Criterion for Judging Acceptability of Analytical Methods Earl F. McFarren, Raymond J. Lishka, and John H. Parker Analytical Reference Service, Bureau of Water Hygiene, Public Health Service, Cincinnati, Ohio A procedure is developed for calculating the so-called total error of a method. On the basis of this total error, it is suggested that methods be divided into three categories: excellent (total error 25% or less), acceptable (total error 50% or less), and unacceptable (total error greater than 50%). This system is then applied to the results obtained in some recent ARS collaborativestudiesin order to categorize the methods objectively.
acceptability of a n analytical method. The difference being, in the case of collaborative study, that the precision as calculated from the data collected by many laboratories will be somewhat larger because of differences in reagents, instrument calibrations, glassware calibrations, etc. These latter errors are also random errors but are in addition to the operator or laboratory random errors calculated when a series of test results are collected by only one operator in one laboratory. The mean error, on the other hand, as calculated for a series THESTANDARD DEVIATlON as used in this paper iS the same as of test results from many laboratories may not bear any relathat which can be found in any statistical book; namely, the tionship to that calculated for a series of test results from one square root of the variance. The relative standard deviation laboratory. The latter may represent either the method bias, is the standard deviation expressed as a percentage of the mean the laboratory bias, or both. The former, however, since it is of the same series. This term is the same as the “coefficient of a n average of the bias from many laboratories, presumably variation” and is used in preference to it as recommended in more truly represents only the method bias (accuracy). ANALYTICAL CHEMISTRY ( I ) . The above are measures of the Using these slightly redefined terms for the precision and precision of the data. As measures of the accuracy of the accuracy of collaborative data, it is possible by means of suitdata, the mean error and relative error are used. The mean able statistical tests, such as the F test ( 4 ) and the t-test ( 5 ) to error is the difference between the average of a series of test determine whether there is a significant difference in either the results, and the true result. The relative error is simply the precision o r the accuracy of two methods. If there is a sigmean error expressed as a percentage of the true result. These nificant difference, then the method that is either more precise definitions are the same as defined in ANALYTICAL CHEMISTRY or more accurate is, presumably, the better method. ( I ) with the exception that the data were collected by many It is not always so simple, however, to determine whether operators rather than one. any of the tested methods are acceptable; that is to say, are the The net result is that the standard deviations are larger than results sufficiently precise and accurate to satisfy the need? they would be if all the data had been collected by one operaThis question is of particular importance to standard methods tor. For this reason, some chemists and statisticians have committees if their selection of methods is to be sensible and tried to redefine these terms when applying them to the data unbiased. from many laboratories. Another problem is that chemists As a result of conducting collaborative studies and evaluatd o not seem to wish to recognize that a method can be inacing the results, Analytical Reference Service (ARS) has frecurate but still acceptable. Furthermore, from a purely quently had to ask itself this question before making a recomstatistical point of view, there is no such term as mean error mendation to a standard methods committee to accept or rebecause the true result (value) is never known or does not ject a method. Our attempt to answer this question is the exist. Youden ( 2 ) , for example, has suggested that duplicates subject of this paper. or single determinations o n each of two closely similar mateProposed Criterion. At first, Analytical Reference Service rials be collected foi measurement of the precision of a method more or less arbitrarily decided that if a method was to be by collaborative study. He further suggests that the precision judged acceptable, it should not produce an error greater than calculated for a method by his procedure is composed of both *20%. However, in attempting to apply this rather arbisystematic (laboratory bias) and random errors. The net trary rule to the judging of methods, some difficulties were result is that terminology becomes confused because the bias of encountered; namely, should the precision as measured by a method (accuracy by the usual definition) is now calculated the relative standard deviation be less than 20%, and, if so, as a part of the standard deviation (which is generally recogshould the accuracy as measured by the relative error also be nized as a measure of precision), and accuracy in the usual less than 20%, or rather should the “total possible error” sense is ignored. Likewise, Pierson and Fay (3) have sug(precision plus accuracy) not be greater than 20%. gested the use of the “mean square error” to take both preciActually, most chemists like to think that the results of their sion and accuracy into account, but as before the contribution analyses are not in error by more than about lo%, but in of each to the overall (“total possible error”) is not clearly practice the error usually is greater. For the sake of arguindicated. ment, therefore, let us assume that the total error may be as Obviously, both precision and accuracy [as defined in large as 2 5 x (if that seems large, the reason for it will soon CHEMISTRY ( I ) ] must be considered in judging the ANALYTICAL become evident) and attempt to visualize the contribution of precision and accuracy to this total error. For example, let us (1) “Guides for Measures of Precision and Accuracy,” ANAL. further assume that we have studied a method in which we had CHEM., 40, 2271 (1968). 80 participants (the exact number is not important), and o n (2) W. J. Youden, “Statistical Techniques in Collaborative Tests,’’ Association of Official Analytical Chemists, Inc., Washington, D.C., 1967. (4) B. Ostle, “Statistics in Research,” Iowa State University Press, 1963, p 123. (3) R. H. Pierson and E. A. Fay, “Guidelines for Interlaboratory (5) Zbid.,pp 119-20. Testing Programs,” ANAL.CHEM., 31 (13), 25A (1959). 358
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
calculation and summation of the results, we found that the relative error of the method was zero-Le., that the mean and true value were equal. If then the standard deviation were large enough to give a relative standard deviation of 12.5 %, presumably, a total error (relative error plus two relative standard deviations) at least as large as 25 could exist since two standard deviations will encompass 95.5 of the possible results (see Figure 1) and in this case the relative error is zero. On the other hand, the relative standard deviation will never be zero, and in fact very seldom has ARS observed a relative standard deviation less than 2.5 %. This means then that we can tolerate a relative error as large as 20 % (see Figure 2) if we are willing to accept a total error as great as 25 %. However, a relative error this large can be permitted only when the relative standard deviation is minimal. For example, if the relative standard deviation was as large as 7.5 %, then the relative error could be only as large as 10% if the 2 5 x total error permitted was to encompass 95.5 of the total possible results (see Figure 3). But if the relative standard deviation cannot be larger than 12.5 and the relative error cannot be larger than 20% (and in most cases must be smaller), the experience of ARS would indicate that only a few methods would qualify. It would seem, therefore, that if we are going to adopt some sort of system for judging the acceptability of a method, it may be desirable to divide methods into at least three different classes; namely, methods that can be rated as excellent or highly satisfactory, methods that are acceptable provided no better method is available, and methods that are unacceptable. Since the experience of ARS has indicated that few methods will qualify even if a total error as large as 25 is permitted, those methods that do qualify might be considered in the excellent category. Those, therefore, that are to be considered acceptable only if no better method is available will have a much larger error, perhaps as great as 50%. Under these conditions, with reasoning similar to the above example, a relative standard deviation as large as 25 and a relative error as large as 45 would be acceptable. As can be seen, however, the permissible relative error is dependent on the size of the relative standard deviation and on the sum of the relative error plus two times the relative standard deviation not exceeding 50%. The third category then would be those methods that have a total error greater than 50% and that would be judged unacceptable. In actual practice, application of the formula:
x
x
Rel. error
+ 2 (Rel. std. dev.) = Total error
=
A B
25 25
1.10 0.90
Figure 1. No relative error but large relative standard deviation 20% Relative Error
I
io
Rel. error
$0.10 -0.10
0.05 0.05
10.0 10.0
30
Percent T o t a l Error
Figure 2. Large relative error but minimal relative standard deviation I
10% R e l o l i v e E r r o l
10
10
0
20
3n
Figure 3. Relative error and relative standard deviation approximately equal
Total error
Std. dev.
,
20
10
0
A.
Mean error
40
30
Percent Total Error
For example, let us assume that the following set of data was collected for two different methods: Meth- No. od results Mean
20
10
0
Percent T o t a l Error
+ 2 (Std. dev.) X 100
10
20
30
20
can lead to some anomalies, and it is better, therefore, to use the formula: Absolute value of mean error True value
I
40
Rel. std. dev. 4.5 5.6
In this case, application of the first formula leads t o the following two results:
B.
+ 2(4.5) = 19% total error 10 + 2(5.6) = 21 % total error 10
and it appears that there is a difference in the two methods, when actually the methods are equally precise and accurate. This phenomenon occurs because, for A, the mean is greater than the true value (1.00), and for B, the mean is less than the true value. Application of the second formula corrects this situation; namely, 2(0*05) x 100 = 2 0 x total error 1.oo
A. B.
O.'
+
2'0.05)
1.oo
x
100
=
20% total error
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
359
Table I. Summary of Data on Metals by Atomic Absorption Spectrophotometry ( 6 ) Sample
True value
No.
Mean
Mean error
Std. dev.
Rel. error
Rel. std. dev.
Total error
Zinc
1 2 3
0.05 0.50 1 .00
51 48 49
0.055 0.502 1.030
0.023 0.041 0.108
9.4 0.4 3.0
41.8 8.2 10.5
102.1 16.8 24.6 -
0.024 0.021 0.013
3.0 2.9 2.3
12.3 22.1 26.4
27.0* 45.0* 54.0
0.031 0.065 0.116
33.6 8.5 3.4
47.3 24.0 11.2
158.0 60.4 26.6*
0.014 0.011 0.005
5.0 8.1 8.5
6.5 10.3 10.2
19.0 -
0.007 0.043 0.030
6.0 1.3 4.4
13.5 8.4 11.6
18.6 20.8 -
+0.005
0.010
-0.007 +0.015
0.010 0.017
10.5 7.1 7.3
17.5 10.7 7.6
50.0* 27.0* 24.5 -
0.047 0.023 0.014
6.2 5.1 19.0
21.5 21.7 23.5
53.0 51.0 76.0
0.009 0.012 0.015
45.6 8.2 7.5
59.3 21.6 13.8
230.0 56.0 38.0*
0.053 0.048 0.050
15.6 4.0 0.6
45.6 9.2 16.5
122.0 23.2 34.0*
+0.005 +0.002 +0.030
Chromium" 1 2 3
0.20 0.10 0.05
14 14 14
0.194 0.097 0.049
-0.006 -0.003 -0.001
Copper 1 2 3
0.25 1.00
57 58 53
0.067 0.271 1.034
$0.017 $0.021 +O. 034
0.20 0.10 0.05
14 13 12
0.210 0.108 0.054
+0.010 +0.008 +0.004
0.05
Magnesium" 1 2 3
30.0* 28.0*
Manganese" 1 2 3
0.50
0.05
1 2 3
0.05 0.10 0.20
0.25
14 14 14
0.053 0.507 0.261
7 7
0.055 0.093 0.215
+0.003 +0.007
+0.011
34.0*
Silver"
7
Leadb 1 2 3
0.20 0.10 0.05
9
1 2 3
0.01 0.05 0.10
25 26 26
8 8
0.21 2 0.105 0.060
+0.012 +0.005 f0.010
0.015 0.054 0.108
+0.005 +0.004 $0.008
Cadmium
Iron 1 2 3 b
0.10 0.50 0.30
45 41 43
0.116 0.520 0.302
+0.014 +0.020 +o. 002
With Boling burner. Extracted.
RESULTS
Let us now apply the latter formula to the calculation ofthe total error of the data from a number of collaborative studies conducted by ARS over the past couple of years (Tables I through XII). In these tables, the values underlined have a error Of less than 25 % and, as discussed above, are judged excellent. Those marked with an asterisk have a total error greater than 2 5 % but are also judged acceptable since 360
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
they have a total error less than 50%. . _ All the others have a total error greater than 50z and are, therefore, judged unacceptable.
(6) "Water Metals No. 4, Study No. 30," US public Health Service Publ. No. 999-UIH-8, Department of Health, Education, and Welfare, Cincinnati, Ohio, 1968.
Substance Sample Lindane Heptachlor Aldrin Heptachlor epoxide p,p’-DDE 1 p,p’-DDE 3 Dieldrin Dieldrin Endrin Endrin o,p’-DDT o,p’-DDT p,p’-DDT p,p’-DDT Methoxychlor
No.
215 210
No. 17 18 18 17 16 16 18 18 17 18 15 17 16 18 18
Table 11. Summary of Data on Pesticides (7) True Mean Std. value Mean error dev. 0.254 -0.046 0.092 0.30 0.212 -0.039 0.078 0.25 0.218 -0.082 0.078 0.30 0.20 0.177 -0.023 0.064 0.04 0.031 -0.009 0.019 0.350 -0.050 0.114 0.40 0.025 O.Oo0 0.012 0.025 0.191 -0.059 0.104 0.25 0.20 0.182 -0.018 0.090 0.301 -0.099 0.175 0.40 0.10 0.096 -0.004 0.010 0.265 -0.035 0.063. 0.30 0.10 0.094 -0.006 0.045 0.25 0.219 -0.031 0.077 1.00 0.921 -0.079 0.235
Rel. error 15.5 15.0 27.6 11.4 23.4 12.5 1.1 23.5 9.1 24.7 4.4 11.8 5.9 12.3 7.8
Rel. std. dev. 36.1 36.9 35.5 35.9 63.4 32.6 46.3 54.1 49.5 58.0 10.3 23.9 46.3 35.2 25.5
Total error 76.6 78.0 79.3 75.5 117.0 69.5 96.0 168.0 99.0 112.0 24.0 53.6 96.0 74.0 54.9
-
Table 111. Summary of Data on Determination of LAS by Methylene Blue ( 8 ) Mean Std. Relative Rel. std. Total Mean Std. Relative Rel. std. Total Mean error dev. error dev. error No. Mean error dev. error dev. error Sample 1. 2.94 mg/l. in river water Sample 3. 0.27 mg/l. in distilled water 2.98 +0.042 0.272 1.43 9.12 19.9 212 0.24 -0.028 0.036 10.58 14.77 37.0* Sample 2. 0.48 mg/l. in tap water 0.49 +0.006 0.048 1.27 9.94 21.2 -
Method
No. results
Electrode Ion-exchange
103 19
Table IV. Summary of Data on Fluoride (9) Mean Mean error Std. dev. Sample 1. 0.85 mg/l. 0.844 -0.006 0.030 0.874 +O. 024 0.052
Electrode Mod. electrode Ion-exchange
100 13 19
Sample 2. 0.90 mg/l. plus aluminum 0.612 -0.288 0.108 0.856 -0.044 0.025 0.785 -0.115 0.095
Electrode Ion-exchange
107 19
Sample 3. 0.75 mg/l. plus phosphate 0.748 -0.002 0.036 $0.034 0.075 0.784
Table V.
Correction
No. results,
4
Summary of Data on Aluminum with Fluoride (0.48 mg/l. aluminum) Mean Mean error Std. dev. Eriochrome Cyanine R Method 0.495 +0.015 0.034
No correction Hydrolysis and F- correction Fusion or distillation F- addition to standards Curve correction for F-
7 4 17 16
0.540
+O. 060
0.390 0.514 0.469
-0.090 $0.034 -0.011
No correction Hydrolysis Fusion or distillation F- added to standards
11 4 11 7
0.324 0.552 0.456 0.444
Aluminon Method -0.155 0.180 +O. 072 0.232 -0.025 0.214 -0.036 0.097
(7) “Water Pesticides No. 2, Study No. 31,” US Public Health Service Publ. 999-UIH-10, Department of Health, Education, and Welfare, Cincinnati, Ohio, 1968. (8) “Water Surfactant No. 3, Study No. 32, US Public Health Service Publ. No. 999-UIH-11, Department of Health, Education, and Welfare, Cincinnati, Ohio, 1968.
0.368 0.289 0.116 0.120
Rel. error
Rel. std. dev.
Total error
0.7 2.8
3.6 6.0
7.7 15.0
32.0 4.9 12.8
17.7 2.9 12.1
10.4 33.8*
0.2 4.5
4.8 9.6
8.2 19.3
56.0
-
Interference (10) Rel. error
Rel. std. dev.
Total error
3.13
6.90
17.2 -
12.4 18.8 7.14 2.3
68.2 74.2 22.5 25.5
165.6 139.1 55.4 52.2
32.4 14.9
55.6 42.0 47.0 21.8
107.2 111.4 94.3 47.9*
5.1
7.6
(9) “Water Fluoride No. 3, Study No. 33,” US Public Health Service Publ. No. 1895, Department of Health, Education, and Welfare, Cincinnati, Ohio, 1968. (10) “Water Metals No. 5, Study No. 34,” US Public Health Service Publ. No. 1910, Department of Health, Education, and Welfare, Cincinnati, Ohio, 1969. ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
361
Table VI. Summary of Data on Aluminum with Phosphate Interference (10) (0.54 mg/l. aluminum) Mean Rel. Rel. No. results Mean error Std. dev. error std. dev.
Correction
Total error
Erichrome Cyanine R Method No correction
Hydrolysis Hydrolysis and F- correction Fusion or distillation F- added to standards Curve correction for F-
12 16
0.492 0.533
-0.048 -0,007
0,242 0.236
8.9 1.3
49.2 44.3
98.7 88.7
6 3 4 5
0.269 0.461 0.450 0.447
-0.271 -0.079 -0.090 -0,093
0.143 0.034 0.125 0.146
50.1 14.7 16.2 17.2
52.9 7.4 27.8 32.7
103.1 27.2* 62.9 71.2
16 8 6
0.491 0.484 0.461
-0.049 -0.056 -0.079
9.4 10.3 14.7
48.2 16.4 17.0
96.8 39.6* 43.5*
Aluminon Method No correction
Hydrolysis Fusion or distillation
0.237 0.079 0.078
Table VII. Summary of Data on Aluminum with No Interference (10) (0.52 mg/l. aluminum)
Mean error
No. results
Mean
No correction Hydrolysis Hydrolysis and F- correction Fusion or distillation F- added to standards Curve correction for F-
27 3
0.511 0.681
-0.009 $0.161
0.338 0.465 0.671 0.595
-0.182
No correction Hydrolysis Fusion or distillation
23 3 6
Correction
Rel. error
Rel. std. dev.
Total error
0.176 0.374
1.7 31 .O
34.4 54.8
69.4 174.8
0.257 0.381 0.175 0.124
35.1 10.6 29.0 14.4
76.1 82.6 26.1 20.8
133.8 157.1 96.3 62.1
0.170 0.348 0.123
5.6 15.4 21.5
34.6 58.0 30.1
70.9 149.2 68.8
Std. dev.
Eriochrome Cyanine R Method
-0.055
+o. 151 +O. 075
Aluminon Method
0.491 0.600 0.408
-0,029
+o. 080 -0.112
Table VIII. Summary of Data on Aluminum with Eight Other Metals as Interference (10) (0.50 mg/l. aluminum)
Mean error
No. results
Mean
No correction Hydrolysis and F- corr ect ion Fusion or distillation F- added to standards Curve correction for F-
26
0.531
$0.031
5 4
4
0.297 0.390 0.681 0.578
-0.203 -0.110 +o. 181 +0.078
No correction Hydrolysis Fusion or distillation
22 3 6
0.566 0.803 0.597
Correction
Rel. error
Rel. std. dev.
Total error
0.153
6.2
28.8
67.4
0.157 0.281 0.181 0.098
40.6 22.0 36.2 15.5
53.0 72.1 26.5 17.0
103.4 134.4 108.6 54.8
0.120 0.174 0.164
13.1 60.7 19.4
21.1 21.2 27.4
61.2 130.2 85.0
Rel. std. dev.
Total error
Std. dev.
Eriochrome Cyanine R Method
5
Aluminon Method
No.
Method
results
+O. 066 +O. 303
+O. 097
Table IX. Summary of Data on Copper and Manganese (10) Mean Re]. Mean error Std. dev. error Copper, 1.0 mg/l.
Bathocuproine disulfonate Cuprethol Atomic absorption
33 17 10
1.003 0.990 1.013
+O. 003
-0.010 +O. 01 3
0.042 0.027 0.026
8.7 -
0.3 1 .o 1.3
4.1 2.7 2.0
6.4 6.5 -
58.0 53.4 61.2 7.2 1.5 4.5
51.4 43.4 76.3 50.3 5.9 23.1
222.0 186.0 310.0 116.0 14.0 49.4*
Manganese, 0.05 mg/l.
Formaldoxime No correction Cyanide added Iron added Persulfate Periodate Atomic absorption 362
9 11 11 17
4 13
0.079 0.074 0.081 0.054 0.051 0.048
+0.029 $0.027 $0.031 +0.004 $0.001 -0.002
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
0.041 0.033 0.062 0.027 0.003 0.011
Method
No. results
Methyl orange Leuco crystal violet Ferrous-DPD SNORT OT OTA Amperometric Ferrous-OT
26 18 17 15 17 23 19 18
Methyl orange Leuco crystal violet Ferrous-DPD SNORT OT OTA Amperometric Ferrous-OT
23 18 17 14 15 22 19 18
Methyl orange Leuco crystal violet Ferrous-DPD SNORT Iodometric OT OTA Amperometric Ferrous-OT
26 18 19 17 32 18 23 24 19
Table X. Summary of Data (11) on Chlorine in Sample 1 Mean Rel. Mean error Std. dev. error 0.83 mg/l. free chlorine 0.647 22.0 -0.183 0.341 0.331 60.1 -0.499 0.372 14.5 -0.120 0.145 0.710 $0.069 0.207 8.3 0.899 -0.305 0.341 36.8 0.525 -0.330 0.323 39.8 0.500 0.581 -0.249 0.237 23.0 -0.314 0.282 37.8 0.516
52.7 112.2 20.4 23.0 65.0 64.6 40.8 54.6
104.0 150.0 49.3* 58.1 119.0 117.0 87.2 106.0
1.OO mg/l. combined chlorine +0.007 0.163 + O . 159 0.572 $0.063 0.077 -0.139 0.186 -0.580 0.160 -0.625 0.168 +0.112 0.161 -0.176 0.258
0.7 15.9 6.3 13.9 58.0 62.4 11.2 17.6
16.2 49.3 7.3 21.6 38.2 44.8 14.5 31.3
33.3* 130.0 21.9 51.1 90.0 96.1 43.4* 69.1
1.698 1.491 1.751 1.603 1.524 1.073 0.923 1.669 1.359
1.83 mg/l. total chlorine -0.132 0.338 -0.339 0.483 -0.079 0.164 -0,227 0.419 -0,306 0.360 -0.757 0.343 -0.907 0.323 -0.161 0.209 -0.471 0.357
7.2 18.5 4.3 12.4 16.7 41.4 49.6 8.8 25.7
19.9 32.4 9.4 26.1 23.6 31.9 35.0 12.5 26.3
44.1* 71.3 22.2 57.9 55.9 79.0 85.0 31.5* 64.8
Rel. std. dev.
Total error
43.0 32.0 39.8 34.7 64.6 52.4 42.3 52.6
89.2 67.8 83.5 73.6 116.7 102.6 88.6 103.2
Table XI. Method
Mean
Methyl orange Leuco crystal violet Ferrous-DPD SNORT OT OTA Amperometric Ferrous-OT
26 17 19 15 15 20 23 19
0.624 0.743 0.642 0.698 0.460 0.462 0.600 0.468
Methyl orange Leuco crystal violet Ferrous-DPD SNORT Iodometric
26 17 19 15 32 15 20 23 19
0.794 0.816 0.725 0.721 0.642 0.625 0.654 0.761 0.602
or
Total error
1.007 1.159 1.063 0.861 0.420 0.376 1.112 0.824
No. results
OTA Amperometric Ferrous- OT
Rel. std. dev.
Summary of Data (11) on Chlorine in Sample 2 Mean Rel. error Std. dev. error 0.80 mg/l. free chlorine -0.176 0.268 22.0 -0.057 0.243 7.1 -0.158 0.255 19.8 -0.102 0,243 12.8 -0.340 0.297 42.5 -0.339 0.242 42.3 -0.200 0.254 25.0 -0.332 0.247 41.4 0.84 mg/l. total chlorine -0.047 0.188 -0.024 0.204 -0.115 0.222 -0.119 0.197 -0.198 0.174 -0.215 0.212 -0.186 0.147 -0.079 0.174 -0,238 0.202
The results of this system of classifying the methods presented in Tables I through XI1 are summarized in Table XIII. F o r the convenience of those needing t o know the acceptability of methods previously studied by ARS, Table XIV summarizes the application of the technique discussed in this paper t o the methods appearing in a n earlier publication (12). (11) “Water Chlorine (Residual) No. 1, Study No. 35,” US Public Health Service Publ. (In Press), Department of Health, Education, and Welfare, Cincinnati, Ohio, 1969.
5.5 2.8 13.6 14.2 23.6 25.6 22.1 9.4 28.4
23.6 25.0 30.6 27.3 27.0 33.9 22.5 22.9 33.6
50.1* 51.1 66.3 61 . O 65.0 76.0 57.1 50.8* 76.8
DISCUSSION I n using Tables XIII and XIV, remember that this system indicates only whether the method produces acceptable precision and accuracy. For example, a very precise and accurate method may be unacceptable for other reasons-e.g., too
(12) E. F. McFarren and R. J. Lishka, “Evaluation of Laboratory Methods for the Analysis of Inorganics in Water,” p 253, Trace Inorganics in Water, Advances in Chemistry Series No. 73, American Chemical Society, Washington, D.C., 1968. ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
363
Table XII. Method Methyl orange Leuco crystal violet Ferrous-DPD SNORT OT
OTA Amperometric Ferrous-OT Methyl orange Leuco crystal violet Ferrous-DPD SNORT Iodometric OT OTA Amperometric Ferrous-OT
No. results
Mean
26 17 17 15 14 20 24
0,572 0.566 0.587 0.589 0.450 0.446 0.494 0.459
16
26 17 19 16 30 17 21 24 18
Substance Zinc ( 6 ) Chromium ( 6 ) Copper (6) Magnesium (6) Manganese (6) Silver ( 6 ) Lead (6) Cadmium (6) Iron (6) Lindane (7) Heptachlor ( 7 ) Aldrin (7) Heptachlor epoxide ( 7 ) P,P’-DDE ( 7 ) Dieldrin ( 7 ) Endrin ( 7 ) o,p’-DDT ( 7 ) P,P’-DDT ( 7 ) Methoxychlor (7) LAS (8) Fluoride ( 9 )
Summary of Data (11) on Chlorine in Sample 3 Mean Rel. error Std. dev. error 0.60 mg/l. combined chlorine -0.028 0.224 4.7 5.7 -0.034 0.172 2.2 -0.013 0.120 -0.011 0.266 1.9 -0.150 0.174 25.0 25.8 -0.155 0.198 -0.106 0.214 17.7 -0.141 0.120 23.5
0.731 0.646 0.588 0.628 0.522 0.511 0.549 0.585 0.476
0.64 mg/l. total chlorine +0.091 0.220 +0.006 0.222 -0.052 0.113 -0.013 0.238 -0.118 0.169 -0.129 0.190 -0,091 0.154 -0.055 0.145 -0.164 0.123
14.2 0.9 8.1 2.0 18.5 20.2 14.2 8.5 25.6
Table XIII. Summary of Method Acceptability Excellent Acceptable Atomic absorption Atomic absorption Atomic absorption Atomic absorption Atomic absorption Atomic absorption
Manganese (10) Chlorine (11)
39.2 30.5 20.4 45.2 38.6 44.5 43.3 26.1
79.4 63.0 42.1* 90.6 83.0 92.0 89.0 63.5
30.1 34.4 19.2 38.0 32.4 37.3 28.0 24.8 25.8
83.0 70.6 43.4* 76.4 71.4 79.6 62.3 53.9 64.0
Unacceptable
Atomic absorption Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Gas chromatography Methylene blue a. Electrode b. Ion-exchange a. ECR b. Aluminon a. Bathocuproine disulfonate b. Cuprethol c. Atomic absorption Ferrous-DPD
complicated, expensive, or exotic. On the other hand, a statistically unacceptable method might, of necessity, be used because no better method is avilable-namely, the ECR procedure for aluminum since it is equally as good as the aluminon procedure and has the advantage of simplicity. For determination of metals by atomic absorption spectrophotometry, the method was, in some cases, found acceptable for determination of a metal at one concentration but not at another (generally smaller). In the summary (Table XIII) the method is judged acceptable for the metal if it is capable of measuring that metal (within acceptable limits) a t the concen364
Total error
Atomic absorption Atomic absorption
Aluminum (10) Copper (10)
Rel. std. dev.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
Atomic absorption a. SNORT b. Amperometric c. Methyl orange d. Leuco crystal violet
Formaldoxime a. OT b. OTA c. Ferrous-OT
tration established by the drinking water standards (13). On the other hand, for phosphates, nitrates, silicates, and ammonia, which were also measured in several samples of differing concentration, the results in Table XIV indicate only that the major portion of the results were or were not satisfactory. In this respect, the results presented for chlorine in Table XI11 are an exception in that if any of the results were (13) “Public Health Drinking Water Standards, 1962,” US Public Health Service Publ. No. 956, US Govt. Printing Office, Washington, D.C., 1962.
~
Substance Aluminum Copper Iron Manganese Silver Cadmium Chromium Lead Selenium Beryllium Boron Arsenic Vanadium Silica Phosphate Nitrate Ammonia
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Table XIV. Summary of Acceptability of Methods Previously Studied (12) Excellent Acceptable Unacceptable Aluminon Bathocuproine a. Cuprethol b. Sodium diethyl dithiocarbamate c. Neocuproine a. Phenanthroline b. Thiocyanate c. Tripyridine Persulfate Periodate Dithizone Dithizone a. Permanganate b. Alk. hypobromite Dithizone Diamino benzidine Aluminon Curcumin Diethyl dithiocarbamate Gallic acid Molybdosilicate Heteropoly blue Stannous chloride Amino-naphtholsulfonic Modified brucine a. Brucine Phenoldisulfonic b. AutoAnalyzer a. Nesslerization a. Distillation with nesslerization b. AutoAnalyzer b. Distillation with titration
acceptable, the method was judged acceptable. The reasoning for this is that since the chlorine samples were prepared as dry powders containing a mixture of chemicals, all the results (regardless of method used) were more variable than normal, presumably because the individual aliquots were not as homogeneous as the usual liquid standards. CONCLUSIONS
As a result of the application of the proposed criterion for judging the acceptability of analytical methods, atomic absorption spectrophotometry was found acceptable for the determination of zinc, chromium, copper, magnesium, manganese, iron, and silver but unacceptable for the determination of lead and cadmium. On the other hand, none of the pesticides studied could be determined satisfactorily by gas chromatography. The methylene blue method, however, was found acceptable for the determination of linear alkylate sulfonate (LAS), and fluoride can be satisfactorily determined by either the electrode or ion exchange methods.
Neither the ECR nor the aluminon method for aluminum was found acceptable, but since no other satisfactory methods are available, it is recommended that the ECR method be used since it is simpler. Copper can be determined satisfactorily by either the bathocuproine disulfonate o r the cuprethol method, but the formaldoxime method for managanese is unacceptable. Chlorine can be satisfactorily determined by using the ferrous-DPD, SNORT (stabilized neutral orthotolidine), arnperometric, methyl orange, or leucocrystal violet methods, but the orthotolidine, orthotolidine-arsenite, and the ferrousorthotolidine methods are unacceptable. Objective reevaluation (with the proposed criterion) of the methods summarized in a previously published paper resulted in conclusions essentially in agreement with those previously determined subjectively.
RECEIVED for review July 1, 1969. Accepted December 22, 1969.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
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