Evaluation of Spectrographic Analytical Data H. V. CHURCHILL
AND
J. R. CHURCHILL
Aluminum Company of America, N e w Kensington, Pa. The authors have two objects in presenting this paper: (I) to furnish accuracy and precision data to those interested in the spectrographic analysis of metals, and (2) to illustrate the value of a simple statistical approach to the handling of a large number of separate data.
The terminology used in the tables is largely self-explanatory. The treatment of data, the specific calculations illustrated, and the interpretation of the results follow the general pattern set by standard texts and reference books on statistics (3, 5, 8) and by recent papers (6, 7 ) dealing with the application of statistical methods to similar analytical problems.
S
P E E D and accuracy are cardinal criteria in the evaluatioii of analytical methods. I n industrial chemical laboratorie-. thcce criteria must be applied with proper regard to the proces; being controlled and available laboratory personnel. Speed IS often essential, even though it may mean some sacrifice of accuracy. Precision or reproducibility of results is of paramount importance in such cases. However, with the development of instrumental methods, which are inherently more nearly objective than traditional methods, speed may be gained with no essential sacrifice of either accuracy or precision. Typical of such a cas? is the use of emission spectrography in metallurgical analytical laboratories. I n most metallurgical uses of the spectrograph, the method replaces chemical methods which produce results adequate in approach to accuracy and precision. Using analytical data derived in the routine operation of plant laboratories of Aluminum Company of America, it has been possible to compare the results obtained by spectrographic methods with those which would have been reported if the work had been done chemically. I t is the practice in Aluminum Company of America plant laboratories to analyze chemically on a routine basis a small number of the aluminum alloy samples that are analyzed and reported spectrographically. Data thus derived are of great value in indicating weaknesses in procedures and their application. Proper use of the data leads to re-evaluation of the standards used, improvements in apparatus, changes in laboratory operation, and better training of personnel. The analytical data of plant laboratories clear through the Analytical Division of illuminum Rcsearch Laboratories where they are studied. The continuous flow of data provides valuable informat ion about the performance of spectrographic standards and also enables the Analytical Division to ascertain what determinztions and what alloys present specific difficulties. ,4 statistical w m mary of a portion of the data for 1944 is given in Table I. -411 the spectrographic and chemical analyses were made by standard routine procedures ( 1 , g ) . The material is arranged as follows: Data for particular elements are arranged in order of increasing average concentration of the element in the group being covered. Each average level of concentration may cover either determinations made on a particular alloy or determinations made using a particular standard. Since the plant laboratories naturally tend to analyze chemically any sample which shows any peculiarities when analyzed spectrographically, the average composition shown is not necessarily representative of the level of composition sought by plant operators, but should be construed as the fortuitous average of the concentrations selected for chemical checking. I t would be misleading to designate specifically the various alloys being tested and thus possibly indicate that the average concentrations shown were metallurgical optimums. They are averages of concentrations in samples selected for checking for other reasons than uniformity or specificity of composition. Data have been included regardless of TI hether they appeared to be normal or abnormal. The authors have not included material when less than ten data were available for a particular determination. Such data will be included in future studies when the amount of data is sufficiently great to be significant.
ERRORS I N SPECTROGRAPHIC A N A L Y S I S
Errors in spectrographic analysis may be divided into two categories, random and systematic. Random errors originate largely in faulty technique, fluctuations in line voltage, variations in humidity, irregularities in photographic emulsions, variations in composition or structure from point to point on the sample, and errors in calculation. Systematic errors in spectrographic analysis arise largely from standardization. They may be caused by errors in the values assigned to standard samples, differences in metallurgical history of samples and standards, and differences in the technique used on standards and samples. The random differences between spectrographic and chemical analyses are measured by the standard deviation, s, which is defined mathematically as
deviation of individual spectrographic results from chemical results n = number of comparisons This equation is more convenient for handling large masses of data than the possibly more familiar equation d
=
in which 2 is the average bias of spectrographic resultb with respect to chemical results. The two equations are mathematically equivalent. This term provides a more useful measure of precision than almost any other conventional expression. I n a normally distributed group of statistics including a sufficient amount of data, 67y0 of the data will differ from the mean by no more than one standard deviation and 95y0 of the data is included within two standard deviations. The standard deviation is always larger than the average error and, while to the casual reader it may present the data in a less favorable light, it is more useful than the average error since it enables a much more complete and rigorous interpretation, especially when used in conjunction with the bias. Since each group of data represents a finite group of spectrographic and chemical comparisons, the accuracy with which the standard deviation of the population represented by the statistical sample is determined will vary with the number of determinations sampled and the magnitude of standard deviation. A measure of the validity of the standard deviation as the authors have calculated it is provided by its own standard deviation, ss, which is calculated from Sa
=
.\/z;E S
This quantity will be found virtually negligible for most of the data presented. A second type of error is introduced by any departure? from normal statistical distribution among the original data. Such departures will affect the validity of the distributional 751
INDUSTRIAL AND ENGINEERING CHEMISTRY
752
-
Yo. of Determinations Compared
Table I. Average % by Chemical Method
Spectrographic ss. Chemical Results Standard Average deviation bias Silicon 0,012 0.009 0.021 0.019 0.010 0 019 0.023 0.018 0.019 0.025 0.028 0.046 0.036 0,059 0.052 0.047 0.258 0.389
311 49 52 146 55 49 1941
0.02 0.06 0.07 0.16 0.16 0.16 0.30
+f 00.0004 .003 f0.007 f0.016 -0.013 - 0.0005 -0.009 -0 006 -0.001 -0.008 f0.004 fO.011 f0.008 -0.01 f0.011 -0.018 f O . 072 t o 11
Statistical Summary
Probability of Significance of Bias 0. li 0.9999+ 0.9993 0.9999f 0,9999 0.87 0.9999f 0 9998 0 42 0.9997 0.996 0 99990.999 0.47 0 9992 0.995 0.9999+ 0,9999
+
+
Iron 0.013 0.013 0.024 0.030 0.029 0.033 0.017 0.031 0.024 0.030 0.025 0.033 0.035 0.032 0.047 0.023 0.055 0.101 0.131
-0.020 -0.009 fO.007 f0.004 +0.010 +0.009 -0.023 -0.004 -0.004 -0.006 f0.020 -0.008 f0.004 f0.030 f 0 004 +o 010 f0 o x -0 076
0.47 0.9999f 0.999 0.9999+ 0.69 0.9999-t 0.9999c 0.9999+ 0.78 0.84 0.9999 0.99990.990 0 9998 0.9999 f 0.9999f 0.996 0,9999 0 9999f
Copper 0.002 0.015 0.013 0.018 0.019 0.026 0.027
-0.002 f0.003 f0.003 1-0.009 -0,014 fO.012 -0.009
0.9999t 0.83 0.89 0.9999 t 0,9999 T 0.998 0.9999f
- 0.0003
Vol. 17, No. 12
+
inferences drawn from t’hestandard deviations. Tests for “skewness]’, “flatness”, and other departures from normality are described in standard statistical texts and allowances can be made for such depart’ures by using special mathematical devices. Analytical data of the type here presented generally approach normal distribution to such a degree that the assumption of normality does not seriously impair the interpretation. A third source of error lies in the fact that the standard deviation properly applies only to a continuous distribution of data. -1discontinuity is introduced by the fact that all of the authors’ analytical results have been rounded off to the nearest hundredth of a per cent. When this grouping unit and the standard deviation are of similar magnitude, as they are in any of the data presented, a correction may be desirable. PvlacColl (6), in an excellent statistical treatment of analytical data, recommends the use of Sheppard’s correction in such cases. This correction was not applied, since it would not contribute materially t c the usefulness of the data under consideration. Systematic errors are measured by the “average bias”. “Average bias” is the algebraic mean difference between chemical and spectrographic results, assigning a positive sign when the spectrographic result is higher and a negative sign when it is lower than the chemical result. “Average bias” thus measures the tendency of the spectrographic result to run higher or lower than the chemical result. It does not represent the systematic error of the spectrographic result’, but rather the algebraic difference of the systematic errors of the spectrographic and chemical results. For example, if the mean absolute error of the spectrographic results happened to be -0.02 and that of the chemical results +0.05, the bias figure as considered here would be -0.07’%.
x o . of Determinations Compared
Spectrographic us. Chemical Results Standard Average deviation bias
hverage % by Chemical Method
49 52 403 168 204 31
0.42 1.73 3.94 4.05 4.07 4.08
Copper (contd.) 0.041 0.146 0.081 0.145 0.155 0.186
18 30 69 145 60 41 3207 86 624 145 443
0.03 0.05 0.06
llanganese 0.024 0.008 0.024
Probability of Significance of Bias
-0.008 -0,013 f0.091 fO.036 -0,027 f0.067
0.82 0.48 0,9999 i0.998 0.99 0.96 0.51 0 50 0.997 O.9999-t 0.9995 0.9997 0.9999 0.9999 0.9999t 0.99997 0 9999+
n RR 0: 9999
1 13
0.040
f0.004 fO.001 -0.009 +0.009 -0.008 -0.017 -0.010 -0,015 -0.009 -0.016 -0.011
27 103 98 57 547 202 3170 1110 402 94 425
0.04 0.36 0.54 0.59 0.91 1.19 1.47 1.48 1.56 1.56 2.37
Magnesium 0.010 0.025 0.028 0.032 0.042 0.038 0.072 0.021 0.054 0,055 0 087
-0.002 f0.014 -0.011 -0.009 -0.007 -0.031 -0.011 +0.011 -0.048 -0.007 -0.062
607 29 110 23 49 81 30 33
0.01 0.02 0.20 0.22 0.23 0.24 0.24 0.25
0.013 0,009 0.016 0.021 0.015 0.055 0.019 0.013
432 203
2.03 2,06
Nickel 0.073 0 098
+
+
0.9998 0.96 0.9999 0.9999f 0.9999 0.9999+ 0.9999-t 0.78 0.9999+
+
Chromium +0.010
+
f0.0015 +o. 010 f0.014 fO.O1O +o. 012 -0.004
0,9999 0.98 0.67 0.97 0.9999f 0.89 0.998 0.91
+0.0006 -0.018
0.13 0.991
+ O . 004
In considering a partirular bias figure, it is important to know whether the calculated bias represents a real difference between the average chemical arid spectrographic analyses or is simply a fortuitous result of the random errors of the two methods. X means of judging the precision ivith which the bias is estimated is provided by the standard error. The standard error of the bias, s d , is givcn by t,he formula S
sa =
z
For example, a bias of -0.012 obtained for a group of 512 samples yielding a standard deviation of 0.021 could be expressed a s 0.021 -0.012 * m2 or -0.012 =t0.001 if we wished to include in the
-
bias figure itself a measure of the precision with which it was dctermined. The probability of the bias being real and not merely a fortuitous result of statistical sampling errors is indicated by the term, “probability of significance of bias”, given in the last column of the table. Strictly speaking, this is the probability that the observed bias is larger than the bias which might have resulted from random errors alope. The probabilities were obtained by applying “Students’ t Test” (3) in which t =
d -S,.
-
d = average bias si = standard error of
2
The probability figures were obtained by referring the calculated t values to standard statistical tables (4). Interpolations
,
ANALYTICAL EDITION
December, 1945
between tabulated figures were made graphically by the use of Keuffel and Esser No. 359-23 Probability paper. Special graph papers of this type greatly facilitate the representation of statistical functions of the type here involved. The probability figures were rounded off to 0.01 below 0.99, to 0.001 from 0.990 to 0.999, and to 0.0001 from 0.9990 to 0.9999. Reporting the figures to a greater number of digits would not be justified because of the errors involved in the estimation of the standard deviation. Probabilities higher than 0.9999 have been reported as 0.99994- to avoid the inferences which might be drawn from rounding such figures off to 1.0000. The magnitude of the probability assists in judging whether the bias is real or fortuitous, but has little direct bearing on whether its magnitude is of practical significance. For example, in one of the groups of iron analyses, the bias is $0.004 a t an average iron content of 0.55%. The probability of significance is 0.9998, but a bias of +0.004 is too small to merit much consideration. INTERPRETATION OF DATA ’
It must be remembered in interpreting the data that both the bias and the standard deviation are net resultants of both spectrographic and chemical errors. If some means were available for determining the absolute bias and the standard deviation of the chemical analyses, estimates of the true bias and standard deviation of the spectrographic results could be obtained by the application of the formulas
cz, = d + Z s, =
4 SQ - s,2
(VI)
in which = the average absolute bias of spectrographic results 2 = the net average bias as given in t,he tables lo = the average absolute bias of chemical results s, = standard deviation of the spectrographic results s = net standard deviation as given in the table sc = standard deviation of chemical results
a,
As an example of the interpretation of the data on the basis of the foregoing principles, let us take as an example one of the groups of data on Magnesium in Table I. The following statistics arc given for the group selected: Number of determinations cornpared Average yo M g b y chemical method Standard deviation Spectrographic saib Probability of significance of bias
ll1U 1 48 0 021 f 0 011 0.90997
Making the assumption of normal distribution, a standard deviation of 0.021 means t,hat the random discrepancies between spectrographic and chemical analyses are 0.021 or less in 67%. of cases and 0.042 or less in 95% of cases. The precision with which the standard deviation has been determined is measured by its own st>andarddeviation, sa, calculated from Formula 11. SI =
0’02’ = 0.00045 v ’ 2 x 1110
On the average, 67% of the observed standard deviations will fall within s8 and 95% within 2s, of the true standard deviation. In this isolated case, we may say, therefore, that there is a 67y0 chance that the observed standard deviation lies within 0.00045 of 0.021 and a 95% chance that it lies within 0.0009 of 0.021. The bias of +0.011 indicates that, on the average, the spectrographic results tend to be 0.011 higher than the chemical results. The accuracy of this conclusion is measured by the standard error, 82, obtained by applying Formula 111. sd=
0.021 --= \I1110
0.00063
The odds are 2 to 1 that the true bias (the bias for an infinite number of samples) is within t0.0006 of the observed value of +0.011, and 19 to 1 that it is within *0.0013 of +0.011. To test the significance of this bias further, “Students’ t Test” is applied. From Formula IV we obtain
753 d L =-
=
17.5
Sd
Referring to standard t tables, we find that the chances of obtaining an apparent bias of +0.011 or more when no true bias exists is less than 1 in a 1,000,000,000 in this particular,case. The probability of significance of the bias is, therefore, far in excess of 0.9999 and is simply reported a s 0.9999$: in the table. The authors, therefore, regard it as a virtual certainty that there is a real difference between spectrographic and chqmical results. Had the probability been less than 0.9999, a graphical interpolation mould have been required to determine its value. The example selected happens to represent the magnesium analyses obtained on a particular type of alloy, using a particular spectrographic standard. Using this standard to analyze a sample of this same alloy having a chemically determined magnesium content of 1.48%, and taking both the standard deviation and average bias into consideration, we may say that the odds are 2 to 1 that the spectrographic result will lie between 1.470 and 1.512%, and 19 to 1that it will lie between 1.449 and 1.533%. Moreover, we have determined the accuracy with which the standard deviation and average bias have been determined, and have evaluated the probability of the average bias representing a real differencebetween the two methods. If data were available for estimating the standard deviation of the chemical results and their average bias with respect to true content, we could go even further with the interpretation by the application of Formulas V and VI. In the absence of such data, our spect’rographic data can only be compared wit,h chemical data, and our direct int’erpretation tends to give a conservative picture of the precision of spectrographic analysis. In the analysis of many alloys, statistical data have been especially valuable in checking the performance of standards. In the analysis of many fabrication alloys, a special type of standard, known as an “SS”standard, is used. “SS”standards are prepared in large quantities and are the daily check standards used in a large number of laboratories. Whed a new standard of the “SS” type is first put into service, all the laboratories using the standard submit comparative spectrographic and chemical data, These data are carefully analyzed and any apparent bias is carefully investigated to determine whether the systematic error lies in thr chemical or in the spectrographic analysis. In most cases the effect is found to bc attributable to the spectrographic bchavior of the standard, and a compensating change is made in t’he composition assigned to the standard. The application of such corrections has usually resulted in the reduction of the bias to insignificance in the. case of the alloys for which “SS” standards are available. Similar corrective measures are taken whenever the statistical studies warrant, but, the effectiveness of such bias corrections diminishes as the total quantity of the standard, and hence of the statistical data, is reduced. I n all cases, however, the statistical studies provide an excellent check on the performance of the standards and the proper execution of the spectrographic techniques. It is interesting to note that copper analyses on some alloys show rather high biases and standard deviations. .4 portion of this effect is ascribable to the fact that the concentration to be determined is rather high, but a large part of the excessive error is caused by the fact that some plant laboratories do not regularly make this determination spectrographically. Up to the present, copper in the neighborhood of 47, has not been determined spcctrographically on certain alloys because the results obt,ained i l l preliminary tests were not completely satisfactory. Since tht, determination has not been run on a routine basis, the laboratories have little significant experience t o produce data to improve the quality of results. Horvever, there are included in the table data on a complicated alloy in which copper is regularly dctermined spectrographically. On this alloy the standard deviation was only 0.081 as compared to 0.145, 0,155, and 0.186 for the three other groups representing similar copper contents in other alloys. The divergence of these standard deviations is caused not
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
754
by any inherent differencein the copper determination among the four alloys, but rather by the simple fact that the alloy for which the very satisfactory standard deviation of 0.081 was obtained is one which is regularly analyzed spectrographically on a largescale routine basis, while the other three alloys are normally anatyzed chemically with only an occasional spectrographic analysis as a high-speed service to the metallurgical staff. The results on some alloys are indicative of specific difficulties. For example, in some cases being analyzed, the complexity of the alloy, its tcndency to show serious segregation, and the apparently large effects of variations in structure and composition tend t o make the spectrographic analyses more variable than one would expect for the contents involved. I n actual plant laboratory practice, these variations are ironed out to a large extent by making multiple determinations and averaging the results. For example, the spectrographic determination of silicon of 11.70’% average concentration does not show the precision required in many laboratories. The low bias suggests that the average of quadruplicates might provide acceptable accuracy. I n general, the statistics indicate that analyses regularly made spectrographically are of consistently high quality. The magnitude of the standard deviations and biases isin general no higher than would be expected had the comparisons been made among chemical analyses made by different routine analysts.
Determination
OF
Vol. 17, No. 12
ACKNOWLEDGMENT
The authors particularly desire to acknowledge gratitude to the chief chemists of plant laboratories of Aluminum Company of America and their staffs who provided the data upon which the study is based. They further gratefully acknowledge their appreciation of the services of G. P. Koch, J. E. Van Dien, and Jean Artman, all members of the staff of the iinalytical Division of Aluminum Research Laboratories, who assembled the data and made the necessary calculations. LITERATURE CITED
(1) Churchill, H. V., and Bridges, R. W., ‘Chemical Analysis of
Aluminum”, New Kensington, Pa., Aluminum Research Laboratories, 1941. (2) Churchill, J. R., IND.ENG.CHEM.,ANAL.ED.,16, 653-70 (1944). (3) Fisher, R. A.. “Statistical Methods for Research Workers”, London, Oliver and Boyd, Ltd., 1941. (4) Fisher, R. A , , and Yates, Frank, “Statistical Tables for Biological, Agricultural, and Medical Research”, London, Oliver and Boyd, Ltd., 1943. ( 5 ) Freeman, H. A., “Industrial Statistics”, New York, John Wiley & Sons, 1942. (6) MacColl, H. G., ChemistryandIndustry, No.49,418-21 (1944). (7) Mandel, John, IND.ENG.CHEM.,AXAL.ED.,17, 201-6 (1945). ( 8 ) Shewhart, W. A , , “Economic Control of QuaIity of Manufactured Product”, New York, D. Van Nostrand Co., 1931.
Ascorbic A c i d
Application of the Indophenol-Xylene Extraction Method to Determination .in Large Numbers of Tomato and Tomato Juice Samples ’1
School
WALTER L. NELSON AND G. FRED SOMERS of Nutrition, Cornell University, and U. S. Plant, Soil and Nutrition Laboratory, U. S. Department of Agriculture, lthaca, N. Y.
The xylene method, as modified for rapid determination of ascorbic acid in tomatoes and tomato juice, i s particularly adaptable to the determination of large numbers of samples and can be handled with accuracy b y comparatively inexperienced technicians. The difficulties involved in the choice of extractant, clarification of extracts, choice of buffer, ascorbic acid losses following addition of buffer, and oxidizing substances in xylene are described, and methods of avoiding these difficulties are given.
IN
PREVIOUS investigations of the ascorbic acid content of plant materials a titrimetric method (6, 7 ) was used in these lahoratories. In the hands of an experienced operator this method was satisfactory and gave values which were in agreement with the photometric method of Bessey (1, 15). Critical evaluations of the titrimetric method have been presented by various workers (8, 9, 11). Since it requires experienced technicians, the authors have recently replaced it with the xylene method (3, 4, 17, 18) which is more objective, gives good results in the hands of comparatively inexperienced technicians, and hence is more suitable for largescale routine analyses. This paper gives a brief description of the xylene method as adapted for analysis of large numbers of tomato and tomato juice samples, the various difficulties encountered, and the precautions which are necessary to avoid them. REAGENTS
ACETATEBUFFER. Dissolve 500 grams of
C.P. sodium acetate trihydrate in enough distilled water to make 1 liter of solution; then mix with 1liter of C.P. glacial acetic acid. ASCORBICACID STANDARD.Prepare daily by dissolving a weighed amount of the vitamin in some of the acid which is used
for extracting the samples. A solution which contains 20 micrograms per ml. is convenient, and 1- to 7-ml. aliquots of such a solution can bc used. The ascorbic acid can be titrated iodometrically ( 2 ) to test its purity. XYLENE. Use C.P. or reagent grade, providing it meets the test for oxidizing substances (see below). Redistill from glass if oxidizing substances are present. 2,6-DICHLOROPHENOLINDOPHENOL SOLUTION. Prepare by dissolving 40 mg. of the crystals in hot water, filter, cool, and dilute to 100 ml. Store this concentrated solution in the cold room a t 3” t o 5’ C., and dilute about 15 ml. t o 100 ml. before use. Use enough of the concentrated dye so that when a 5-ml. aliquot of the diluted dye is mixed with 2 ml. of the buffer and 5 ml. of the extracting acid and then is transferred t o 15 ml. of xylene, the xylene solution gives 30% transmission in the Evelyn colorimeter with filter 520. M E T H O D AND A P P A R A T U S
The extract is prepared and filtered essentially as described by Morel1 (16). The first portion of the filtrate is poured back through the fdter if it is not perfectly clear. An aliquot of from 1 to 10 ml. of the filtrate, depending on the ascorbic acid concentration, is pipetted into a large test tube, and about 2 ml. of the acetate buffer, followed immediately by 5 ml. of the dye, are added from automatic pipets. The solution is mixed thoroughly, but briefly, after each addition. After about 15 seconds, 15 ml. of xylene are added from another automatic pipet, and the tube is stoppered with a rubber stopper and shaken vigorously for 10 to 15 seconds. The xylene layer is drawn through a cotton plug into a colorimeter tube by means of the apparatus illustrated in Figure 1. This solution is read in an Evelyn colorimeter with filter 520 or 515. The use of a rubber stopper has no harmful effect on the xylene solution. However, it is necessary t o avoid rubber connections on the automatic pipets by using glass siphons for filling them. It is essential to allow about 15 seconds for the reaction with the dye, because even with moderate amounts of ascorbic acid the reaction is not, completed in less time (10).
