EPA-650/4-74-028 MAY 1974 Environmental Monitoring Series -fX-S-XwSSifCvI ------- EPA-650/4-74-028 COLLABORATIVE STUDY OF METHOD FOR THE DETERMINATION OF NITROGEN OXIDE EMISSIONS FROM STATIONARY SOURCES (NITRIC ACID PLANTS) Prepared by H.F. Hamil and R.E. Thomas Southwest Research Institute 8500 Culebra Road San Antonio, Texas 78284 Contract No. 68-02-0626 ROAP No. 26AAG Program Element No . 1HA327 EPA Project Officer: M. Rodney Midgett Quality Assurance and Environmental Monitoring Laboratory National Environmental Research Center Research Triangle Park, North Carolina 27711 Prepared for OFFICE OF RESEARCH AND DEVELOPMENT U.S. ENVIRONMENTAL PROTECTION AGENCY WASHINGTON, D.C. 20460 May 1974 ------- This report has been reviewed by the Environmental Protection Agency and approved for publication. Approval does not signify that the contents necessarily reflect the views and policies of the Agency, nor does mention of trade names or commercial products constitute endorsement or recommendation for use. 11 ------- SUMMARY AND CONCLUSIONS This report presents the results obtained from a collaborative test of Method 7 promulgated by the Environmental Protection Agency for determining the nitrogen oxide emissions trom stationary sources. Method 7 specifies the collection of a grab sample in an evacuated flask con- taining a dilute sulfuric acid-hydrogen peroxide absorbing solution and the colorimetric measure- ment of the nitrogen oxides, except nitrous oxide, using the phenoldisulfonic acid procedure. The test was conducted at u nitric acid plant using four collaborating laboratories. A total of 22 samples were taken over a three-day period In addition, standard gas samples were taken, and nitrate solutions whose true concentrations were unknown to the collaborators were prepared for concurrent analysis. The concentrations determined by the collaborators from all three phases of the test were submitted to statistical analysis to obtain estimates of the accuracy and precision that can be expected with the use of Method 7. The statistical analysis provides the basis for the following conclusions* Accuracy -Samples of standard gas mixtures at three concentrations, 107, 344, and 784 ppm, were taken and analyzed according to Method 7 Using the values determined by the collaborators, we can say that the method is accurate at the 95 percent level of confidence Precision-The precision of Method 7 is given in terms ol within-laboratory and between- laboratory components and a laboratory bias component The precision estimates are derived from the stack concentration determinations, with some adjustment Due to plant upset, there was considerable variation in the actual NOX concentrations in the stack during the first day's sampling. The fluctuation was reflected in the NOX concentrations values obtained by the col- laborators and necessitated a correction in the data for the fluctuating mean However, the net effect likely left the precision estimates obtained higher than the actual piecision values I Im- precision components are shown to be proportional to the mean of the Method 7 determinations. given by 6, and can be summarized as follows (a) Within-laboratory The estimated within-laboratory standard deviation is 14 NX ',/ ol 6, and has 67 degrees of freedom associated with it (b) Between-laboratoiy The estimated between-laboratory standard deviation is 18 471'/ of 6, with 3 degrees of freedom. (c) Laboratory bias. From the above, we can estimate u laboratory bias standard deviation of 10.49% of 5. Analytical Procedure—The unknown nitrate solution data provides a basis for measuring the accuracy and precision of the analytical procedure taken by itself. At three levels of concen- tration, the procedure is shown to be accurate at the 95 percent level of confidence The witlnn- laboratory standard deviation is not a function of the concentration, ju. and is estimated as 1.199 Mg/mC. The laboratory bias standard deviation is a linear function of the true concentration and is estimated by 0 725 + (0.092)^. From an analysis of variance, the only consistently significant factor affecting the precision of the concentrations obtained is the day-to-day vari- ations within a given laboratory. This implies a need for recalibration of the spcctropliotoinctcr on a daily basis to negate the effect on the values of drift. Recommendations are made for the improvement of the precision of Method 7. and con- siderations given for the use of the method in field testing. 111 ------- TABLE OF CONTENTS LIST OF ILLUSTRATIONS jr LIST OF TABLES v I. INTRODUCTION I II. COLLABORATIVE TESTING 2 A. Collaborative Test Site 2 B. Collaborators and Test Personnel • ... ... 6 C. Philosophy of Collaborative Testing . .... ... 6 III. STATISTICAL DESIGN AND ANALYSIS . . 7 A. Statistical Terminology 7 B. The Collaborative Test Plan . ...... 8 C. The Collaborative Test Data . . ^ D. The Accuracy of Method 7 . ... II E. The Precision of Method 7 . . ... . . . 12 F. The Accuracy and Precision of the Analytical Procedure . . . 14 IV. COMPARISONS WITH PREVIOUS STUDY 16 V. RECOMMENDATIONS . . . .... 17 APPENDIX A-Method 7. Determination of Nitrogen Oxide Emissions From Stationary Sources - • - 'tj APPENDIX B-Statistical Methods .... .23 B.1 Preliminary Analysis of the Original Collaborative Test Data . 25 B.2 Significance of the Port Effect. . ... 26 B.3 Transformations . . . . 27 B.4 Empirical Relationship Between the Mean and Standard Deviation in the Collaborative Test Data .... . 27 B.5 Underlying Relationship Between the Mean and the Standard Deviation 29 B.6 Estimating the Standard Deviation Components B.7 The Nitrate Solution Data .... .... .... 33 B.8 Variance Components From the Nitrate Solution Data . ... 33 REFERENCES .... . . 37 IV ------- LIST OF ILLUSTRATIONS Figure Page I Tail Gas Vent Line and Sample Manifold 3 2 Test Setup at Mobay Chemical Company Test Site 4 3 Collaborators Sampling at the Mobay Chemical Company Test Site 4 4 Schematic of Gas Standard Sample Preparation Train 5 5 Collaborative Test ot" Method 7, Instructions for Analysis of Unknown Nitrate Solutions 10 B.I Intcrlaboratory Run Plot 29 B.2 Intralaboratory Collaborator Block Plot 30 ------- LIST OF TABLES Table Page 1 Corrected Nitrogen Oxides Collaborative Test Data, NOX as NOS (Dry Basis)... 11 2 Nitrogen Oxide Emissions From NBS Samples 12 3 Confidence Intervals for Gas Sample Means 12 4 Accuracy of the Analytical Procedure 14 B.I Original Collaborative Test Data, NOX as NO2 25 B.2 Corrected Values for Block 1, Adjusted for Common Mean 26 B.3 Test for Port Effect 27 B.4 Data Transformation to Achieve Run Equality of Variance 27 B.5 Interlaboratory Run Summary 28 B.6 Intralaboratory Collaborator Block Summary 29 B.7 Reported Nitrate Solution Concentrations 34 B.8 Laboratory Day Averages for Nitrate Solution Data 34 B.9 Average Laboratory Nitrate Solution Concentration 34 B.10 Nitrate Solution Data Analysis of Variance 35 B ' F-Ratios and Probabilities 35 B.I 2 Variance Components of Nitrate Solution Data 36 VI ------- I. INTRODUCTION This report describes the work performed and results obtained on Southwest Research Institute Project 01-3462-004, Contract No. 68-02-0626, which includes collaborative testing of Method 7 for nitrogen oxide emissions as given in "Standards of Performance for New Stationary Sources."(2) This report describes the collaborative testing of Method 7 in a nitric acid plant, the statistical analysis of the data from the collaborative tests, and the conclusions and recommendations based on the analysis of data. ------- II. COLLABORATIVE TESTING A. Collaborative Test Site 'I IK- collaborative test of Method 7 in u nitric acid plant was conducted at Mobay Chemical Company. liaytown. Texas. The nitric acid unit at Mobay Chemical Company utilizes a proprietary process in which ammonia is catalytrcally oxidized. Due to the proprietary nature of the process, no information concerning production rates, operational parameters, or unit design could he made available lo Southwest Research Institute by Mobay Chemical Company for publication Lmission data from the unit on-stream analyzer indicated normal NOX concentration in the vent gas duct (Figure I) leading to the stack to be in the range of 200-250 ppm. We were assured by plant per- sonnel that this NOX concentration placed them below the maximum pcrmissable emission levels speciliecl by the New Source Performance Standards for nitric acid plants/2* In Figure J is shown the configuration of the tail gas vent leading into the vertical stack and the configuration of the sampling manifold. The sample manifold consisted of a ten-foot lenglli ol 2-inch ID stainless steel tubing, fitted with four sample outlet valves (Whitey® toggle valves) spaced at two-toot centers. The sample valves were installed in the sample manifold m such a manner as to have the sample inlet at the centroid of the sample manifold The sample manifold was fitted with a stainless steel gauze diffuscr 2 inches from the 1/2-inch tubing sample inlet line, in order to provide a mixing '/one to prevent channeling of the incoming sample. The sample manifold was connected through a valve to the tail gas vent by means of a 1/2-inch stainless steel line The sample manifold connection was at a point approximately three feet downstream from the sample tukeofl for the on-stream analyzer The tail gas vent on the unit was maintained at 3-4 psig which provided sufficient pressure head to provide a high sample How rate through the sample manifold. The sample manifold was continually purged with a moderate sample flow during the course of a day's sampling Approximately two min- utes before a sample was taken, the sample flow rate was increased to a high flow rate to assme that the gas in the sample manifold was representative of the gas in the tail gas vent. The exhaust gas from the sample manifold was exhausted to atmosphere through a hydrogen peroxide bubbler to scrub out nitrogen oxides. Figure 2 shows the test setup at Mobay, while Figure 3 shows the col- laborators taking a sample. The original collaborative test plan called for each collaborator to collect six samples (rotating among sample points) on each of four days. However, on the first day of sampling, a minor explo- sion, caused by rupture of a high pressure gas line, occurred in another unit in the plant Since the nitric acid produced at Mobay is used internally as an intermediate in other processes, it was nec- essary for plant personnel to reduce the nitric acid production. Only limited storage space in one nitric acid tank was available to accept continued production. Arrangements were made with Mobay to reduce the production rate m order that two more days of sampling could be conducted. As a result, six samples were taken on the first day, and eight samples were taken on the second and third days, respectively. On the fourth day, gas standard samples were taken by the collaborators at the SwRI Houston laboratory. The gas standard samples were prepared at the time of sampling by personnel from the National Bureau of Standards. The gas standard preparation tram is shown schematically in Figure 4. The method used for producing the nitric oxide in air standards con- sisted of metering a controlled, known small amount of a 0.98 mole percent NO in N2 mixture into an air stream flowing at a known and much higher flow rate. The mixture passed through two mixing chambers and into a sampling manifold from which the collaborators took their samples ------- Top View Stack / H202 Bubbler Vent to Atmosphere Pressure Regulator Valve (3 to 4 psi) Tail Gas Vent \ v A $ ^^SRf To On-Stream NOX Analyzer SS Gauze Diffuser "Sampling Point FIGURE I. TAIl GAS VIAT I IM \\DSAMPLEMANIFOLD. ------- FIGURE 2. TEST SETUP AT MOBAY CHEMICAL COMPANY TEST SITE. FIGURE 3. COLLABORATORS SAMPLING AT THE MOBAY CHEMICAL COMPANY TEST SITE. ------- 1%NOinN2 Regulator with SS diaphragm 0-30 psi gauge Ruby orifice Flow controller Trap (drierite and charcoal1 Rotameter Mixing chamber No. 1 Mixing chamber No. 2 Samplmq manifold 12/5 Air Supply FIGURE 4. SCHEMATIC 01 CAS STANDARD SAMPI I PREPARATION 1R\I\ ------- Tin cc concentration levels of nitrogen oxide standards were generated, and the collaborators took three samples ol~ each standard B. Collaborators and Test Personnel The collaborators lor the Mobay nitric acid plant test were Or. Robert James and Mr. Thomas Jay McMiLkle. Texas Air Control Board, State of Texas, Messrs. Quinno Wong and Randy Creighton. Depaitment of Public Health. City of Houston, Houston Texas, Mr Mike Taylor, Southwest Research Institute. Houston Laboratory. Houston. Texas and Mr. Ron Hawkins of Southwest Research Insti- tute. San Antonio Laboratory, San Antonio. Texas.* The standard gas samples were prepared and the concentrations verified under the supervision of Mr. William D. Dorko, Chemist, Air Pollution Analysis Section, Analytical Chemistry Division. The National Bureau of Standards, Washington, D.C. The collaborative test was conducted under the supervision of Mr. Nolhe Swynnerton of South- west Research Institute. Mr Swynnerton had the overall responsibility for assuring that the col- laborators were competent to perform the test, that the test was conducted in accordance with the collaborative test plan, and that all collaborators adhered to Method 7 as written in the Federal C. Philosophy of Collaborative Testing The concept of collaborative testing followed in the tests discussed in this report involves con- ducting the test in such a manner as to simulate "real world" testing as closely as possible "Real world" testing implies that the results obtained during the test by each collaborator would be the same results obtainable if he were sampling alone, without outside supervision and without any additional information from outside sources, i.e. test supervisor or other collaborators The function of the test supervisor in such a testing scheme is primarily to see that the method is adhered to as written and that no individual innovations are incorporated into the method by any collaborator During the test program, the test supervisor observed the collaborators during sampling and sample recovery II random experimental errors were observed, such as mismeasurement of volume of absorbing solution, improper rinsing of flasks, etc , no interference was made by the test supervisor Since such random errors will occur in the every day use of this method in the field, unduly restrictive supervision of the collaborative test would bias the method with respect to the field test results which will be obtained when the method is put into general usage However, if gross deviations were observed, of such magnitude as to make it clear that the collaborator was not following the method as written, these would be pointed out to the collaborator and corrected by the test super- visor While most of the instructions in the Federal Register are quite explicit, some areas are subject to interpretation. Where this was the case, the individual collaborators were allowed to exercise their professional judgement as to the interpretation of the instructions. The overall basis for this so-called "real-world" concept of collaborative testing is to evaluate the subject method in such a manner as to reflect the reliability and precision of the method that would be expected in performance testing in the field. "Throughout the remainder or this report, the collaborative laboratories are referenced by assigned code numbers as Lab 101. Lab 102 Lab 103. and Lab 104 These code numbers do not necessarily correspond to the above ordered listing of collaborators ------- I. STATISTICAL DESIGN AND ANALYSIS A. Statistical Terminology To facilitate the understanding of this report and the utilization of its findings, this section explains the statistical terms used in this leport. The procedures for obtaining estimates of the pertinent values are developed and justified in the subsequent sections. We say that \\nestimator, 6, is unbiased Jur a parameter 6 if the expected value of 0 is 0, or m notational (orm,E(8) = 6. Let .v, ,x2 , . . .,xn be a sample of/i replicate method determinations. Then we define 1 " (1) A = — 2 A-, as tnc sample mean, an unbiased estimate of the true mean, 5,oJ the determination^ This term gives an estimate of the center of the distribution of the A-,'S. 1 " (2) i2 = 5^ (v, - \ )2 as the sample variance, an unbiased estimate of the true raiiani c. o- . This term gives a measure of the dispersion m a distribution. (3) s =\ as the sample standard deviation, an alternative measure of dispersion, whn.li estimates a. the true standard deviation The sample standard deviation, s, however, is not unbiased for a,(I * so a correction liu toi needs to be applied. The correction factor for a sample of size 11 is an , and the product of a,, and s is imhiaseil for a That is, £'(a,,s) = a As n increases, the value of a,, decreases, going for example Irom c^ = I I 2X4. «4 = 1 0854 toa,0 = 1.0281 We do tine as the true tocf Intent oj variation for the distribution of the method determinations To estimate tins parameter, we use -A sample coefficient oj vanation. 0, defined by where |3 is the ratio of the unbiased estimates of a and 5, respectively. The coefficient of variation measures the percentage scatter in the observations about the mean and thus is a readily under- standable way to express the precision of the observations. The modified experimental plan for this test called for 22 runs On each run, the collaborative teams were expected to collect simultaneous samples from the stack in accordance with Method 7 Suite the actual NOX emission concentration m the stack fluctuates, one can in general ex pet. I ditferent tiue concentrations for each run. To permit a complete statistical analysis, the individual inns aie ------- gi on pod into />/<>< A.s. when.' each block has approximately the same true emission coiKenli.il ion level We can apply the statistical terms of the preceding paragraphs both to the collaborators' values during a given inn and to each collaborator's values in a given block. In this report, statistical results* Irom the hrst situation are referred to as run results Those from the second situation are relerred to as lolluhorutoi block result* For example, a run mean is the average of each collaboiator's loncentiutiuii level for the run as obtained by Method 7 A collaborator block coefficient of variation is the ratio ol the unbiased standard deviation estimate to the sample mean for all of a collaborator's runs grouped in the block. The variability associated with a Method 7 concentration determination is estimated in terms of the wi thin-laboratory and the between-laboratory precision components In addition, a laboratory hias lomponent can be estimated. The following definitions of these terms arc given with respect to a tun- utatk concentration,^- • Wnhin-lahoratitiv The within-laboratory standard deviation, a, measuies the di\pcnutn;// replicate single determinations made using Method 7 by one laboratory team (same held operators, laboratory analyst, and equipment) sampling the same true concentration, p. The value of a is estimated from within each collaborator block combination • Between-laboratory-The between-laboratory standard deviation, a/,, measures the lolal variability in a concentration determination due to simultaneous Method 7 determinations by different laboratories sampling the same true stack concentration, JLI The between lab- oratory variance, o\, may be expressed as ol=al+ a2 and consists of a within-laboratory variance plus a laboratory bias variant e. o£ The between- laboratory standard deviation is estimated using the run results. Laboratory bia\— The laboratory bias standard deviation, o/, =\/o£ ~ °2 • 1S tnat portion ot the total variability that can be ascribed to differences in the field operators, analysts and instrumentation, and due to different manners of performance of procedural details left unspecified in the method. This term measures that part of the total variability m a deter- mination which results from the use of the method by different laboratories, as well as from modifications in usage by a single laboratory over a period of time. The laboratory bias standard deviation is estimated from the within-and between-laboratory estimates previously obtained. B. The Collaborative Test Plan The collaborative test plan called for samples to be drawn on four successive days by four col- laborative teams sampling simultaneously. The samples were to be taken through the four sample ------- ports (Jescnbcil in Section II, and these were arbitrarily assigned the labels A, B, C, and I) Due to the plant problems discussed earlier, however, the sampling period was shortened to three days. While the ports are located so as to be as nearly equivalent as possible, the stack flow char- acteristics can lead to a difference in concentrations dependent upon the port from which the sample was taken. To offset this possibility, the teams rotated and sampled through different ports on each run. The starting port for each collaborator was chosen by a randomization method, and sub- sequently each crew rotated in a systematic manner to an adjacent port While it would be more desirable to re-randomize after each run, the difficulties involved in the movement of equipment and in having four crews operating on a small platform at the same time made this impracticable The Mobay plant had a split beam analyzer which monitored the NOX levels during operation. These values were used as a basis for establishing blocks for the analysis of the data The values are presented in Table Bl. During the second day and the third day of sampling, the level reported by the on-stream analyzei remained essentially constant. Each of these days, then, was used as a block of si/e X The data from the first day's run were not homogeneous with respect to concentration level, but these values were taken to be a block since other conditions were comparable throughout. The data were then adjusted for a common mean level with regard to the on-stream analyzer, and these adjusted values were used to obtain collaborator block variability estimates The result, then, was 22 runs divided among three blocks where each day of samples constituted a block. The blocks were ol size 6, 8, and 8, respectively In addition to the 22 samples taken from the stack, samples were taken from standard gas mixtures at the Southwest Research Institute Laboratory Three samples were obtained by eaeli collaborator at each of three levels of NC\ concentration, under conditions which closely mirrored those Lindei which the stack samples were drawn These standards were prepared and verified by per- sonnel from the National Bureau of Standards, and were used to obtain a measure of the accuracy of Method 7 at varying concentration levels. To estimate the amount of variation in a test result due to the analytical procedure, three standard solutions were prepared. The collaborators were instructed to analyze these in three replicates on each of three days during which the test samples were being analyzed. A copy of the instruction and reporting form is shown in Figure 5. These results should contain no variation except that due to the laboratory work necessary to determine the concentration level. C. The Collaborative Test Data The collaborative test data upon which the analysis was based are shown in Table 1. These valuer represent the concentrations reported by the collaborators as verified by preliminary calculation checks and, in some cases, recalculated to correct errors in the reported values. In Appendix B I. the originally reported data are shown and the rationale behind the recalculation explained ------- A series of nitrate solutions are provided to each collaborator. These solutions are labeled A, B, and C , and the concentrations are unknown to the collaborators. Each unknown solution is to be analyzed in triplicate on each of three separate days. Use a 10 ml aliquot and follow the procedure in Section 5.2 (and 4.3) of Method 7 and report results as micrograms of per ml of unknown solution. Submit the results on this sheet along with your other collaborative test data. Analyst Day Day 1 Date Day 2 Date Day 3 Date Replicate 1 2 3 1 2 3 1 2 3 Concentration, jig NO^ per ml Solution A Solution B Solution C * FIGURE 5 COLLABORATIVE TEST OF METHOD 7, INSTRUCTIONS FOR ANALYSIS OF UNKNOWN NITRATE SOLUTIONS 10 ------- TAULL 1 CORRI-.CThD NITROGLN OXIDLS COLLABORATIVE 1KST DATA,NON AS NO2 (DRY BASIS), Ibs/scf X 107 The values lor lab 102 in block 3 were treated as missing values, due to fullure ol the analyst to neutrali/e the samples prior to cvaponzution to dry- ness, with resultant loss ot the nitrogen containing species as HNO3. The values of lab 102 in run 8 and lab 104 in run 7 were omitted from the analysis as erroneous values due to the magnitude of the difference between these values and the other collaborators for those runs, following an outlier test as shown in Appendix B.I. In these cases, no attempt is made to substitute for these values in the analysis. Rather than this, it is better to work only with those values which are the direct result of a Method 7 test. Substituted values generally tend to minimize the effect of the substitution on the error terms, but by so doing may inordinately decrease the estimate Thus it is preferable to operate with the missing results when the si/e ol the test permits. In Appendix B 2 the hypothesis of no poit effect is tested I his test is performed according to YoudenV5 ' rank test at the 5'/ level of significance Differences among the sample values due to the port from which the sample was taken are not found to be significant. As a result, no allowance for a port factor is included in the subsequent analyses. D. The Accuracy of Method 7 In order to ascertain the accuracy of Method 7, samples were drawn from mixtures prepared by personnel from the National Bureau of Standards. Three NOX concentration levels were used, low, medium, and high, and these levels were generated by mixing a known amount of 0.98 mole percent NO in N2 mixture into a controlled air flow. The samples were drawn into an evacuated flask, and these were then analyzed according to Method 7. The values obtained by the collaborators are presented in Table 2, with values for Lib 102 m repetition 3 for the medium concentration and Lib 103 in repetition 3 for the high coiuentr.ilion not reported due to analyst error. The actual concentration levels for the samples weie venlied by NBS after the test, and these are also shown. Hlock 1 2 3 Kun 1 •> \ 4 S 6 7 S 9 in 11 12 13 14 IS 16 17 18 19 20 21 22 Lib 101 IXil.i 335 448 254 12l> 251 203 105 112 112 108 107 107 93 112 119 US 120 144 127 133 120 163 Port A 1) r 1) \ H C D A B C D A B D C B A D C B A Uh 102 O.it.1 337 344 3ll(< 105 166 63 102 333* 104 103 62 89 98 102 2t 3t 3t 3t 3t 2f 2f 3t Port U C 1) A It C D A B C D A B C A D C B A D C B L..H 103 D.iU 257 310 394 217 188 187 97 89 86 91 98 94 101 96 89 100 94 94 101 121 98 98 Port C 1) A It C D A B C D A B C D B A D C B A D C Lab 104 Data 203 410 391 279 255 230 45* 98 93 111 107 108 96 103 85 76 84 97 95 87 87 113 Port D A » C D A B C D A B C D A C B A U C B A D *Vjlues eliiuin.iled Iriim I lie and lysis as outliers f V.i lues regarded .is nnssint> due to unjlyst error Mole I'A polity is 10 express .ill niLMsurcinunts in A^emy doiumenls in menu nulls When iinplcnienlinu this pr.ii.liie. will result in undue cost or dittiuilly in il.mty NIIU/KII' is providing conversion .ittors lor the p.irluul.ir iioii-incirii units used in the document I'or this report, the factor IS 10-' lb/scf= 1 6018 X lO'/ug/m3 11 ------- TABLE 2. NITROGEN OXIDE EMISSIONS FROM NBS SAMPLES (Parts Per Million) 1 CVl'l 107 344 784 Kepi-mum 1 •> 3 1 2 3 1 2 3 L.ihs 101 112 120 124 341 341 341 637 661 597 102 131 115 139 344 350 - 802 817 764 101 109 90 99 325 408 343 823 768 - 104 118 115 104 365 385 347 769 785 737 TABLE 3. CONFIDENCE INTERVALS FOR GAS SAMPLE MEANS Coiiccnlrjlion, ppm 107 344 784 Mcjn 115 354 742 St Dcv n 24 76 Si h.rror 4 7 21 ' 2 201 2 228 2 228 <•!„, KIM 21 U8-370 695-789 Confidence intervals around the sample mean for each concentration across the collaborators are used to determine the accuracy of the NOX concentrations obtained. Values of the pertinent statistics are given in Table 3. The method may be said to be accurate at each level ij the ui tual concentration lies within the 95% confidence interval around the sample mean For each of the concentrations, the true value does he in the confidence interval, tailing in the low range for the 107 ppm and 344 ppm values, and in the high range for the 784 ppm value I mm tins, then, we c.m conclude that in all three ranges, low, medium, and high, the method does pm\ide .in accmatc estimate ol the true concenliation level. However, there is considciable scallei ainoiis.1 ilu- obseivahons at the lughei concentrations, as reflected hy their standard deviations E. The Precision of Method 7 Of prime importance in the evaluation of Method 7 is the estimation of the precision that is associated with the determination of NOX concentrations. This precision is estimated in terms ol between-laboratory and within-laboratory standard deviations, as previously defined In analysing the data, the first consideration is to determine, if possible, the distributional nature of the reported concentrations To accomplish this, the concentrations are transformed using two common variance-stabilizing transformations, the logarithmic and the square root, and the degree ol equality of variance obtained is determined In addition, the untransformed data are also tested, and the three forms are compared in Appendix B 3. For the run data, the logarithmic transformation produces the best results and is accepted as the most likely model for the data. This acceptance implies that there is a proportional relationship between the true mean and standard deviation (3) To further this argument, the sample mean and standard deviation arc examined by means of a regression through the origin to see if the theoretical relationship proposed seems valid on an empn- ical basis. The details are provided in Appendix B.4, and the least squares fit and the individual points are shown in Figure B.I The paired sample means and standard deviations exhibit an apparent linear trend, and an investigation of the correlation terms confirms this. The coefficient of correlation for these values is 0 936 which is a significant value at the 5 percent level of significance. The coefficient of deter- mination for the no intercept model is 0 876, indicating that 87 6 percent of the change in magnitude of the standard deviation is due to a change in the magnitude of the mean 12 ------- A similar analysis is used on the collaborator block mean and standard deviation, again using a regression through the origin. The line which provides the least squares fit through the origin is shown in Figure B.2. The value of the coefficient of correlation is 0.907 which also is significant at the 5 per- cent level This gives a coefficient of determination tor the collaborator block data of 0 823. Thus, on both a theoretical and an empirical basis, we can say that the mean and standard deviation lor the run data are proportional to one another. In terms of the between-laboratory standard deviation o/, , for the true determination mean, 6, where fa is the true between-laboratory coefficient of variation. For the collaborator block data, on an empirical basis, we can also say that there is a proportionality between the mean and standard deviation. In terms of the within-laboratory component, a, and the true mean determination, 6, where $ is the true within-laboratory coefficient of variation. Thus, we can obtain estimates of o and a/, by estimating the proportionality factors, or coefficients of variation, and expressing the estimates as percentages of the true mean determination In Appendix B 5 the technique for obtaining best estimates of the coefficients of variation is discussed, and it is demon- strated that the resulting estimates are unbiased for the standard deviations of interest. We refer to these estimates as a and a/, , and express them as a=06 and ob where 0 and fa are the estimated coefficients of variation, and 5 represents the true mean ot the determinations. In Appendix B.6, the estimates of 0 and fa are obtained. The within-laboratory coefficient of variation is|3 = (0.1488), which gives an estimated within-laboratory standard deviation of a = (0.1 488)5 with 67 degrees of freedom. Similarly, we obtain from the run data, fa = (0.1847), which gives an estimated between-laboratoi> standard deviation of with 3 degrees of freedom = V/(0.1847)262 - (0.1488)262 OL = V(0.1847)2 - (0 1488)2 = (0 1094)6. 13 ------- F. The Accuracy and Precision of the Analytical Procedure As previously discussed, the collaborators were given three standard nitrate solutions tor analysis in conjunction with the collaborative test samples. The actual concentration was unknown lo the collaborators, and this gave a basis for determining accuracy and precision for the lab procedine alone The true concentration for solutions A, B, and C were 38.2, 7 2, and 22.3 Mg/mfi, respectively. The test for accuracy was as for the gas samples in section 111, D, by constructing confidence inter- vals around the sample mean values. The mean is the average of the nine individual determinations for all four collaborators taken together and thus has an estimated variance of oi /4 + o2 /36. Using the values in Appendix B.8 for each solution of MSi and o2r, we obtain the confidence intervals shown in Table 4. TABLE 4. ACCURACY OF THE ANALYTICAL PROCEDURE Solution A B C True Concentration MgNO,/mS 38.2 7 2 223 Sample Mean MgNO,/mfi 37.94 600 2221 Confidence Interval 33.26<«i<4262 425 |