reducing the 95%-confidence interval of the log(EC50) mean. In theory, infinite primary sampling would result in no uncertainty at all. At the laboratory sampling level, an infinite experimental effort would contribute to reduce the 95%-confidence interval significantly when compared to the pqr ) 1 situation. At last, it is noticeable that making experimental efforts at the toxicity test level is of limited interest since the corresponding 95%-confidence interval remains almost as large as the one determined for the pqr ) 1 situation. Undoubtedly, predicting uncertainty levels allows better elaboration of suitable sampling procedures for solid waste ecotoxicological assessment. Yet, it could be of great practical interest in ecotoxicological studies of solid wastes not only for ensuring a safe classification for these materials, but also for facilitating less time-consuming and less expensive ecotoxicological evaluations.
Acknowledgments This research is part of a French national research program on waste ecocompatibility funded by the Agency for Environment and Energy Management (ADEME).We are grateful to Davide A. L. Vignati and also to the reviewers who provided helpful suggestions for improving the manuscript.
Supporting Information Available Detailed description of protocols for toxicity testing plus 1 figure and 5 tables. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review December 13, 2005. Revised manuscript received September 5, 2006. Accepted September 7, 2006. ES052491Z VOL. 40, NO. 22, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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