ANALYTICAL CHEMISTRY Marion, L., Lavigne, R . , and Lemay. L., Can. J . Chem., 29, 347-51 (1951).
Markham, R., and Smith, J. D., Nature, 168, 406-8 (1951). Meister, A., Soher, H., and Tice, S., J . Bid. Chem.. 189, 577-90 (1951).
RPitsushima, S., Shimanouchi, R., and Sugita, T., Mikrochemie per. Mikrochim. Acta, 36/37, 573-5 (1950). Mowery, D. P., J . Am. Chem. Soc., 73, 5047 (1951). Selson, L. S., and Laskowski, D. E., ANAL.CHEM.,23, 1495 (1951).
O’Connor, R. T., Field, E. T., and Singleton, W. S., J . Am. Oil Chemists’ SOC., 28, 1 5 P 6 0 (1951). Okumrt, S., J . J a p a n . Chem., 4, 622-9 (1950). Pardee, A. B., J . Biol. Chem., 190, 757 (1951). Parke, T. V., Ribley, A. M., Kennedy, E. E., and Hilty, W. W., ANAL.CHEM.,23, 953 (1951). Partridge, M. W., and Chilton, J., Nature, 167, 79-80 (1951). Pasternack, R., Bavley, A., Hess, G. B., and Conover, L. H., Abstracts of Papers, X I I t h International Congress of Pure and Applied Chemistry, Kew York, Sept. 10-13, 1951, p. 281.
Peck, R. L., ANAL.CHEM.,22, 121 (1950). Ihid., 23, 97 (1951). Peck, R. L., Wolf, D. E., and Folkers, K., J . Am. Chem. SOC.,in press. Perry, J. A,, A N ~ LCHEM,, . 23, 495-7 (1951). Pew, J. C., J . Am. Chem. SOC.,73, 1678-85 (1951). Ritter, D. M., Ihid., 73, 255&3 (1951). Roberts, J. D., and Chambers, V. C., Ibid., 73, 5030 (1951). Rock, S. M., ANAL.CHEM.,23, 261 (1951). Sakaguchi, S., J . Biochem. ( J a p a n ) , 38, 91 (1951). Sanger, F., Abstracts of Papers, 120th Meeting AM. CHEM.SOC., Kew York, 1951, p. 2Q. Schoniger, W., 2.anal. Chem., 133, 4 (1951). Siggia, S., ANAL.CHEM.,23, 667 (1951).
(76) Siggia, S., Hanna, J. G., and Kervenski, I. R., Ibad., 22, 1295-7 (1950). (77) Smith, F., J . Chem. Soc., 1944, 633. (78) Snell, E. E., Brown, G. M., Peters, V. J., Craig, J. A , Wittle, E. L., Moore, J. A., McGlohon, V. -M., and Bird, 0. D.. J . Am. Chem. Soc., 72, 5349 (1950). (79) Sobotka, M., Mikrochemie Der. Mikrochim. Acta, 36/37, 408-12 (1951).
(80) Southern, A. L., Morgan, H. W.,Keilholtz, G. W.. and Smith, W.V., ANAL.CHEM.,23, 1000 (1951) (81) Spies, J. R., and Chambers, D. C., J . B i d . Chem., 191, 787 (195 1).
Svensson, H., and Brattsten, I., A r k i t K e m i , 1, 401 (1949). Taylor, G. B., and Hall, hI. B., ANAL. CHEX.,23, 947 (3951). Thompson, A. R., Nature, 168, 390-1 (1951). Tomicek, O., Blasek, 9., and Roubal, Z., Chem. & e s t ? , 4, 479
(82) (83) (84) (85)
(1950). (86) Trenner, N. R., Walker, R. W., Arison, B., and Trumbauer, C., ANAL.CHEM.,23, 487-90 (1951). (87) Udenfriend, S., and Velick, S.F., J . B i d . Chem., 190, 733-40 (1951). (88) Vacher, M., Mikrochemie vet. Milzrochim. Acta, 36/37, 330-48 (195 1). (89) Velick, S. F., and Udenfriend, S.,J . Bid. Chem., 190, 721 (1951). (90) Vellus, L., and Pesez, M., Bull. soc. chim. France, 1950, 868-70. (91) Verzele. hI., and Govaert, F., Bull. SOC. chim. Belg., 58, 432 (1949). (92) Viebel, s., B N A L . CHEM., 23, 665 (1951). (93) Wieland, H., Be?., 58, 102 (1925). (94) Wieland, H., and Marts, E., Ibid., 59, 2352 (1926). (95) Wolfrom, M., Montgomery, R., Karabinos, J., and Rathgelo, P., J . Am. Chem. Soc., 72, 5796-7 (1950). (96) Wollmer, W.,Ber., 58, 672 (1925). RECEIVED Korember 23, 1951.
EXPERIMENTAL STATISTICS’ R. J. H A D E R Institute of Statistics, .V. C . State College, Raleigh, N . C .
W. J. Y O U D E N National Bureau of Standards, Washington, D . C.
T
HE utility of modern statistical techniques for handling experimental data continues t o be increasing13 appreciated by research workers in the physical sciences. The literature grows exponentially. Literally, hundreds of articles on statistics have appeared since the earlier review on this subject by Wernimont (January 1949) (196). Only a modest fraction of these has been included here, I n making a selection the authors have taken the position that, by and large, this revien is intended to seive those having, a t most, a nodding acquaintance with statistical methods. Consequently, they have leaned heavily on expository articles, trving especially to pick those 1% ith a predominantly chemical flavor. More advanced and purely technical articles have been purposely omitted, a s i t was felt t h a t a relatively small group would be interested in such papers. PIIost of these people will already be well acquainted with the statistical periodicals and, consequently, will have much less need for a review of the type given here. On the other hand, they have also omitted a large class of papers in which statistical methods have been used to analyze experimental data, b u t in which the emphasis has not been primarily on these techniques as such. Though these articles could not be included, i t was indeed gratifying to find such widespread use of the various statistical tools.
cards, from among a h i c h the majority of selections F-ere eventually made. Several other statistical bibliographies should be called to the readers’ attention. The first of these is the very recent Wiley publication edited by Buros (18). This consists of reviews of 342 statistical methodology books and pamphlets written in the 10-year period indicated. Buros’ book, plus the book review section of the Journal of the Amerzcan Statistical Asson’atim, provides a fairly complete coverage of the nonperiodical literature. I n the field of quality control Butterbaugh’s “Bibliography of Quality Control Literature” (1946) (21) and its Supplement (1951) (22) are most comprehensive. A running bibliography in Industrial Quality Control covers the period from 1949 to date. So far as is known to the authors, these represent the principal bibliographical sources likely t o be useful to chemists and other physical scientists. BOOKS
Theory. Several books are devoted primarily t o statistical and/or probability theory (24,48,59,92,97 131). Methodology. Books in this group are devoted either entirely to techniques or to a combination of theory and practice (3,14, 18, 22, 27, 34, 40, 69-66, 60, 77, 84, 96, 103, 105, 192, 123, 126, 126,1b9,139,141,151,154).
OTHER BIBLlOGRAPHIES
This review is intended as a continuation of Wernimont’s article (135). Wernimont also deserves a large measure of credit for his assistance on this paper. H e furnished a set of some 300 reference
PRECISION, ACCURACY, .4ND RESOLUTION OF ERRORS
I n this section are included articles on precision, accuracy, and 25, 28, 36,62, 64, 68, 71,81, 90, 119, 121, closely related topics (4,
V O L U M E 24, NO. 1, J A N U A R Y 1 9 5 2 1 2 7 , 1 3 4 , 1 3 7 , 1 ~ 8 , 1 4 4 , 1 4 5 , 1 ~ 0 , 1 ~ &In J ~the ~ ~past ) . twoor three years there has been a considerable upsurge of interest among statisticians in the subject of “components of variance.” In chemical applications the term “resolution of errors” is perhaps more appropriate. This subject is concerned with the estimation of the relative importance of different sources of variability contributing t o the over-all errors. An esample of hoiv much can bc accomplished in this direction is given by Weybrew, Matrone, and Basley (137), though unfortunately the calculations are not shown. An important phase of the variance components problem is t h a t of separation of errors of measurement and inherent product variability when repeated measurements on the same item are mot possible-e.g., destructive tests. To achieve this separation, it is necessary to be able t o make simultaneous observations with two or more measuring devices. T h e papers of Grubbs, Smith, and \Yhitwell discuss this technique ( ? l ,119, 138). CURVE FITTING
Relatively few research workers in the physical sciences are awai’e of the elaborate and powerful theory t h a t has been developed in connection with curve fitting. Substitution of objective criteria (principally t h a t of least squares) for rule of thumb procedures has been merely the first step. Use of fitted curves to predict future values of a dependent variable gave rise t o techniques for evaluating the expected errors of such predictions. \\.hen basic structural relationships are being estimated we need some measure of the reliability of our estimates. Confidence intervals for parameters in such relationships have been found. T h e curve fitting techniques have been generalized t o include several independent variables simultaneously. Statisticians often refer t o this whole subjpct as ,‘regi,ession.” For elementary espositions, the Brownlee anti Olds papers are suggested (6, 9, I S , 52, 43, 7 4 , 101,107, 130). DESIGN OF EXPERIMENTS
In :ill probability, the most important contribution that, statisticians have to make to the advancement of science is in the field of experimental design. l l a n y phases of this subject are nothing more than the eserriye of a good measure of common sense in the planning stagr of a 1,esearch program. Decisions must he made on the size and scope of the program, the factors t o he investigated, arid the type of data to be gathered. One must carefully consider what questions the esperiment will be capable of ansITering. H e must be sure the factors being investigated do not become confounded with earh other or with some estraneous variable. H e must make an effort to get precise and accurate mensurements. Inderd, it is usually advisable to have a method for estimating precision built into the experiment. Design of esperiments, however, goes considerably beyond these basic considerations. Having done n-hat one can to remove estraneous sources of variation niid to make measurements as precise as possible, one can frequentlj- decrease the effective experimental error dramatically by the application of ingenious arrangements within the experimental program. A considerable variety of such arrangements (designs) has been worked o u t in the fields of agriculture and biology. l l a n y of these can be carried out equally well in the chemistry laboratory. Systematic methods of statistical analysis (analysis of variance and covariance) are available for these designs. So-called factorial experimentation is particularly being emphasized in the literature. I n investigating the effects of several factors, say time of reaction, temperature, concentration, etc., on a process, the traditional approach has been t o vary one factor a t a time, the others being temporarily held constant,. The modern approach is t o investigate all possible combinations of the various levels of the factors. Its principal advantage is in the detection of so-called interaction effects. I n many cases, a n investigation involving all possible combinations would be prohibitively large; however, there now exist systems of constructing so-called “frac-
121 tional factorials” in which the numbei of combinations is drastically reduced Fvithout sacrificing anj- important information (5, 27, 3 6 , 50,66, 7 6 , 88, 100, 104,106, 111, 133, 148).
T h e statistical techniques useful in bioassay work are set forth in some detail in Finney’s book ( 5 3 ) . In addition several recent contributions to the periodical literature are listed ( 7 , 15, 16, 4 1 , 51-53, 65, 83, 91 ). The authors would like especially to call attention to the usefulness of many of these techniques in fields considerably removed from bioassay-e.g., in the testing of sensitivity of explosives, in plastics life tests, etc. The characteristic feature of data amenable to treatment by these methods is t h a t the response of each individual specimen to a given stimulus is measured only as being either positive or negative, the outcome in each case depending on whether or not the stimulus excreds an unknown threshold value for the specimen.
.
TEACHING O F STATISTICS
An increasing amount of attention is being given to the problem of providing formal statistical training for the student in engineering and the physical sciences (45,67, 102, 117, 120, 142). The authors, and many of their colleagues, take the position t h a t eventually a sequence of courses in modern statistical concepts and methodology will b r regarded as indispensable in the curriculum, as are the basic mathenlatics courses a t present. They feel the objective should be a generation of statistically minded engineers and physical science research workers, rather than a large group of professional statisticians. QUALITY CONTROL
The subject of quality control has enjoyed aphenomenalgrowth since the early war years (1,3, 8, 12, 19, 21, 22, 29, 68, 6 1 , 63, 80, 82, .98, 103, 108, 110, 114, 116, 126, 128, 136). It is one of the simplest, )-et most useful of all the statistical techniques. Though not restricted t o large scale manufacturing operations, it has thus far found the hulk of its applications in this connection. Basically, ststistical quality control consists of keeping a graphical record of some qualit>- indes. On this so-called “control chart” are drawn certain ”control liniits” ivhose function it is to call attention to abnormal quality variations. \\’hen properly placed, these limits malie the distinction between quality variations inherent in the manufacturing technique and variability which calls for corrective action. The place of the control chai~ttechnique iii research investigations has, thus far, received all too little attention. Almost 311 of the common statistical techniques are based on the tacit assumption t h a t the data can he treated as a random sample from a stable probability distribution. Control charts provide a simple method of checking on this assumption. I t is frequently the case particularly Jvhen the data have been gathered over a period of several days, t h a t the assumption of stability becomes untenable. An escellent discussion of this subject is given by Shewhart (114). This reference appeared in the Kernimont reviev, b u t is worth repeating here, hIISCELLANEOUS
I n this review, the authors have attempt,ed to give separate lists of articles for several special topics within the general field of stat’istics. They hope t h a t this has been a convenience. The remaining papers are included in this miscellaneous category ( 1 , 7 , 10, 11! 17, 20, 25, 26, 30, 31, 33,37-39,42?, 44,46, 47, 49,67, 69, 70, 72, 7 S , 75, 78, 79, 85-87, 89, 93-95, 99, 109, 112, 11S , 115, 118, 124, 1 5 2 , 1 3 5 , 1 ~ 0 , 1 4 S146, , 247, 149). They cover a very wide variety of subjects, as is evident from their titles. In some instances, individual papers deal with as many as four or five different techniques. Finall)-, the authors xould like to single o u t for special com-
122
ANALYTICAL CHEMISTRY
mendation the publication of statistical syniposia in various periodicals. Several very fine examples of these have appeared rein Industrial a n d E n g i n e e r i n g cently in h . 4 L Y T I C A L CHEMISTRY, Chemistry, in the P r o c e e d m g s of A S T M , and in the A n n a l s of the h'ew Y o r k A c a d e m y of Sciences. This technique is believed to be one of the best available for arousing interest in statistics on a really large scale. LITERATURE CITED
(1) Adams, C. H., I n d . Qual. Control, 7, No. 4, 17 (1951).
Appliration of Statistical Techniques to Physical Testing of Plastics. (2) .im. Soc. Qual. Control, 5th Annual Convention (1951). Conference Papers. (3) Am. Soc. Testing Materials, Special Tech. Pub. 15C (1951). 4 S T M Manual on Quality Control of Materials. (4) .krchibald, R. M., d x . 4 ~ .CHEM.,22, 639 (1950). Critei ia of AAnalyticalMethods for Clinical Chemistry. (5) Bainbridge, J. R., I n d . E n g . Chem., 43, 1300 (1951). Fartoi,ial Experiments in Pilot Plant Studies. (6) Bartlett 11.S.,Biometrics, 5, 207 (1949). Fitting a Straight Line *-hen Both Variables Are Subject to Error. (7) Beer, E. J. de, Ann. S. Y . Acad. Sci., 52, 789 (1950). Place of Statistical Methods in Biological and Chemical Experimentation. (8) Bennett, C. .A,, I n d . Eng. Chem., 43, 2053 (1951). Application of Tests for Randomness. (9) Berkson, J., J . A m . Stat. Assoc., 45, 164 (1950). Are There Two Regressions? (10) Bicking. C. A , , P u l p and P a p e r , 49, 181 (1948). Industrial Statistics. Their Place in Manufacture of Pulp and Paper. (11) Box, G. E. P., Biometrics, 6, 362 (1950). Problems in Analisis of Growth and Xear Curves. (12) Brownlee, K. -4., I n d . E n g . Chem., 43, 1307 (1951). Consti.uction and Use of Statistical Control Charts on Continuous Variables. (13) Ihid., p. 2053. ' Correlation Methods Applied to Production Data. (14) Brownlee, K. .A,, "Industrial Experimentation," 3rd American ed., Brooklyn, 5 . Y., Chemical Publishing Co., 1949. (15) Brownlee, K . A . . Delves, C. S., Dorman, If.,Green, C. A., Grenfell, E., Johnson, J. D. A , and Smith, S . , J . Grii. M i crobiol., 2 , 40 (1948). Biological Assay of Streptomycin hy a Modified Cylinder Plate Method. (16) Brownlee, K. A.. Loraine, P. K., and Stephens, J., Ibid.. 3, 347 (1949). Biological dssay of Penicillin by a Modified Plate Method. (17) Brumbaugh, M. A., and Koel, R. H., I n d . Qu,al. Control., 7, N o . 2, 7 (1950). Applications of Statistics to Drug llanufacture. (18) Buros, 0. K., "Statistical Methodology Reviews 1941-1950." New York, John \Tiley & Sons, 1951. and Tl-eaver. W.R.. Ind. Oual. Control. 5. KO. (19) ~, Burr. I. W.. 5, 10 ~(1949). Stratification Control Charts. (20) Buslik, David, A S T M Bull., 165, 92 (1950). Mixing and Sampling with Special Reference to Multi-Sized Granular Materials. (21) Butterbaugh, G., Bibliography of Statistical Quality Control Literature, Seattle, University of Washington Press, 1946. (22) Ihid., Supplement (1951). (23) Cameron, J. bl., Biometrics, 7, 83 (1951). Use of Components of Variance in Preparing Schedules for Sampling of Baled Wool. (24) Churchman, C. W., "Theory of Experimental Inference," Xew York. Macmillan Co., 1948. (25) Clarke, B . L., Chem. Eng. News, 27, 1426 (1949). Statistical Methods in the Chemical Industry. (26) Cochran, W. G., Biometrics, 6, 105 (1950). Estimation of Bacterial Densities by Means of the Most Probable Sumber. (27) Cochran, K.G., and Cox. G. AI., "Experimental Designs," New York, John Wiley Bi Sons, 1950. (28) Coleman, R. D.. Thompson, J. B., and Branum, Ira, .%SAL. CHEM.,20, 365 (1948). Trace Metal Determination in Fats with Special Reference to Copper in Milk Fat. (29) Cornell, G. N., Chem. I n d s . , 64, 568 (1949). Case Study of How Statistical Control Expedites Chemical Operations. (30) Craig, .I.T., Ind. Qual. Control, 7, No. 5, 36 (1951). Confidence Intervals. (31) Dallavalle, J. M., Orr, C., and Blocker, H. G., I n d . Eng. Chena., 43, 1377 (1951 ). Fitting Bimodal Particle Size Distribution Cnrws. - . ._ ~ ~ (32) Daniel, C., Ihid., 43, 1298 (1951). Design of Experiments for Most Precise Slope Estimation. (33) Daridson, J. H., ANAL.CHEM.,20, 1132 (1948). Statistical Test of Significance. (34) Davies, 0. L., "Statistical Methods in Research and Production ,
I
with Special Reference to the Chemical Industry," London, Oliver and Boyd, 1949. (35) Davies, 0 . L., Giles, C. H., and Vickerstaff. T., J . 8oc. Duers Colourists, 63, 80 (1947). Accuracy of Colorimetric Instruments in Dye Strength Determinations. (36) Davies, 0 . L., and Hay, IT. A , Biometrics, 6 , 233 (1950). Construction and Uses of Fractional Factorial Designs in Industrial Research. (37) Dean, R. B., and Dixon, W.J., ANAL.CHEM.,23, 636 (1951). Simplified Statistics for Small Numbers of Observations. (38) Deming, W,E., and Tanner, L., A m . SOC.Testing Materiuls, Proc., 1949, 1181. Some Problems in Sampling of Bulk hlaterials. (39) Dixori, W.J., Ann. M a t h . Stat.. 21, 488 (1950). .halysis of Extreme Values. (40) Dixon, W.J.. and Rfassey. F. J., "Introduction to Statistical Analysis," New T o r k , RlcGraw-Hill Book Co., 1951. (41) Dixon, W.J., and Mood. .A. AI., J . A m . Stat. Assoc.. 43, 109 (1951). Method for Obtaining and dnalyzing Sensitivity Data. (42) Edinoff, hI. L., Aiv.4~.CHEX.,22,529 (1950). Measurement of Radiocarbon as Carbon Dioxide inside Geiger-Muller Couiiters. (43) Eisenhart, C., Ann. M a t h . Stat.. 10, 162 (1939). Interpretation of Certain Regression Methods and Their Use in Biological and Industrial Research. (44) Eliassen, Rolf, Biometrics, 6, 1 1 T (1950). Statistical lnalysis in Sanitary Engineering Laboratory Studies. 145) Elving, P. J.. and ;\Tellon, M .G., ;1xar.. CHEU.,20, 1140 (1948). Teaching Students How to Evaluate Data. 146) Epstein, B., Ann. M a t h . Stat., 1, 99 (1949). Modified Extreme Value Problem. 147) Epstein, B., J . Am. Stat. Assoc.. 43, 403 (1918). dpplication of Theory of Extreme Values in Fracture Problems. (48) Feller, William, "Introduction to Probability Theory and Its Applications," New York, John Wiley d Sons, 1950. 149) Fertig. J. IT., and Heller, .A. S . , Biometrics, 6 , 127 (1950). .-\pplication of Statistical Techniques to Sewage Treatment Processes. (50) Fevell, A. J., and Wagg. R. E., Restnrch, 2, 334 (1949). Statistical Methods in Detergency Investigations. (51) Fieller, E. C.. Annlgst, 72, 37 (1947). Statistical Background in Bio-.hay. (52) Finney, D. J.. Biometrics. 5 , 261 (1949). Choice of a Response Netameter in Bioassay. (53j Finney, D. J., "Probit Analysis: h Statistical Treatment of the Sigmoid Response Curve," London, Cambridge L-nirersity Press, 1947. (54) Fisher, R. d.,"Design of Experiments," London Olirer and Boyd, 1949. "Statistical Methods foi Research Workers," (55) Fisher, R. il., London, Oliver and Boyd, 1950. (56) Fisher, R. A., and Yates, Frank, "Statistical Tables for Biological, Agricultural and Sfedical Research," New York, Hafner Publishing Co., 1949. (57) Fizzel, J. .4., I n d . Qual. Control, 4, 50.4, 22 (1948). Let's T1.y Analysis of Variance. (58) Fortune, 40, No. 6 , 161 (1949). Statistical Quality Control. (59) Freedman, Paul, "Principles of Scientific Research." Washington, D. C., Public Affairs Press. 1950. (60) Freeman, H . A , , "Industrial Statistics," S e w York. John JTiley & Sons, 1946. (61) Gause, G. R., Am. Soc. Testing Materials, Proc., 48, 886 (1948). Amount of Inspection as a Function of Control of Quality. (62) Genung, L. B., A s a ~CHEM., . 22, 401 (1950). Analysis of Cellulose Derivatives. (63) Girschig, R.. Congr. groupe, nmnce. methodes anal. spectrograph., produits metal., 10, 159 (1948). Statistical Fluctuations in Spectrographic Analysis. 164) Girschig, R., Rev. mdt., 46, 719 (1949). .Application of Methods of Statistical Control to Spectrographic Analysis. (65) Gore, IT. L., AXAL.CHEM.,22, 684 (1950). Analysis of Data. on Plastics Life Tests. (66) Gore, IT. L., Znd. Eng. Chena., 42, 320 11950). Statistical Procedures in Chemical Investigations. (67) Gore, IT. L., J . Chem. Education, 27,419 (1950). S e w Educational Requirements in Etperimental Methods. (68) Greenwood, J. .A,, and Sandomire, RI. AI., J . Am. Stat. dssoc., 45,257 (1950). Sample Size Required for Estimating Standard Deviation as a Per Cent of Its True Value. (69) Griffith, B. A , Westman, A. E. R., and Lloyd, B. H., I n d . Qual. Control, 4, KO.5, 20 (1948). Analysis of T-ariance. (70) Grubbs, F. E.. Ann. X o t h . Stat., 21, 1, 2 i (1950). Sample Criteria for Testing Outlying Observations. (71) Grubbs, F. E.. J . Am. Stat. Assoc., 43 243 (1948). Estimating Precision of lleasuring Instrunients and Product Variability.
V O L U M E 24, N O . 1, J A N U A R Y 1 9 5 2 G.,and Mood, .A. M.,J . A m . Stat. 43, 243, 391 (1948). Determination of Sample Sizes in Designing Experiments. ( 7 3 ) Harrison, S., and Elder, L. IT,,Food Technol., 4, 434 (1950). Applications of Statistics to Laboratory Taste Testing. (74) Hausner. G. W., and Hrennan, J. F., Ann. M a t h . Stat., 19, 380 (1948). Estimation of Linear Trends. ( 7 8 ) Hill, R. JV., Cook, G. 8.. and Moyer, W.E., A S T M B u l l . , 164, 32 i 1950). Correlation of .Accelerated Weathering Machines. (71:) Hintermaier, J. C., .ks.u,. CHEM.,20, 1144 (1948). Foundations for Exuerinientai Design. ( 7 7 ) llogben I , , “Chance and C‘hoire by C a d p a c k and Chesshoard,” S e w Yolk, (‘hatititleer Piess, 1950. ( 7 8 ) Holler, A C., A S T M Bull., 174, 66 (1951) Sampling of 1;eti’ous and Sonferrous Alloys. (79) Hopkins. J. IT., C a n . J . Research, 24. 203 (1946). Precision of .-\ssessment of Palatability of Food Stuffs by Laboratory Panels. c30) Howell, J. RI., A n n . M a t h . S t a t . , 20, 305 (1949). Control (’hart for Largest and Smallest Values. ( X I ) IIuhnforfT. R. F., Z n d . Eng. C‘hem., 41, 1300 (1949). Statistical Pro:edures Applied to a Pilot Cnit. Reproducibility Study. (821 T n d . Qual. Control, 6 , No. 5, 11 (1950) (ASQC Committee Report). Proposed Standard Definitions and Symbols for (‘ontrol (:harts. (83) .Jwrle. K.K.. and TVood, E;. C , , Biomctrics, 5, 273 (1949). Validity and Meaning of Results of Biological Assays. (84).Tohiison. P. 0.. “Statistical Methods in Research,” Kew Sork, Prentice-Hall, 1949. 185) Kennedy, 17. R., I d . Qual. Control, 7, No. 5, 24 (1951). Legal .\spects of Sampling. 1 8 ( i ) Kohman, T. P., ANAL.CHEM.,21, 352 (1949). Measurement Techniques of AAppliedRadiochemistry. ( 8 7 ) Kottler, F., J . F r a n k l i n Inat., 250, 339, 419 (1950). Distribution of Particle Sizes. Facts. Probability Graphs. (8X) lIandel, J.. J . Chem. Education, 26, 534 (1949). Statistical llethods in bnalytiral Chemistry. ( 5 : ) ) lfandel, J., and Marin, C. IT.,.I. Research S a t l . B u r . Standards, 46, 99 (1951). Statistical Solution of a Problem Arising in Sampling of Leather. (90) Sfarcuse, Sophie, B i o m d r i c s . 5, 189 (1949). Optimum Allocation and Variance Coniponents in Nested Sampling with ApIdication to Chemical Analysis. iH1j llather, K., Ihid., 5, 127 (1949). .Analysis of Extinction Time Data in Bioassay. (9.’) )food, d. XI., “Introduction to Theory of Statistics.” Senl-ork, RlrGraw-Hill Book Co., 1950. (03) llosteller, F., I n d . Eng. C h m . , 43, 1295 (1951). Theoretical Hackgrounds of Statistical .\lethods Underlying Probability 1IodeI r s e d in Slaking a Statistical Inference. (04) Mosteller, F.,J.Am. Stnt.Sssuc.,43,231 (1948). PoolingData. (95) Slosteller, F., and Tukey, J. TY.,Ihid., 44, 174 (1949). Uses mid Usefulness of Binomial Probability Paper. (96) S a t l . Bur. Standards, Applied Llatheniatirs Series 6, “Tables of Binomial Probahility Distribution” (1949). (97) Xeyinan, J., “Fii st Course in Probability and Statistics,” Boston, Henry Holt and Co., 1950. (OS) Soel. R . H., I n d . Qual. Control, 7, KO.2, 14 (1950). Statistical Quality Control in Manufacture of Pharmaceuticals. (99) Soel, R. H.. and Brumbaugh, &I. A , I b i d . , 7, No. 2, 7 (1950). .Applications of Statistics to Drug Manufacture. (100) Ogg, C. L., Willits, C . O., Ricciuti, Constantine, and Connelly, .J, A.. ANAL.CHEY.,23, 911 (1951). Microdetermination of C‘arbon and Hydrogen. Statistical Study of Factors. (101) Olds, E. G., and Actori, F. S.,Elec. Eng., 67, 988 (1948). llathematics for Engineers. Fitting Functions to Engineering Data. (102) Olds, E. G., and Knowler, L. .I., J . A m . Stat. Assoc., 44, 246 (1949). Teaching Statistical Quality Control for Town and Gown. (103) Peach, Paul, “Introduction to Industrial Statistics and Quality Control.” Raleigh, S . C., Edwards and Broughton Co., 1947. (104) I’oritsky, H . , Elec. Eng., 67, 1061 (1948). Mathematics for Engineers. 11. Method of Greco-Latin Squares. (105) Read, D. R., “Statistical Methods m-ith Special Reference to Analytical Chemistry,” London, Royal Inst. of Chemistry Lectures, Monographs and Reports, No. 1, 1951. (101;) Reitz, L. K., O’Brien, A . S., and Davis, T. L., .%SAL. CHEM., 22, 1470 (1950). Evaluation of Three Iron Methods Using a Factorial Experiment. (107) Rogers, \\-. T.. A m . Soc. Metals, T r a n s . , 40, 935 (1948). hlultiple Correlation Applied to Steel Plant Problems. (108) Rogers. IT.T.. Steel, 124, 102 (1949). Operation of Statistical Quality Control in a Steel Mill. (7.’) Harris, h l . , Horvitz, D. Sssoc.,
123 (109) Scheffe, H., I n d . Eng. Chem., 43, 1292 (1951). Theoretical Backgrounds of Statistical Rlethods. (110) Seder, L. A , , Ibid., 43, 2053 (1951). S e w Science of Trouble Shooting. (111) Seder, L. .I.,I n d . Qual. Control, 4, No. 5, 6 (1948). Technique of Experimenting in the Factory. (112) Shepherd, Ll., SAL. CHEM.,22, 881 (1950). Analysis of a Carbureted 11-ater Gas. (113) Ihtd., p. S85. llnalysis of Xatural Gas. Comparison of T n o Chemical Jlethods. (114) Shewhart, TV. A , “Statistical Method from the 1-iewpoint of Quality Control,” Graduate School, L-. S. Department of .kgriculture, Washington, D. C., 1939. (115) Simon, L. E., A m . SOC.Testing Mnteririls, Pro Variation in Materials, Testing and Sample (116) Simon, L. E., Instruments, 19, 654 (1946). Relation of Instrumentation to Quality Control. (117) Smallmood. H. M.,I n d . Erig. Chem., 43, 2053 (1951). Statistical Training for Chemists. (118) Smith, H . F., Biometrics, 7, TO (1951). Analysis of Variance with Unequal But Proportionate Sumbers of Observations in Subclasses of a Two-Way Classification. (119) Smith, H . F., J . A m . Stat. Assoc., 45, 447 (1950). Estimatiiig Precision of Measuring Instruments. Ibid., 43, 53 (1948). Proposed Basic Course (120) Snedecor, G. W., in Statistics. (121) Starr, C. E., Jr., and Lane, T., ANAL.CHERI.,21, 572 (1949). dccuracy of Analysis of Light Hydrocarbon Mixtures. (122) Statistical Research Group, Columbia Vniv., “Sampling Inspection Principles, Procedures and Tables for Single, Double, and Sequential Sampling in Acceptance Inspection and Quality Control Based on Per Cent Defective,” S e w York, McGraw-Hill Book Co., 1948. ( 1 2 3 ) Statistical Research Group, Columbia Univ., “Selected Techniques of Statistical Analysis for Scientific and Industrial Research and Production and Management Engineering.” S e w York, McGraw-Hill Book Co., 1947. (124) Steiner, E . H . , A n a l y s t . 74, 429 (1949). Statistical Use of 8erera1 Analytical Constituents for Calculating Proportions of Ingredients in Certain Food Products. (125) Tippett, L. H . C., “Methods of Statistics,” London, TTXiams and Norgate. 1948. (1 26) Tippett, L. H . C., “Technological -kpplications of Statistics.” S e w Tork, J o h n \Tiley & Sons, 1950. (127) Toner, R. K . , Bowen, C . F., and Khitwell, J . C., Tertilc RPsearch J.. 18, 526 (1948). hloisture Determination in Textiles by Electrical Meters. (128) Traylor, TY.S., I n d . Qual. Control, 4 , N o . 4, 18 (1948). Use of Statistical Methods for Time Study of Batch Processes. (129) Yillars, D. S., “Statistical Design and .knalysis of Experiments for Development Research,”*Wm. C. Brown Co., Dubuque, Iowa, 1951. (130) Wald, A, Ann. M a t h . Stat., 11, 284 (1940). Fitting of Straight Lines If Both 1-ariables Are Subject to Error. (131j Keatherburn, C. E., ”First Course in Mathematical Statistics,” 2nd ed., London, Cambridge University Press, 1949. (,1321 ITeir, C. D., T r a n s . Am. Soc. M e c h . Eilgrs., 70, 253 (1948). Statistics of Boiler Embrittlenient. (133) Wernimont, G., A S T X Bull., 166, 45 (1950). Design and Interpretation of Interlaboratory Test Programs. (134) IVernimont,, G., Am. So?. Testing Materials, S p e c . Tech. P u b . 103 (1950). Precision and -kccuracy of Test Methods. . 21, 115 (1949). Statistics -4p(135) TVernimont, G., h n - . ~ ~CHEM.. plied to dnalysis.” (136) TVestnian, .A. E. R.. and Lloyd, B. H , I n d . Q u a l . Control, 5, No 5, 5 (1949). Quality Control Chai ts for X and R Adjusted for.within Subgroup Pattern. (137) Weybrew, J. .A,, Rlatrone, G., and Eaxley, H . SI., ASAL. CHExf., 20, 759 ( I 948). Spectrophotometric Determinations of Serium Calcium. (138) Whitwell. J. C., Biometrics. 7, 102 (1951). Estimating Precision of Textile Instruments. (139) Wilcoxon, Frank, “Some Rapid -Approximate Statistical Procedure,” Yew York, .kmerican Cyanamid Co., 1949. (140) Kilks, S.S., Am. Soc. Testing Materials, Proc., 48, 859 (1948). Sampling and Its Uncertainties. (141) Wilks, S. S., “Elementary Statistical Analysis,” Princeton, K. J., Princeton University Press, 1949. (142) )\-ilks, S. S., J . Am. Stat. Assoc., 46, 253, 1 (1951). Undeygraduate Statistical Education. (143) Williams, C. A , , J . Am. Stat. Assoc., 45, 7 7 (1950). Choice of Kumber and Width of Classes for Chi-square Test of Goodness of Fit. (144) Wood, E. C.. A n a l . C h i m . Acta, 2, 441 (1948). Statistical -4spects of Chemical dnalysis. (1451 Wood, E . C.. Ann. Repts. Progress C h e m . (Chrm. S O C .Londoll”,
ANALYTICAL CHEMISTRY
124 44, 2G4 (1947). Application of Statistics to Chemical Anal-
ysis. (146) Wood, E. C., J . Soc. Chem. Ind. ( L o n d o n ) , 68, 128 (1949). Organoleptic Tests in Food Industry. Statistical Considerations in Organoleptic Tests. (147) Woods, -4.P., and Taylor, C. R., Blust Purnacc und Steel Plant, 34, 847 (1940). Statistical Method and Results of a Study of Factors Affecting ODen Hearth Production Rate. Touden, W. J., A s ~ - C H E Y .20, , 1136 (1948). Multiple Factor Experinieiits in Analytical Chemistry. Touden, W. J., A S T M Bull., 166, 48 (1950). Comparative Tests in a Single Laboratory.
(150) Youden, W. J., Ind. Eng. Chenz., 43, 2053 (1951). Locating Sources of Variability in a Process. (151) Touden, \T, J., “Statistical Methods for Chemists,” Sew l-ork, John Wiley & Sons, 1951. (152) Youden, W.J., Tech. A-ews Bull. ~ V a t l Bur. . Stundurds, 33, 7 (1949). Fallacy of Best Two Out of Three. (153) Ibid., Misuse of the Average Deviation, 34, 9 (1950). (154) Tule, G. E., and Kendall, M .G., “Introduction to the Theory of Statistics,” London, Charles Griffin. 1950. R E C E I V ENovember D 5 , 1981.
BIOCHEMICAL ANALYSIS P4L-L I,. KIRK
~ N DEDWARD
L. DUGGAN
C’niaersity of California, Berkeley, Culif.
I
li A previous review of this subject (139), the authors stressed
t h e fundamental differences of biochemical and ordinary chemical analysis. These differences emchasize t h e impoitance of t h e preparative as compared with t h e determinative phases of t h e analysis, t h e fractionation as compared a i t h the determination. Because of t h e great extent and nide ramifications of t h e subject, the subdivisions reviewed were chcsen somewhat arbitrarily and on the basis of the best evaluation available a t the time. The developments of t h e two intervening years have confirmed t h e choices made then, n i t h a few possible minor exceptions. The main topics discussed have developed in importance or have continued their importance nithout interruption. Accordingly, t h e topics chosen here for discussion are largely those that were included previously, along with some additional analytical techniques that were not discussed earlier. Because most of the significant techniques of t h e biochemical analjst are also important in other fields of chemistry, considerable duplication and repetition of other review material are inevitable. Analysis, though fundamental to biochemical progress, has received far less attention from biochemists than it deserves. Eiochemical training rarely includes sufficient consideration of analytical chemistry, because t h e requirements in other phases of chemistry and biology are so extensive. This deficiency of training has led to many analytical shortcomings in t h e biochemical literature and in practice, in both routine and research analysis. Perhaps t h e outstanding example is in t h e field of clinical analysis, which has been influenced more by t h e requirement for speed than for either accuracy or dependabilitj . I t s deficiencies have often been justified on the ground of a large “biological variation” which is supposed t o cover any degree of variation that happens to exist in t h e currently employed method in t h e particular laboratory. The true biological variation has probably never been determined for most constituents because methods accurate enough to determine it have been largely lacking and rarelv applied. It is a hopeful sign that renewed interest in this import a n t phase of biochemical analysis is am-akening in t h e form of a re-examination and evaluation of t h e magnitude of t h e problem. Thus, Belk and Sunderman (11) and Snavely and Golden (257) haveconducted surveys of clinical laboratory operation which have brought to light errors that are far larger t h a n those usually assumed and often so large as to invalidate t h e utility of t h e results. Such studies as that of Shore and T h o m o n (661) of total error in widely employed methods are becoming more numerous and point to improvement in this matter. Perhaps a referee system such as that of the Association of Official Agricultural Chemists might be established to control themore serious deviations. Unfortunately research workers, though more competent and careful than routine analysts, also have fallen into serious analytical pitfalls. Realization of these facts, and interest in their correction, may be expected to produce continued improvement.
FRACTIONATION OF BIOCHEMICAL SYSTEMS Separation of biochemical systems into their constituents remains one of t h e most necessary and difficult of analytical operations because of t h e complexity of t h e systems, the lability of their components, their extensive interaction, and t h e close similarity of t h e constituents of a group to each other. S n important trend has been toward determination of constituents in situ, thus avoiding t h e necessity of separating and altering t h e sample material. DIFFERENTIAL CENTRIFUGATION
The past two years have seen t h e acceptance in principle of t h e process of centrifugal fractionation of cell materials by biochemists, generally. T h e technique has remained identical in fundamentals, although more precise media and fraction evaluation techniques have developed. The separation and properties of cell components by this method have been discussed by Hogeboom (120). Developments in determination of enzyme locale have been reported ($48) and t h e progress in the field has been examined critically
(221). CHROMATOGRAPHY
The techniques of paper partition and column chromatography, including ion exchange, have emerged as indispensable and almost universally applicable tools for biochemical analysis ($04). Their routine and research applications are so numerous and varied a s to place detailed consideration out of the scope of this review. Several trends have become apparent: Considerable standardization of method has been achieved in the separation of common constituents such as t h e amino acids. Basic understanding of the processes has been furthered b y fundamental research, as compared with empirical research only, though this is still the rule. New techniques, approaches, and applications have been numerous. Combinations of the chromatographic techniques with each other and with other analytical operations are becoming more common and producing highly significant results.
It is with these trends that the present review is particularly concerned. Ion Exchange. Ion exchangers have long been used for removal of inorganic ions from water and industrial solutions, b u t in recent years they have become a very powerful tool for biochemical separations. This development depends on the fact that many very significant components of the biological system such as proteins and their hydrolysis products, components of nucleic acid, and other organic substances are normally ions in their natural state or can be converted into ions at some practical pH. Adsorp-
